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NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

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NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

Edited By Ramraj Saini | Updated on Feb 07, 2024 04:53 PM IST

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals are discussed here. These NCERT solutions are created by the expert team at Careers360 keeping in mind the latest CBSE syllabus 2023. These solutions are simple and comprehensive and cover step by step solutions to each problem. In the solutions of NCERT Class 7 chapter 2 Fractions and Decimals, we will learn questions related to the multiplication and division of fractions and decimals. The study of fractions includes mixed fractions, proper fraction and improper fraction with their addition and subtraction, equivalent fractions, comparison of fractions, ordering of fractions and representation of fractions on a number line.

NCERT Solutions are the detailed explanation of each and every question of NCERT textbook and this helps to score good marks in the class exams. Some questions related to real-life situations are also explained in the NCERT Solutions for Class 7 . Here you will get solutions to all five exercises of NCERT. Before referring to the solutions, students must complete the NCER Class 7 Maths Syllabus.

Also, read - NCERT Books

NCERT Solutions for Class 7 Maths Chapter 2 - Important Formulae

fraction = p/q, Where p is the numerator and q is the denominator.

Mixed fraction: = p + q/r, Where p is the whole number, q is the numerator and r is the denominator.

Improper fraction to mixed fraction: (p/q) = (p ÷ q) + ( remaining fraction: p % q)/q.

Mixed Fraction to improper fraction: ( p + q/r ) = (( p×r)+ q)/c

(p/q)(a/b) = (pa)/(qb)

(p/q)/(a/b) = (p/q)(b/a)

p/q + a/b = (pb + aq)/(qb)

p/q - a/b = (pb - aq)/qb

NCERT Solutions for Class 7 Maths Chapter 2 - Important Points

Important points for maths class 7 chapter 2 are listed below.

Fractions:

  • A fraction is written as p/q, where p is the numerator and q is the denominator.
  • There are three main types of fractions: proper, improper, and mixed.
  • Proper fractions have the numerator (p) smaller than the denominator (q).
  • Improper fractions have the numerator (p) greater than or equal to the denominator (q).
  • Mixed fractions consist of a whole number and a proper fraction.

Conversions:

  • Improper fractions can be converted to mixed fractions.
  • To convert an improper fraction to a mixed fraction, divide the numerator by the denominator.
  • Mixed fractions can be converted to improper fractions.
  • To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator.

Operations:

  • Multiplication of fractions involves multiplying the numerators and denominators.
  • Division of fractions requires finding the reciprocal of the second fraction and then multiplying.
  • Reciprocal of a fraction is the fraction flipped, swapping the numerator and denominator.

Addition and Subtraction:

  • Adding or subtracting fractions with the same denominator is straightforward.
  • When denominators differ, find the least common multiple (LCM) and then proceed.

Decimals:

  • Decimals represent fractions with denominators of powers of 10.
  • Decimal place value determines the value of each digit in a decimal number.
  • Tenth place, hundredth place, thousandth place, etc., indicate positions after the decimal point.

Operations with Decimals:

  • Multiplying decimals involves ignoring the decimal points, multiplying the numbers, and then placing the decimal point in the product.
  • Dividing decimals requires moving the decimal point in the divisor and dividend to make the divisor a whole number. Then divide as usual.

Comparing Decimals:

  • Start comparing decimals from the left and move towards the right.
  • If digits match up to a certain place value, compare the next digit to determine which decimal is greater.

Free download NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals PDF for CBSE Exam.

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

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NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals (Intext Questions and Exercise)

NCERT Solutions for chapter 2 maths class 7 Fractions And Decimals Topic 2.3.1

1.(a) Find:

(a)\frac{2}{7}\times 3

If the product is an improper fraction express it as a mixed fraction.

Answer: Given,

\\\Rightarrow \frac{2}{7}\times 3\\=\frac{2\times3}{7}\\=\frac{6}{7}

The product is a proper fraction.

1.(b) Find:

(b)\frac{9}{7}\times 6

If the product is an improper fraction express it as a mixed fraction.

Answer:

Given the product

\Rightarrow \frac{9}{7}\times 6

=\frac{9\times6}{7}

=\frac{54}{7}

This is an improper fraction, so convert it into a mixed fraction.

\Rightarrow \frac{54}{7}=\frac{49+5}{7}=\frac{49}{7}+\frac{5}{7}=7+\frac{5}{7}=7\frac{5}{7} .

1.(c) Find:

(c)3 \times \frac{1}{8}

If the product is an improper fraction express it as a mixed fraction.

Answer: Given, the product

\Rightarrow 3 \times \frac{1}{8}

= \frac{3\times1}{8}

= \frac{3}{8}

This is a proper fraction.

1.(d) Find:

(d)\frac{13}{11}\times 6

If the product is an improper fraction express it as a mixed fraction.

Answer: Given the product:

\Rightarrow \frac{13}{11}\times 6

= \frac{13\times6}{11}

= \frac{78}{11}

This is an improper fraction, so we convert this into a mixed fraction. that is

\Rightarrow \frac{78}{11}=\frac{77+1}{11}=\frac{77}{11}+\frac{1}{11}=7+\frac{1}{11}=7\frac{1}{11} .

1.(i) Find:

(i)5\times 2\frac{3}{7}

Answer: \Rightarrow 5\times 2\frac{3}{7}=5\times\frac{7\times 2+3}{7}

\Rightarrow 5\times 2\frac{3}{7}=5\times\frac{17}{7}

\Rightarrow 5\times 2\frac{3}{7}=\frac{5\times17}{7}

\Rightarrow 5\times 2\frac{3}{7}=\frac{85}{7}

\Rightarrow 5\times 2\frac{3}{7}=\frac{84+1}{7}

\Rightarrow 5\times 2\frac{3}{7}=\frac{84}{7}+\frac{1}{7}

\Rightarrow 5\times 2\frac{3}{7}=12 +\frac{1}{7}

\Rightarrow 5\times 2\frac{3}{7}=12\frac{1}{7}

1.(ii) Find :

(ii)1\frac{4}{9}\times 6

Answer: \Rightarrow 1\frac{4}{9}\times 6=\frac{9\times1+4}{9}\times 6

\Rightarrow 1\frac{4}{9}\times 6=\frac{13}{9}\times 6

\Rightarrow 1\frac{4}{9}\times 6=\frac{13\times 6}{9}

\Rightarrow 1\frac{4}{9}\times 6=\frac{78}{9}

\Rightarrow 1\frac{4}{9}\times 6=\frac{72+6}{9}

\Rightarrow 1\frac{4}{9}\times 6=\frac{72}{9}+\frac{6}{9}

\Rightarrow 1\frac{4}{9}\times 6=8+\frac{2}{3}

\Rightarrow 1\frac{4}{9}\times 6=8\frac{2}{3} .

1. Can you tell, what is (i) \frac{1}{2} of 10? , (ii) \frac{1}{4} of 16? , (iii) \frac{2}{5} of 25?

Answer: As we know, of means multiply so,

\frac{1}{2} o\!f\:\:10=\frac{1}{2}\times10=5

And

\frac{1}{4} o\!f\:\:16=\frac{1}{4}\times16=4

And

\frac{2}{5} o\!f\:\:25=\frac{2}{5}\times25=10

1. Find: \frac{1}{3}\times \frac{4}{5};\frac{2}{3}\times \frac{1}{5}

Answer: As we know in the multiplication of a fraction, the numerator of one fraction is multiplied by the numerator of other fraction, and same for denominator, hence,

\Rightarrow \frac{1}{3}\times \frac{4}{5}=\frac{4\times1}{5\times3}=\frac{4}{15}

\Rightarrow \frac{2}{3}\times \frac{1}{5}=\frac{2\times1}{3\times5}=\frac{2}{15}.

1. Find : \frac{8}{3}\times \frac{4}{7};\frac{3}{4}\times \frac{2}{3}

Answer: As we know in the multiplication of a fraction, the numerator of one fraction is multiplied by the numerator of other fraction, and the same for the denominator, hence,

\\\Rightarrow \frac{8}{3}\times \frac{4}{7}=\frac{8\times4}{3\times7}=\frac{32}{27}\\\\\Rightarrow \frac{3}{4}\times \frac{2}{3}=\frac{3\times2}{4\times3}=\frac{6}{12}=\frac{1}{2}

NCERT Solutions for chapter 2 maths class 7 Fractions And Decimals Topic 2.3.2

1. Fill in these boxes:

(i) \frac{1}{2}\times \frac{1}{7}= \frac{1\times 1}{2\times 7}= (ii) \frac{1}{5}\times \frac{1}{7}=

(iii) \frac{1}{7}\times \frac{1}{2}= (iv) \frac{1}{7}\times \frac{1}{5}=

Answer: (i) \frac{1}{2}\times \frac{1}{7}= \frac{1\times 1}{2\times 7}=\frac{1}{14}

(ii) \frac{1}{5}\times \frac{1}{7}=\frac{1}{35}

(iii) \frac{1}{7}\times \frac{1}{2}=\frac{1}{14}

(iv) \frac{1}{7}\times \frac{1}{5}=\frac{1}{35}

NCERT Solutions for chapter 2 maths class 7 Fractions And Decimals Topic 2.4.1

1. Find :

(i)7\div \frac{2}{5} (ii)6\div \frac{4}{7} (iii)2\div \frac{8}{9}

Answer: As we know, The division of a number by a / b is equivalent to multiplication of that number with b / a. So,

(i)7\div \frac{2}{5}

\Rightarrow 7\div \frac{2}{5}=7\times\frac{2}{5}=\frac{14}{5}

(ii)6\div \frac{4}{7}

\Rightarrow 6\div \frac{4}{7}=6\times\frac{4}{7}=\frac{24}{7}

(iii)2\div \frac{8}{9}

\Rightarrow 2\div \frac{8}{9}=2\times\frac{8}{9}=\frac{16}{9}

NCERT Solutions for Class 7 Chapter 2 Fractions And Decimals Topic 2.4.2

2. Find:

(i)6\div 5\frac{1}{3} (ii)7\div 2\frac{4}{7}

Answer: As we know, The division of a number by a / b is equivalent to the multiplication of that number with b / a. So,

(i)6\div 5\frac{1}{3}

\Rightarrow 6\div 5\frac{1}{3}=6\div\frac{16}{3}=6\times\frac{3}{16}=\frac{18}{16}=\frac{9}{8}=1\frac{1}{8}

(ii)7\div 2\frac{4}{7}

\Rightarrow 7\div 2\frac{4}{7}=7\div\frac{18}{7}=7\times\frac{7}{18}=\frac{49}{18}=2\frac{13}{18}

NCERT Solutions for chapter 2 maths class 7 Fractions And Decimals Topic 2.4.3

3. Find:

(i)\frac{3}{5}\div \frac{1}{2} (ii)\frac{1}{2}\div \frac{3}{5} (iii)2\frac{1}{2}\div \frac{3}{5} (iv)5\frac{1}{6}\div \frac{9}{2}

Answer: As we know, The division of a number by a / b is equivalent to the multiplication of that number with b / a. So,

(i)\frac{3}{5}\div \frac{1}{2}

\Rightarrow \frac{3}{5}\div \frac{1}{2}=\frac{3}{5}\times\frac{2}{1}=\frac{6}{5}=1\frac{1}{5}

(ii)\frac{1}{2}\div \frac{3}{5}

\Rightarrow \frac{1}{2}\div \frac{3}{5}=\frac{1}{2}\times\frac{5}{3}=\frac{5}{6}

(iii)2\frac{1}{2}\div \frac{3}{5}

2\frac{1}{2}\div \frac{3}{5}=\frac{5}{2}\div \frac{3}{5}=\frac{5}{2}\times\frac{5}{3}=\frac{25}{6}=4\frac{1}{6}

(iv)5\frac{1}{6}\div \frac{9}{2}

5\frac{1}{6}\div \frac{9}{2}=\frac{31}{6}\div\frac{9}{2}=\frac{31}{6}\times\frac{2}{9}=\frac{62}{54}=1\frac{8}{54}

NCERT Solutions for Class 7 Chapter 2 Fractions And Decimals Topic 2.6

1. Find:

(i)2.7\times 4 (ii)1.8\times 1.2 (iii)2.3\times 4.35

Answer: As we know, The multiplication of the decimal number is just like the multiplication of normal numbers, we just have to put decimal before a digit such that the number of digits after decimal should remain the same.

In other words,

The number of digits after the decimal should be the same before and after the multiplication.

So.

(i)2.7\times 4=10.8

(ii)1.8\times 1.2=2.16

(iii)2.3\times 4.35=10.005

2. Arrange the products obtained in descending order.

(i)2.7\times 4 (ii)1.8\times 1.2 (iii)2.3\times 4.35

Answer:(i)2.7\times 4=10.8

(ii)1.8\times 1.2=2.16

(iii)2.3\times 4.35=10.005

The products in descending order are:

10.8>10.005>2.16

NCERT Solutions for Class 7 Chapter 2 Fractions And Decimals Topic 2.6.1

1. Find:

(i)0.3\times 10 (ii)1.2\times 100 (iii)56.3\times 1000

Answer: As we know, The multiplication of the decimal number is just like the multiplication of the normal numbers, we just have to put decimal before a digit such that the number of digits after decimal should remain the same.

In other words,

The number of digits after the decimal should be the same before and after the multiplication.

So.

(i)0.3\times 10=3

(ii)1.2\times 100=120

(iii)56.3\times 1000=56300

NCERT Solutions for Class 7 Chapter 2 Fractions And Decimals Topic 2.7.1

1. Find:

(i) 235.4 ÷ 10 (ii) 235.4 ÷100 (iii) 235.4 ÷ 1000

Answer: As we know, while dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.

So,

(i) 235.4 ÷ 10 = 23.54

(ii) 235.4 ÷100 = 2.354

(iii) 235.4 ÷ 1000 = 0.2354

NCERT Solutions for Class 7 Chapter 2 Fractions And Decimals Topic 2.7.2

2. ( i) 35.7 ÷ 3 = ?;
(ii) 25.5 ÷ 3 = ?

Answer: As we know, dividing by a number is equivalent to multiplying by the reciprocal of that number. So

(i) 35.7 ÷ 3

35.7\div3=\frac{357}{10}\div3=\frac{357}{10}\times\frac{1}{3}=\frac{129}{10}=12.9

(ii) 25.5 ÷ 3

25.5\div3=\frac{255}{10}\div3=\frac{255}{10}\times\frac{1}{3}=\frac{85}{10}=8.5

3. (i) 43.15 ÷ 5 = ?;
(ii) 82.44 ÷ 6 = ?

Answer: As we know, dividing by a number is equivalent to multiplying by the reciprocal of that number. So

(i) 43.15 ÷ 5

43.15\div5=\frac{4315}{100}\div5=\frac{4315}{100}\times\frac{1}{5}=\frac{863}{100}=8.63

(ii) 82.44 ÷ 6

82.44\div6=\frac{8244}{100}\div6=\frac{8244}{100}\times\frac{1}{6}=\frac{2374}{100}=23.74

4. Find:

(i) 15.5 ÷ 5

(ii) 126.35 ÷ 7

Answer: As we know, dividing by a number is equivalent to multiplying by the reciprocal of that number. So

(i) 15.5 ÷ 5

15.5\div5=\frac{155}{10}\div5=\frac{155}{10}\times\frac{1}{5}=\frac{31}{10}=3.1

(ii) 126.35 ÷ 7

126.35\div7=\frac{12635}{100}\div7=\frac{12635}{100}\times\frac{1}{7}=\frac{1805}{100}=18.05

NCERT Solutions for C lass 7 Chapter 2 Fractions And Decimals Topic 2.7.3

1. Find:

(i)\frac{7.75}{0.25} (ii)\frac{42.8}{0.02} (iii)\frac{5.6}{1.4}

Answer: As we know, in the dividing of decimal, we first express the decimal in term of fraction and then divides it, So

(i)\frac{7.75}{0.25}

\frac{7.75}{0.25}=\frac{\frac{775}{100}}{\frac{25}{100}}=\frac{775}{25}\times\frac{100}{100}=\frac{31}{1}=31

(ii)\frac{42.8}{0.02}

\frac{42.8}{0.02}=\frac{\frac{428}{100}}{\frac{2}{100}}=\frac{428}{2}\times\frac{100}{100}=214

(iii)\frac{5.6}{1.4}

\frac{5.6}{1.4}=\frac{\frac{56}{10}}{\frac{14}{10}}=\frac{56}{14}\times\frac{10}{10}=4

NCERT Solutions for Class 7 Maths Chapter 2 Fractions And Decimals Exercise 2.1

1. Solve:

(i) 2 - \frac{3}{5} (ii) 4 + \frac{7}{8} (iii) \frac{3}{5} + \frac{2}{7} (iv) \frac{9}{11} - \frac{4}{15}

(v) \frac{7}{10} + \frac{2}{5} + \frac{3}{2} (vi) 2\frac{2}{3} +3 \frac{1}{2} (vii) 8\frac{1}{2}-3 \frac{5}{8}

Answer: As we know we have to make the denominator the same in order to add or subtract the fractions. So,

(i) 2 - \frac{3}{5}=\frac{2}{1}\times\frac{5}{5}-\frac{3}{5}=\frac{10}{5}-\frac{3}{5}=\frac{10-3}{5}=\frac{7}{5}

(ii)

4 + \frac{7}{8}=\frac{4}{1}\times\frac{8}{8}+\frac{7}{8}=\frac{32}{8}+\frac{7}{8}=\frac{39}{8}

(iii)

\frac{3}{5} + \frac{2}{7}=\frac{3}{5}\times\frac{7}{7}+\frac{2}{7}\times\frac{5}{5}=\frac{21}{35}+\frac{10}{35}=\frac{31}{35}

(iv)

\frac{9}{11} - \frac{4}{15}=\frac{15\times 9-11\times 4}{11\times15}=\frac{135-44}{165}=\frac{91}{165}


(v)

\frac{7}{10} + \frac{2}{5} + \frac{3}{2}=\frac{7}{10}+\frac{2}{5}\times\frac{2}{2}+\frac{3}{2}\times\frac{5}{5}=\frac{7}{10}+\frac{4}{10}+\frac{15}{10}=\frac{7+4+15}{10}=\frac{26}{10}

(vi)

2\frac{2}{3} +3 \frac{1}{2}=\frac{8}{3}+\frac{7}{2}=\frac{16}{6}+\frac{21}{6}=\frac{16+21}{6}=\frac{37}{6}=6\frac{1}{6}

(vii)

8\frac{1}{2}-3 \frac{5}{8}=\frac{17}{2}-\frac{29}{8}=\frac{68}{8}-\frac{29}{8}=\frac{68-29}{8}=\frac{39}{9}=4\frac{1}{3}

2. Arrange the following in descending order:

(i) \frac{2}{9}, \frac{2}{3}, \frac{8}{21} (ii) \frac{1}{5}, \frac{3}{7}, \frac{7}{10}

Answer: (i)

\frac{2}{9}=\frac{2}{3\times3}\times\frac{7}{7}=\frac{14}{3\times3\times7}

\frac{2}{3}=\frac{2}{3}\times\frac{7}{7}\times\frac{3}{3}=\frac{42}{3\times3\times7}

\frac{8}{21}=\frac{8}{3\times7}\times\frac{3}{3}=\frac{24}{3\times3\times7}

As 14 < 24 < 42

\frac{2}{3}>\frac{8}{21}>\frac{2}{9}

(ii) \frac{1}{5}=\frac{1}{5}\times\frac{14}{14}=\frac{14}{70}

\frac{3}{7}=\frac{3}{7}\times\frac{10}{10}=\frac{30}{70}

\frac{7}{10}=\frac{7}{10}\times\frac{7}{7}=\frac{49}{70}

As 14 < 30 < 49

\frac{7}{10}>\frac{3}{7}>\frac{1}{5}

3. In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?

(Along the first row \frac{4}{11} + \frac{9}{11} + \frac{2}{11} = \frac{15}{11} ).

Answer: As, we can see that the sum of every row, column or diagonal is 15 / 11 . so yes this is a magic square.

4. A rectangular sheet of paper is 12\tfrac{1}{2} cm long and 10\tfrac{2}{3} cm wide. Find its perimeter.

Answer: Given,

Length of the rectangle :

l=12\tfrac{1}{2}cm=\frac{12\times 2+1}{2}=\frac{25}{2}cm

Width of the rectangle :

b=10\tfrac{2}{3}cm=\frac{10\times 3+2}{3}=\frac{32}{3}cm

Now, As we know,

Perimeter of the rectangle = 2 x ( length + width )

So,

The perimeter of the given rectangle :

=2\times(l+b)

=2\times\left ( \frac{25}{2}+\frac{32}{3} \right )

Now let's make the denominator of both fractions equal.

=2\times\left ( \frac{25}{2}\times\frac{3}{3}+\frac{32}{3}\times\frac{2}{2} \right )

=2\times\left ( \frac{75}{6}+\frac{64}{6} \right )

=2\times\left ( \frac{139}{6} \right )

=\frac{139}{3}cm

Hence, the perimeter of the rectangle is \frac{139}{3}cm .

5. Find the perimeters of (i)\bigtriangleup\! ABE (ii) the rectangle BCDE in this figure. Whose perimeter is greater?

xyz7

Answer: The perimeter of \bigtriangleup\! ABE^{} = AB + BE + AE

=\frac{5}{2}+2\frac{3}{4}+3\frac{3}{5}

=\frac{5}{2}+\frac{4\times2+3}{4}+\frac{3\times5+3}{5}

=\frac{5}{2}+\frac{11}{4}+\frac{18}{5}

Noe, The LCM of 2,4 and 5 is 20. So let's make the denominator of all fractions, 20.

So,

The perimeter of \bigtriangleup\! ABE^{} :

=\frac{5}{2}\times\frac{10}{10}+\frac{11}{4}\times\frac{5}{5}+\frac{18}{5}\times\frac{4}{4}

=\frac{50}{20}+\frac{55}{20}+\frac{72}{20}

=\frac{50+55+72}{20}

=\frac{177}{20}cm

Now,

The perimeter of rectangle BCDE = 2 x ( BE + ED )

=2\times\left (2\frac{3}{4}+\frac{7}{6} \right )

=2\times\left (\frac{4\times2+3}{4}+\frac{7}{6} \right )

=2\times\left (\frac{11}{4}+\frac{7}{6} \right )

The LCM of 4 and 6 is 12. So let's make the denominator of both fractions equal to 12.

=2\times\left (\frac{11}{4}\times\frac{3}{3}+\frac{7}{6}\times\frac{2}{2} \right )

=2\times\left (\frac{33}{12}+\frac{14}{12} \right )

=2\times\left (\frac{33+14}{12} \right )

=2\times\left (\frac{47}{12} \right )

=\frac{47}{6}cm

Hence The perimeter of the Triangle is 177/20 \:cm and the perimeter of the rectangle is 47/6 \: cm .

Now, we have

\frac{177}{20} \:\: and\:\:\frac{47}{6}

LCM of 20 and 6 is 60, so let's make the denominator of both fractions equal to 60.

So,

\frac{177}{20} =\frac{177}{20}\times\frac{3}{3}=\frac{531}{60}

And

\frac{47}{6}=\frac{47}{6}\times\frac{10}{10}=\frac{470}{60}

Now, Since 531 > 470

\Rightarrow \frac{177}{20}>\frac{47}{6}.

\Rightarrow Area of Triangle > Area of Rectangle.

5. Salil wants to put a picture in a frame. The picture is 7\tfrac{3}{5} cm wide. To fit in the frame the picture cannot be more than 7\tfrac{3}{10} cm wide. How much should be trimmed?

Answer: Given, the width of the picture = 7\tfrac{3}{5} cm.

The maximum width of the picture which can fit in the frame = 7\tfrac{3}{10} cm.

Hence the length Salil should trim :

\Rightarrow 7\tfrac{3}{5}-7\tfrac{3}{10}

\Rightarrow \frac{7\times5+3}{5}-\frac{10\times7+3}{10}

\Rightarrow \frac{38}{5}-\frac{73}{10}

Now LCM of 5 and 10 is 10. So, let's make the denominator of both fractions equal to 10. So,

\Rightarrow \frac{38}{5}\times\frac{2}{2}-\frac{73}{10}\times\frac{1}{1}

\Rightarrow \frac{76}{10}-\frac{73}{10}

\Rightarrow \frac{76-73}{10}

\Rightarrow \frac{3}{10}

Hence Salil should cut 3/10 cm of the picture in order to fit it in the frame.

7. Ritu ate \frac{3}{5} part of an apple and the remaining apple was eaten by her brother Somu. How much part of the apple did Somu eat? Who had the larger share? By how much?

Answer: Given,

Part of Apple eaten by Ritu = \frac{3}{5} .

Part of Apple eaten by Somu:

\Rightarrow 1-\frac{3}{5}

\Rightarrow \frac{1}{1}-\frac{3}{5}

LCM of 1 and 5 is 5. So making the denominator of both fractions equal to 5, we get

\Rightarrow \frac{1}{1}\times\frac{5}{5}-\frac{3}{5}

\Rightarrow \frac{5}{5}-\frac{3}{5}

\Rightarrow \frac{5-3}{5}

\Rightarrow \frac{2}{5}

Hence, The Part of Apple eaten by Somu is 2/5.

Now, As

\frac{3}{5}> \frac{2}{5}

\frac{3}{5}- \frac{2}{5}=\frac{3-2}{5}=\frac{1}{5}

Hence, Ritu had a larger share of the apple by \frac{1}{5} part.

8. Michael finished colouring a picture in \frac{7}{12} hour. Vaibhav finished colouring the same picture in \frac{3}{4} hour. Who worked longer? By what fraction was it longer?

Answer: Time taken by Michal in colouring = \frac{7}{12} hours.

Time taken by Vaibhav in colouring = \frac{3}{4} hours.

The LCM of 12 and 4 is 12. So making the denominator of both fractions equal to 12, we get,

\frac{7}{12}\:\:and\:\:\frac{3}{4}\times\frac{3}{3}

\Rightarrow \frac{7}{12}\:\:and\:\:\frac{9}{12}

As

\frac{9}{12}>\frac{7}{12}

For calculating by how much, we do Subtraction

\frac{9}{12}-\frac{7}{12}=\frac{9-7}{12}=\frac{2}{12}=\frac{1}{6}

Vaibhav worked longer by the fraction \frac{1}{6} .

NCERT Solutions for Class 7 Maths Chapter 2 Fractions And Decimals Exercise 2.2

1. Which of the drawings (a) to (d) show :

(i)2\times \frac{1}{5} (ii)2\times \frac{1}{2} (iii)3\times \frac{2}{3} (iv)3\times \frac{1}{4}

xyz5

Answer: i)

(d) represents two circles with 1 part shaded out of 5 parts So, it represents

2\times \frac{1}{5} .

ii) b represents two squares one part out of two of both squares are shaded, So it represents

2\times \frac{1}{2}

(iii)

(a) represents 3 circles 2 parts out of three of all circles are shaded. So it represents

3\times \frac{2}{3}

(iv)

(c) represents 3 squares with one part out of four-part shaded in each square hence it represents

3\times \frac{1}{4} .

2. Some pictures (a) to (c) are given below. Tell which of them show:

(i) 3\times \frac{1}{5}= \frac{3}{5} (ii) 2\times \frac{1}{3}= \frac{2}{3} (iii) 3\times \frac{3}{4}= 2\frac{1}{4}

xyz3


Answer:(i) 3\times \frac{1}{5}= \frac{3}{5}

As in option (c), In the Left-hand side, there are three figures in which one part out of three-part is shaded and in the right-hand side, three out of five portions are shaded.

Hence this represents

3\times \frac{1}{5}= \frac{3}{5} .

(ii) 2\times \frac{1}{3}= \frac{2}{3}

Option (a) represents the equation pictorially.

(iii) 3\times \frac{3}{4}= 2\frac{1}{4}

Option (b) represents this equation pictorially.

3. Multiply and reduce to lowest form and convert into a mixed fraction:

(i) 7\times \frac{3}{5} (ii) 4\times \frac{1}{3} (iii) 2\times \frac{6}{7} (iv) 5\times \frac{2}{9} (v) \frac{2}{3}\times 4

(vi) \frac{5}{2}\times 6 (vii) 11\times \frac{4}{7} (viii) 20\times \frac{4}{5} (ix) 13\times \frac{1}{3} (x) 15\times \frac{3}{5}

Answer: (i) 7\times \frac{3}{5}

On Multiplying, we get

\Rightarrow \frac{7\times3}{5}=\frac{21}{5}=\frac{20+1}{5}=\frac{20}{5}+\frac{1}{5}=4+\frac{1}{5}=4\frac{1}{5}

(ii) 4\times \frac{1}{3}

On Multiplying, we get

\Rightarrow \frac{4\times1}{3}=\frac{4}{3}=\frac{3+1}{3}=\frac{3}{3}+\frac{1}{3}=1+\frac{1}{3}=1\frac{1}{3}

(iii) 2\times \frac{6}{7}

On Multiplying, we get

\Rightarrow \frac{2\times6}{7}=\frac{12}{7}=\frac{7+5}{7}=\frac{7}{7}+\frac{5}{7}=1+\frac{5}{7}=1\frac{5}{7}

(iv) 5\times \frac{2}{9}

On Multiplying, we get

\Rightarrow \frac{5\times2}{9}=\frac{10}{9}=\frac{9+1}{9}=\frac{9}{9}+\frac{1}{9}=1+\frac{1}{9}=1\frac{1}{9}

(v) \frac{2}{3}\times 4

On Multiplying, we get

\Rightarrow \frac{2\times4}{3}=\frac{8}{3}=\frac{6+2}{3}=\frac{6}{3}+\frac{2}{3}=2+\frac{2}{3}=2\frac{2}{3}

(vi) \frac{5}{2}\times 6

On Multiplying, we get

\Rightarrow \frac{5\times6}{2}=\frac{30}{2}=15

(vii) 11\times \frac{4}{7}

On Multiplying, we get

\Rightarrow \frac{11\times4}{7}=\frac{44}{7}

Converting this into a mixed fraction, we get

\Rightarrow \frac{44}{7}=\frac{42+2}{7}=\frac{42}{7}+\frac{2}{7}=6+\frac{2}{7}=6\frac{2}{7}.

(viii) 20\times \frac{4}{5}

On Multiplying, we get

\Rightarrow \frac{20\times4}{5}=\frac{80}{5}=16

(ix) 13\times \frac{1}{3}

On multiplying, we get

\Rightarrow \frac{13\times1}{3}=\frac{13}{3}

Converting this into a mixed fraction,

\Rightarrow\frac{13}{3}=\frac{12+1}{3}=\frac{12}{3}+\frac{1}{3}=4+\frac{1}{3}=4\frac{1}{3} .

(x) 15\times \frac{3}{5}

On multiplying, we get,

\Rightarrow \frac{15\times3}{5}=\frac{45}{5}=9 .

4. Shade:

(i) \frac{1}{2} of the circles in box (a) (ii) \frac{2}{3} of the triangles in box (b)

(iii) \frac{3}{5} of the squares in box (c).

xyz2

Answer: 1) In figure a there are 12 circles: half of 12 = 6

2) In figure b there are 9 triangles: 2/3 of 9 = 6

3) In figure c there are 15 triangles: 3/5 of 15 = 9

1643865076786

5. Find:

(a)\; \frac{1}{2}\;\; of\; (i)24\; \; (ii)46 (b)\; \frac{2}{3}\;\; of\; (i)18\; \; (ii)27

(c)\; \frac{3}{4}\;\; of\; (i)16\; \; (ii)36 (d)\; \frac{4}{5}\;\; of\; (i)20\; \; (ii)35

Answer: (a)(i)\; \frac{1}{2}\;\; of\; 24

On Multiplying we get,

\; \frac{1}{2}\;\; of\; 24=\frac{1}{2}\times24=\frac{1\times24}{2}=12

(a)\;ii) \frac{1}{2}\;\; of\;46

On multiplying, we get

\Rightarrow \frac{1}{2}\;\; of\;46=\frac{1}{2}\times46=\frac{1\times46}{2}=23.

(b)(i)\; \frac{2}{3}\;\; of\;18

On Multiplying, we get

\Rightarrow \frac{2}{3}\;\; of\;18=\frac{2}{3}\times18=\frac{2\times18}{3}=\frac{36}{3}=12.

(b)(ii)\; \frac{2}{3}\;\; of\;27

On multiplying, we get

\Rightarrow \frac{2}{3}\:\:of\:\:27=\frac{2}{3}\times27=\frac{2\times27}{3}=\frac{54}{3}=18

(c)(i)\; \frac{3}{4}\;\; of\; 16

On multiplying, we get

\Rightarrow \frac{3}{4}\:\:of\:\:16=\frac{3}{4}\times16=\frac{3\times16}{4}=\frac{48}{4}=12.

(c)(ii)\; \frac{3}{4}\;\; of\; 36

\Rightarrow \frac{3}{4}\:\:of\:\:36=\frac{3}{4}\times36=\frac{3\times36}{4}=\frac{108}{4}=27

(d)(i)\; \frac{4}{5}\;\; of\; 20\;

On multiplying, we get

\frac{4}{5}\;\; of\; 20\;=\frac{4}{5}\times20=\frac{4\times20}{5}=\frac{80}{5}=16

(d)(ii)\; \frac{4}{5}\;\; of\; 35\;

On Multiplying, we get,

\; \frac{4}{5}\;\; of\; 35\;=\frac{4}{5}\times35=\frac{4\times35}{5}=\frac{140}{4}=28

6. Multiply and express as a mixed fraction :

(a) 3\times 5\frac{1}{5} (b) 5\times 6\frac{3}{4} (c) 7\times 2\frac{1}{4}

(d) 4\times 6\frac{1}{3} (e) 3\frac{1}{4}\times 6 (f) 3\frac{2}{5}\times 8

Answer:(a) 3\times 5\frac{1}{5}

On Multiplying, we get

\Rightarrow 3\times\frac{5\times5+1}{5}=3\times\frac{26}{5}=\frac{3\times26}{5}=\frac{78}{5}

Converting This into Mixed Fraction,

\Rightarrow \frac{78}{5}=\frac{75+3}{5}=\frac{75}{5}+\frac{3}{5}=15+\frac{3}{5}=15\frac{3}{5}

(b) 5\times 6\frac{3}{4}

On Multiplying, we get

\Rightarrow 5\times\frac{6\times4+3}{4}=5\times\frac{27}{4}=\frac{5\times27}{4}=\frac{135}{4}

Converting This into Mixed Fraction,

\Rightarrow \frac{135}{4}=\frac{132+3}{4}=\frac{132}{4}+\frac{3}{4}=33+\frac{3}{4}=33\frac{3}{4}

(c) 7\times 2\frac{1}{4}

On multiplying, we get

7\times 2\frac{1}{4}=7\times \frac{4\times2+1}{4}=7\times\frac{9}{4}=\frac{7\times9}{4}=\frac{63}{4}

Converting it into a mixed fraction, we get

\frac{63}{4}=\frac{60+3}{4}=\frac{60}{4}+\frac{3}{4}=15+\frac{3}{4}=15\frac{3}{4}

(d) 4\times 6\frac{1}{3}

On multiplying, we get

4\times 6\frac{1}{3}=4\times\frac{3\times6+1}{3}=4\times\frac{19}{3}=\frac{4\times 19}{3}=\frac{76}{3}

Converting it into a mixed fraction,

\frac{76}{3}=\frac{75+1}{3}=\frac{75}{3}+\frac{1}{3}=25+\frac{1}{3}=25\frac{1}{3}

(e) 3\frac{1}{4}\times 6

Multiplying them, we get

3\frac{1}{4}\times 6=\frac{4\times3+1}{4}\times6=\frac{13}{4}\times6=\frac{13\times6}{4}=\frac{78}{4}

Now, converting the result fraction we got to mixed fraction,

\frac{78}{4}=\frac{76+2}{4}=\frac{76}{4}+\frac{2}{4}=19+\frac{1}{2}=19\frac{1}{2}

(f) 3\frac{2}{5}\times 8

On multiplying, we get

3\frac{2}{5}\times 8=\frac{5\times3+2}{5}\times8=\frac{17}{5}\times8=\frac{17\times8}{5}=\frac{136}{5}

Converting this into a mixed fraction, we get

\frac{136}{5}=\frac{135+1}{5}=\frac{135}{5}+\frac{1}{5}=27+\frac{1}{5}=27\frac{1}{5}


7. Find:

(a)\frac{1}{2} \; \; o\! f\; \; (i)\; \; 2\frac{3}{4} \; \; \;(ii)\; 4\frac{2}{9} (b)\frac{5}{8} \; \; o\! f\; \; (i)\; \; 3\frac{5}{6} \; \; \;(ii)\; 9\frac{2}{3}

Answer: (a) (i)\frac{1}{2} \; \; o\! f\; \;\; \; 2\frac{3}{4} \;

As we know that of is equivalent to multiply,

\frac{1}{2} \; \; o\! f\; \;\; \; 2\frac{3}{4} \;=\frac{1}{2}\times2\frac{3}{4}=\frac{1}{2}\times\frac{11}{4}=\frac{11}{8}=1\frac{3}{8}

(a)(ii)\frac{1}{2} \; \; o\! f\;\; 4\frac{2}{9}

As we know that of is equivalent to multiply,

\frac{1}{2} \; \; o\! f\;\; 4\frac{2}{9}=\frac{1}{2}\times4\frac{2}{9}=\frac{1}{2}\times\frac{38}{9}=\frac{38}{18}=\frac{19}{9}=2\frac{1}{9}

(b)(i)\frac{5}{8} \; \; o\! f\; \; 3\frac{5}{6} \; \;

As we know that of is equivalent to multiplication, so

\frac{5}{8} \; \; o\! f\; \; 3\frac{5}{6} \; =\frac{5}{8}\times3\frac{5}{6}=\frac{5}{8}\times\frac{23}{6}=\frac{115}{48}=2\frac{19}{48}

(b)(ii)\frac{5}{8} \; \; o\! f\; \;\; 9\frac{2}{3}

As we know that of is equivalent to multiplication, so

\frac{5}{8} \; \; o\! f\; \;\; 9\frac{2}{3}=\frac{5}{8}\times \frac{29}{3}=\frac{145}{24}=6\frac{1}{24}

8. Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed \frac{2}{5} of the water. Pratap consumed the remaining water.

(i) How much water did Vidya drink?
(ii) What fraction of the total quantity of water did Pratap drink?

Answer: Given

Total water = 5 litre.

i) The amount of water vidya consumed :

=\frac{2}{5}\:\:o\!f 5\:liter=\frac{2}{5}\times5=2\:liter

Hence vidya consumed 2 liters of water from the bottle.

ii) The amount of water Pratap consumed :

=\left (1-\frac{2}{5} \right )\:\:o\!f 5\:liter=\frac{3}{5}\times5=3\:liter

Hence, Pratap consumed 3 liters of water from the bottle.


NCERT S olutions for fractions and decimals class 7 Exercise 2.3

1. Find:

(i)\frac{1}{4}\; o\! f\;\; \; \; (a)\; \frac{1}{4}\; \;\; \; \; (b)\frac{3}{5}\; \; \; \; (c)\frac{4}{3}

(ii)\frac{1}{7}\; o\! f\;\; \; \; (a)\; \frac{2}{9}\; \;\; \; \; (b)\frac{6}{5}\; \; \; \; (c)\frac{3}{10}

Answer: As we know, the term "of " means multiplication. So,

(i)(a)\frac{1}{4}\; o\! f\;\; \frac{1}{4}=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}

(i)(b)\frac{1}{4}\; o\! f\;\; \frac{3}{5}=\frac{1}{4}\times\frac{3}{5}=\frac{3}{20}

(i)(c)\frac{1}{4}\; o\! f\;\; \frac{4}{3}=\frac{1}{4}\times\frac{4}{3}=\frac{4}{12}=\frac{1}{3}

(ii) (a)\frac{1}{7}\; o\! f\;\; \frac{2}{9}=\frac{1}{7}\times\frac{2}{9}=\frac{2}{63}

(ii) (b)\frac{1}{7}\; o\! f\;\; \frac{6}{5}=\frac{1}{7}\times\frac{6}{5}=\frac{6}{35}

(ii) (c)\frac{1}{7}\; o\! f\;\; \frac{3}{10}=\frac{1}{7}\times\frac{3}{10}=\frac{3}{70}

2. Multiply and reduce to lowest form (if possible) :

(i) \; \frac{2}{3}\times 2\frac{2}{3} \; \; \; (ii) \frac{2}{7}\times \frac{7}{9}\; \; \; \; \; (iii)\frac{3}{8}\times \frac{6}{4}\; \; \; \;

(iv)\; \; \frac{9}{5}\times \frac{3}{5}\; \; \; \; \; (v)\frac{1}{3}\times \frac{15}{8}\; \; \; (vi)\; \; \frac{11}{2}\times \frac{3}{10} \; \; \; (vii)\; \; \frac{4}{5}\times \frac{12}{7}

Answer: As we know, in the multiplication of fraction, the numerator gets multiplied with numerator and denominator gets multiplied by the denominator. So,

\\(i) \; \frac{2}{3}\times 2\frac{2}{3}=\frac{2}{3}\times\frac{8}{3}=\frac{2\times8}{3\times3}=\frac{16}{9}=1\frac{7}{9} \; \; \;\\\\ (ii) \frac{2}{7}\times \frac{7}{9}=\frac{2\times7}{7\times9}=\frac{2}{9}\; \; \; \; \;\\\\ (iii)\frac{3}{8}\times \frac{6}{4}=\frac{3\times6}{8\times4}=\frac{18}{32}=\frac{9}{16}\; \; \; \;

\\(iv)\; \; \frac{9}{5}\times \frac{3}{5}=\frac{9\times3}{5\times5}=\frac{27}{25}=1\frac{2}{25} \\\\ (v)\frac{1}{3}\times \frac{15}{8}=\frac{1\times15}{3\times8}=\frac{15}{24}=\frac{5}{8}\; \; \; \\\\ (vi)\; \; \frac{11}{2}\times \frac{3}{10}=\frac{11\times3}{2\times10}=\frac{33}{20}=1\frac{13}{20} \; \; \; \\\\ (vii)\; \; \frac{4}{5}\times \frac{12}{7}=\frac{4\times12}{5\times7}=\frac{48}{35}=1\frac{13}{35} .

3. Multiply the following fractions:

(i) \; \frac{2}{5}\times 5\frac{1}{4}\; \; \; \; (ii)\; 6\frac{2}{5}\times \frac{7}{9}\; \; \; \; \; (iii) \frac{3}{2}\times 5\frac{1}{3}

(iv) \; \frac{5}{6}\times 2\frac{3}{7}\; \; \; \; (v)\; 3\frac{2}{5}\times \frac{4}{7}\; \; \; \; \; (vi) 2\frac{3}{5}\times 3\; \; \; \; (vii)3\frac{4}{7}\times \frac{3}{5}

Answer: As we know in the multiplication of fractions, the numerator is multiplied with numerator and denominator is multiplied by the denominator.

So,

\\(i) \; \frac{2}{5}\times 5\frac{1}{4}=\frac{2}{5}\times\frac{21}{4}=\frac{2\times21}{5\times4}=\frac{42}{20}=\frac{21}{10}=2\frac{1}{10}\; \; \; \;\\ \\(ii)\; 6\frac{2}{5}\times \frac{7}{9}=\frac{32}{5}\times\frac{7}{9}=\frac{32\times7}{5\times9}=\frac{224}{45}=4\frac{44}{45}\; \; \; \; \; \\\\(iii) \frac{3}{2}\times 5\frac{1}{3}=\frac{3}{2}\times\frac{16}{3}=\frac{3\times16}{2\times3}=\frac{48}{6}=8

\\(iv) \; \frac{5}{6}\times 2\frac{3}{7}=\frac{5}{6}\times\frac{17}{7}=\frac{5\times17}{6\times7}=\frac{85}{42}=2\frac{1}{42}\; \; \; \; \\\\(v)\; 3\frac{2}{5}\times \frac{4}{7}=\frac{17}{5}\times\frac{4}{7}=\frac{17\times4}{5\times7}=\frac{68}{35}=1\frac{33}{35}\; \; \; \; \; \\\\(vi) 2\frac{3}{5}\times 3=\frac{13}{5}\times3=\frac{13\times3}{5}=\frac{39}{5}=7\frac{4}{5}\; \; \; \;\\\\ (vii)3\frac{4}{7}\times \frac{3}{5}=\frac{25}{7}\times\frac{3}{5}=\frac{25\times3}{7\times5}=\frac{75}{35}=\frac{15}{7}=2\frac{1}{7}

4. Which is greater:

(i)\; \frac{2}{7}\; o\! f\; \frac{3}{4}\; \; or\; \; \frac{3}{5}\; \; of \; \frac{5}{8}

(ii)\; \frac{1}{2}\; o\! f\; \frac{6}{7}\; \; or\; \; \frac{2}{3}\; \; of \; \frac{3}{7}


Answer: (i)\; \frac{2}{7}\; o\! f\; \frac{3}{4}\; \; or\; \; \frac{3}{5}\; \; of \; \frac{5}{8}

\Rightarrow \; \frac{2}{7} \times\ \frac{3}{4}\; \; or\; \; \frac{3}{5}\; \times \frac{5}{8}

\Rightarrow \frac{2\times3}{7\times4}\:\:or\:\:\frac{3\times5}{5\times8}

\Rightarrow \frac{3}{14}\:\:or\:\:\frac{3}{8}

Now, As we Know, When the numerator of two fractions is the same the fraction with lesser denominator is the bigger fraction. So,

\Rightarrow \frac{3}{14}\:\:<\:\:\frac{3}{8}

Thus,

\; \frac{2}{7}\; o\! f\; \frac{3}{4}\; \; <\; \; \frac{3}{5}\; \; of \; \frac{5}{8} .

(ii)\; \frac{1}{2}\; o\! f\; \frac{6}{7}\; \; or\; \; \frac{2}{3}\; \; of \; \frac{3}{7}

\Rightarrow \; \frac{1}{2}\; \times\; \frac{6}{7}\; \; or\; \; \frac{2}{3}\; \; \times \; \frac{3}{7}

\Rightarrow \frac{1\times6}{2\times7}\:\:or\:\:\frac{2\times3}{3\times7}

\Rightarrow \frac{3}{7}\:\:or\:\:\frac{2}{7}

As we know, When the denominator of two fractions are the same, the fraction with the bigger numerator is the bigger fraction, so,

\Rightarrow \frac{3}{7}\:\:>\:\:\frac{2}{7}

Thus,

\; \frac{1}{2}\; \times\; \frac{6}{7}\; \; >\; \; \frac{2}{3}\; \; \times \; \frac{3}{7} .

6. Lipika reads a book for 1\frac{3}{4} hours everyday. She reads the entire book in 6 days.How many hours in all were required by her to read the book?

Answer: Number of time spent in one day = 1\frac{3}{4} hour

The number of time spent in 6 days :

=6\times1\frac{3}{4}=6\times\frac{7}{4}=\frac{6\times7}{4}=\frac{42}{4}=\frac{21}{2}=10\frac{1}{2}\:hours

Hence 10\frac{1}{2}\:hours are required by Lipika to complete the book.

7. A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2\frac{3}{4} litres of petrol.

Answer: Distance covered in 1 liter petrol = 16 km

The distance that will be covered in 2\frac{3}{4} liter petrol.

=16\times2\frac{3}{4}

=16\times\frac{11}{4}

=\frac{11\times16}{4}

=11\times4

=44\:km

Hence 44 km can be covered using 2\frac{3}{4} liter petrol.

8. (a) (i) Provide the number in the box xyz8 , such that \frac{2}{3}\times xyz8 = \frac{10}{30} .

(ii) The simplest form of the number obtained in xyz8 is _________.

(b) (i) Provide the number in the box xyz8 , such that \frac{3}{5}\times xyz8 = \frac{24}{75} .

(ii) The simplest form of the number obtained in xyz8 is _________.

Answer: As we Know, That in the multiplication of fraction, the numerator of both fraction are multiplied to give numerator of new fraction, and denominator of both fractions is multiplied to give the denominator of answer fraction. So,

\frac{2}{3}\times xyz8 = \frac{10}{30} .

We have to multiply 5 with 2 in the numerator to get numerator equal to 10 and 10 with 3 in the denominator to get 30. So,

\Rightarrow \frac{2}{3}\times\frac{5}{10}=\frac{10}{30}

The Simplest Form :

\Rightarrow \frac{5}{10}=\frac{1}{2} .

NCERT Solutions for fractions and decimals class 7 Exercise 2.4

1. Find:

(i) 12\div \frac{3}{4} (ii) 14\div \frac{5}{6} (iii) 8\div \frac{7}{3} (iv) 4\div \frac{8}{3} (v) 3\div 2\frac{1}{3} (vi) 5\div 3\frac{4}{7}

Answer: As we know, The division of a number by a / b is equivalent to multiplication of that number with b / a. So,

(i) 12\div \frac{3}{4}

\Rightarrow 12\div \frac{3}{4}=12\times\frac{4}{3}=\frac{48}{3}=16

(ii) 14\div \frac{5}{6}

\Rightarrow 14\div \frac{5}{6}=14\times\frac{6}{5}=\frac{84}{5}=16\frac{4}{5}

(iii) 8\div \frac{7}{3}

\Rightarrow 8\div \frac{7}{3}=8\times\frac{3}{7}=\frac{24}{7}=3\frac{3}{7}

(iv) 4\div \frac{8}{3}

\Rightarrow 4\div \frac{8}{3}=4\times\frac{3}{8}=\frac{12}{8}=\frac{3}{2}=1\frac{1}{2}

(v) 3\div 2\frac{1}{3}

\Rightarrow 3\div 2\frac{1}{3}=3\div\frac{7}{3}=3\times\frac{3}{7}=\frac{9}{7}=1\frac{2}{7}

(vi) 5\div 3\frac{4}{7}

\Rightarrow 5\div 3\frac{4}{7}=5\div\frac{25}{7}=5\times\frac{7}{25}=\frac{35}{25}=\frac{7}{5}=1\frac{2}{5}


2. Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.

(i)\frac{3}{7} (ii)\frac{5}{8} (iii)\frac{9}{7} (iv)\frac{6}{5} (v)\frac{12}{7} (vi)\frac{1}{8} (vii)\frac{1}{11}

Answer: As we know, in the reciprocal of any fraction, the numerator and denominator get exchanged. Basically, we flip the number upside down. So

i)Reciprocal\:\: o\!f \: \frac{3}{7}=\frac{7}{3}

As numerator is greater than the denominator, it is an improper fraction.

ii)Reciprocal\:\: o\!f \: \frac{5}{8}=\frac{8}{5}

As numerator is greater than the denominator, it is an improper fraction.

iii)Reciprocal\:\: o\!f \: \frac{9}{7}=\frac{7}{9}

As the Denominator is greater than Numerator, it is a proper fraction.

iv)Reciprocal\:\: o\!f \: \frac{6}{5}=\frac{5}{6}

As the Denominator is greater than Numerator, it is a proper fraction.

v)Reciprocal\:\: o\!f \: \frac{12}{7}=\frac{7}{12}

As the Denominator is greater than Numerator, it is a proper fraction.

vi)Reciprocal\:\: o\!f \: \frac{1}{8}=\frac{8}{1}=8

It is an integer and hence a whole Number.

vii)Reciprocal\:\: o\!f \: \frac{1}{11}=\frac{11}{1}=11

It is an integer and hence a whole Number.


3. Find:

(i)\; \frac{7}{3}\div 2 (ii)\; \frac{4}{9}\div 5 (iii)\; \frac{6}{13}\div 7 (iv)\; 4\frac{1}{3}\div 3

(v)\; 3\frac{1}{2}\div 4 (vi)\; 4\frac{3}{7}\div 7


Answer: As we know, The division of a number by a / b is equivalent to multiplication of that number with b / a which is also called the reciprocal of a / b. So,

(i)\; \frac{7}{3}\div 2

\Rightarrow \; \frac{7}{3}\div 2=\frac{7}{3}\times\frac{1}{2}=\frac{7}{6}=1\frac{1}{6}

(ii)\; \frac{4}{9}\div 5

\Rightarrow \; \frac{4}{9}\div 5=\frac{4}{9}\times\frac{1}{5}=\frac{4}{45}

(iii)\; \frac{6}{13}\div 7

\Rightarrow \; \frac{6}{13}\div 7=\frac{6}{13}\times\frac{1}{7}=\frac{6}{91}

(iv)\; 4\frac{1}{3}\div 3

\Rightarrow \; 4\frac{1}{3}\div 3=\frac{13}{3}\div3=\frac{13}{3}\times\frac{1}{3}=\frac{13}{9}=1\frac{4}{9}

(v)\; 3\frac{1}{2}\div 4

\Rightarrow \; 3\frac{1}{2}\div 4=\frac{7}{2}\div4=\frac{7}{2}\times\frac{1}{4}=\frac{7}{8}

(vi)\; 4\frac{3}{7}\div 7

\Rightarrow \; 4\frac{3}{7}\div 7=\frac{31}{7}\div7=\frac{31}{7}\times\frac{1}{7}=\frac{31}{49}


4. Find:

(i)\; \frac{2}{5}\div \frac{1}{2} (ii)\; \frac{4}{9}\div \frac{2}{3} (iii)\; \frac{3}{7}\div \frac{8}{7} (iv)\;2 \frac{1}{3}\div \frac{3}{5} (v)\;3 \frac{1}{2}\div \frac{8}{3} (vi)\;\frac{2}{5}\div 1\frac{1}{2} (vii)\;3\frac{1}{5}\div 1\frac{2}{3} (viii)\;2\frac{1}{5}\div 1\frac{1}{5}

Answer: As we know, The division of a number by a / b is equivalent to multiplication of that number with b / a which is also called the reciprocal of a / b. So,

(i)\; \frac{2}{5}\div \frac{1}{2}

\Rightarrow \; \frac{2}{5}\div \frac{1}{2}=\frac{2}{5}\times\frac{2}{1}=\frac{4}{5}

(ii)\; \frac{4}{9}\div \frac{2}{3}

\Rightarrow \; \frac{4}{9}\div \frac{2}{3}=\frac{4}{9}\times\frac{3}{2}=\frac{12}{18}=\frac{2}{3}

(iii)\; \frac{3}{7}\div \frac{8}{7}

\Rightarrow \; \frac{3}{7}\div \frac{8}{7}=\frac{3}{7}\times\frac{7}{8}=\frac{3}{8}

(iv)\;2 \frac{1}{3}\div \frac{3}{5}

\Rightarrow \;2 \frac{1}{3}\div \frac{3}{5}=\frac{7}{3}\div\frac{3}{5}=\frac{7}{3}\times\frac{5}{3}=\frac{35}{9}=3\frac{8}{9}

(v)\;3 \frac{1}{2}\div \frac{8}{3}

\;3 \frac{1}{2}\div \frac{8}{3}=\frac{7}{2}\div\frac{8}{3}=\frac{7}{2}\times\frac{3}{8}=\frac{21}{16}=1\frac{5}{16}


(vi)\;\frac{2}{5}\div 1\frac{1}{2}

\Rightarrow \;\frac{2}{5}\div 1\frac{1}{2}=\frac{2}{5}\div\frac{3}{2}=\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}

(vii)\;3\frac{1}{5}\div 1\frac{2}{3}

\Rightarrow \;3\frac{1}{5}\div 1\frac{2}{3}=\frac{16}{5}\div\frac{5}{3}=\frac{16}{5}\times\frac{3}{5}=\frac{48}{25}=1\frac{23}{25}

(viii)\;2\frac{1}{5}\div 1\frac{1}{5}

\Rightarrow \;2\frac{1}{5}\div 1\frac{1}{5}=\frac{11}{5}\div\frac{6}{5}=\frac{11}{5}\times\frac{5}{6}=\frac{11}{6}=1\frac{5}{6}

NCERT Solutions for fractions and decimals class 7 Exercise 2.5

1. Which is greater?

(i) 0.5 or 0.05 (ii) 0.7 or 0.5 (iii) 7 or 0.7
(iv) 1.37 or 1.49 (v) 2.03 or 2.30 (vi) 0.8 or 0.88.

Answer: As we know, Any decimal is equivalent to the number without decimal divided by 10 x (number of integers after the decimal). in other words,

0.5=\frac{5}{10} \:\:and\:\:0.05=\frac{5}{100}

So,

(i) 0.5 > 0.05

(ii) 0.7 > 0.5

(iii) 7 > 0.7

(iv) 1.37 < 1.49

(v) 2.03 < 2.30

(vi) 0.8 < 0.88.

2. Express as rupees using decimals :

(i) 7 paise (ii) 7 rupees 7 paise (iii) 77 rupees 77 paise
(iv) 50 paise (v) 235 paise.

Answer: As we know, there are 100 paise in 1 rupee. i.e.

\:1\:paise=\frac{1}{100}Rupees

So,

i) 7 \:paise=\frac{7}{100}=0.07\:Rupees

ii) 7 \:Rupees ,7 \:paise=7+\frac{7}{100}=7+0.07=7.07\:Rupees

iii) 77 \:Rupees ,77 \:paise=77+\frac{77}{100}=7+0.77=7.77\:Rupees

iv)50 \:paise=\frac{50}{100}=0.5\:Rupees

v)235 \:paise=\frac{235}{100}=\frac{200+35}{100}=\frac{200}{100}+\frac{35}{100}=2+0.35=2.35\:Rupees


3.(i) Express 5 cm in metre and kilometre

(ii) Express 35 mm in cm, m and km

Answer: As we know,

1 centimeter = 10 millimeter

1 meter = 100 centimeter.

And

1 kilometer = 1000 meter

So,

i) 5 cm

5 \:cm=\frac{5}{100}m=0.05m

5 \:cm=\frac{5}{100}m=0.05m=\frac{0.005}{1000}=0.000005\:km

ii) 35 mm

35\:mm=\frac{35}{10}cm=3.5cm

35\:mm=\frac{35}{10}cm=3.5cm=\frac{3.5}{100}m=0.035m

35\:mm=\frac{35}{10}cm=3.5cm=\frac{3.5}{100}m=0.035m=\frac{0.035}{1000}km=0.000035km

4. Express in kg:

(i) 200 g (ii) 3470 g (iii) 4 kg 8 g

Answer: As we know,

1 kg = 1000 g.

1\:g=\frac{1}{1000}kg

So,

i) 200 g

200g=\frac{200}{1000}kg=0.2kg

(ii) 3470 g

3470g=\frac{3470}{1000}kg=3.47kg

(iii) 4 kg 8 g

4kg,\:\:8g=4kg+\frac{8}{1000}kg=4kg+0.008kg=4.0008kg

5. Write the following decimal numbers in the expanded form:
(i) 20.03 (ii) 2.03 (iii) 200.03 (iv) 2.034

Answer: Decimal in their expanded form are

(i) 20.03

20.03=2\times10+0\times1+\frac{1}{10}\times0+\frac{1}{100}\times3

(ii) 2.03

2.03=2\times1+\frac{1}{10}\times0+\frac{1}{100}\times3

(iii) 200.03

200.03=2\times100+0\times10+0\times1+\frac{1}{10}\times0+\frac{1}{100}\times3

(iv) 2.034

2.034=2\times1+\frac{1}{10}\times0+\frac{1}{100}\times3+4\times\frac{1}{1000}

6. Write the place value of 2 in the following decimal numbers:
(i) 2.56 (ii) 21.37 (iii) 10.25 (iv) 9.42 (v) 63.352.

Answer: (i) 2.56

2 is in one's position.

(ii) 21.37

2 is in ten's position

(iii) 10.25

2 is in one-tenths position

(iv) 9.42

2 is in one-hundredths position.

(v) 63.352.

2 is in one-thousandth's position.

7. Dinesh went from place A to place B and from there to place C. A is 7.5 km from B and B is 12.7 km from C. Ayub went from place A to place D and from there to place C. D is 9.3 km from A and C is 11.8 km from D. Who travelled more and by how much?

xyz1

Answer: Total distance travelled by Dinesh = AB + BC

= 7.5km + 12.7km

= 20.2 km

Total distance travelled by Ayub = AD + DC

= 9.3km + 11.8 km

= 21.1 km

Hence Ayub travelled More distance than Ayub as 21.1 > 20.2

The difference between path travelled by them = 21.1km - 20.2 km

= 0.9 km.

Hence Ayub travelled 0.9 km more than Dinesh.

8. Shyama bought 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits?

Answer: For comparing two quantities, we should make their unit the same first. So,

Fruits bought by Shyama in kg = 5 kg + 300 g + 3 kg + 250 g

= 8 kg + 550 g

= 8 kg + 0.55 kg

= 8.55 kg.

Fruits bought by Sarala in kg = 4 kg + 800 g + 4 kg + 150 g

= 8 kg + 950 kg

= 8 kg + 0.95 kg

= 8.95 kg.

Hence Sarala bought more fruits as 8.95 > 8.55

The difference between the amount of Fruits they bought = 8.95 kg - 8.55 kg

= 0.4 kg

9. How much less is 28 km than 42.6 km?

Answer: Difference = 42.6 km - 28 km

= 14.6 km

Hence 28 is 14.6 km less than 42.6.

NCERT Solutions for maths class 7 chapter 2 Fractions And Decimals Exercise 2.6

1. Find:

(i) 0.2 × 6 (ii) 8 × 4.6 (iii) 2.71 × 5 (iv) 20.1 × 4

(v) 0.05 × 7 (vi) 211.02 × 4 (vii) 2 × 0.86

Answer: As we know, The multiplication of the decimal number is just like multiplication of normal number, we just have to put decimal before a digit such that the number of digits after decimal should remain same.

In other words,

The number of digits after the decimal should be the same before and after the multiplication.

So.

(i) 0.2 × 6 = 1.2

(ii) 8 × 4.6 = 36.8

(iii) 2.71 × 5 = 13.55

(iv) 20.1 × 4 = 80.4

(v) 0.05 × 7 = 0.35

(vi) 211.02 × 4 = 844.08

(vii) 2 × 0.86 = 1.72

2. Find the area of rectangle whose length is 5.7cm and breadth is 3 cm.

Answer: Given, Length of rectangle = 5.7 cm.

Width of rectangle = 3 cm

Area of the rectangle = Length x width

= 5.7 x 3

= 17.1 cm^2 .

Hence Area of the rectangle is 17.1 cm^2 .

3. Find:

(i) 1.3 × 10 (ii) 36.8 × 10 (iii) 153.7 × 10 (iv) 168.07 × 10

(v) 31.1 × 100 (vi) 156.1 × 100 (vii) 3.62 × 100 (viii) 43.07 × 100

(ix) 0.5 × 10 (x) 0.08 × 10 (xi) 0.9 × 100 (xii) 0.03 × 1000

Answer: As we know, The multiplication of the decimal number is just like multiplication of normal number, we just have to put decimal before a digit such that the number of digits after decimal should remain same.

In other words,

The number of digits after the decimal should be the same before and after the multiplication.

So.

(i) 1.3 × 10 = 13

(ii) 36.8 × 10 = 368

(iii) 153.7 × 10 = 1537

(iv) 168.07 × 10 = 1680.7

(v) 31.1 × 100 = 3110

(vi) 156.1 × 100 =15610

(vii) 3.62 × 100 = 362

(viii) 43.07 × 100 = 4307

(ix) 0.5 × 10 = 5

(x) 0.08 × 10 = 0.8

(xi) 0.9 × 100 = 90

(xii) 0.03 × 1000 =30

4. A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?

Answer: Distance covered by two-wheeler in 1 liter of petrol = 55.3 km.

Distance two-wheeler will cover in 10 liters of petrol = 10 x 55.3 km

= 553 km

Hence two-wheeler will cover a distance of 553 km in 10 liters of petrol.

5. Find:

(i) 2.5 × 0.3 (ii) 0.1 × 51.7 (iii) 0.2 × 316.8 (iv) 1.3 × 3.1 (v) 0.5 × 0.05 (vi) 11.2 × 0.15 (vii) 1.07 × 0.02

(viii) 10.05 × 1.05 (ix) 101.01 × 0.01 (x) 100.01 × 1.1

Answer: As we know, The multiplication of the decimal number is just like multiplication of normal number, we just have to put decimal before a digit such that the number of digits after decimal should remain same.

In other words,

The number of digits after the decimal should be the same before and after the multiplication.

So.

(i) 2.5 × 0.3 = 0.75

(ii) 0.1 × 51.7 = 5.17

(iii) 0.2 × 316.8 = 63.36

(iv) 1.3 × 3.1 = 4.03

(v) 0.5 × 0.05 = 0.025

(vi) 11.2 × 0.15 = 1.680

(vii) 1.07 × 0.02 = 0.0214

(viii) 10.05 × 1.05 = 10.5525

(ix) 101.01 × 0.01 = 1.0101

(x) 100.01 × 1.1 = 110.11

NCERT Solutions for maths class 7 chapter 2 Fractions And Decimals 2.7

1. Find:

(i)\; 0.4\div 2 (ii)\; 0.35\div 5 (iii)\; 2.48\div 4 (iv)\; 65.4\div 6

(v)\; 651.2\div 4 (vi)\; 14.49\div 7 (vii)\; 3.96\div 4 (viii)\; 0.80\div 5

Answer: As we know, while dividing decimal, we first express the decimal in term of fraction and then divides it,

And

Dividing by a number is equivalent to multiplying by the reciprocal of that number. So

So

(i)\; 0.4\div 2

\; 0.4\div 2=\frac{4}{10}\div2=\frac{4}{10}\times\frac{1}{2}=\frac{2}{10}=\frac{1}{5}

(ii)\; 0.35\div 5

\; 0.35\div 5=\frac{35}{100}\div5=\frac{35}{100}\times\frac{1}{5}=\frac{7}{100}=0.07

(iii)\; 2.48\div 4

\; 2.48\div 4=\frac{248}{100}\div4=\frac{248}{100}\times\frac{1}{4}=\frac{62}{100}=0.62

(iv)\; 65.4\div 6

\; 65.4\div 6=\frac{654}{100}\div6=\frac{654}{100}\times\frac{1}{6}=\frac{109}{100}=1.09

(v)\; 651.2\div 4

\; 651.2\div 4=\frac{6512}{10}\div4=\frac{6512}{10}\times\frac{1}{4}=\frac{1628}{10}=162.8

(vi)\; 14.49\div 7

\; 14.49\div 7=\frac{1449}{100}\div7=\frac{1449}{100}\times\frac{1}{7}=\frac{207}{100}=2.07

(vii)\; 3.96\div 4

\; 3.96\div 4=\frac{396}{100}\div4=\frac{396}{100}\times\frac{1}{4}=\frac{99}{100}=0.99

(viii)\; 0.80\div 5

\; 0.80\div 5=\frac{80}{100}\div5=\frac{80}{100}\times\frac{1}{5}=\frac{16}{100}=0.16

2. Find:

(i)\; 4.8\div 10 (ii)\; 52.5\div 10 (iii)\; 0.7\div 10 (iv)\; 33.1\div 10

(v)\; 272.23\div 10 (vi)\; 0.56\div 10 (vii)\; 3.97\div 10

Answer: As we know, When we divide a decimal number by 10, the decimal point gets shifted by one digit in the left.

So

(i)\; 4.8\div 10

\; 4.8\div 10=0.48

(ii)\; 52.5\div 10

\; 52.5\div 10=5.25

(iii)\; 0.7\div 10

\; 0.7\div 10=0.07

(iv)\; 33.1\div 10

\; 33.1\div 10=3.31

(v)\; 272.23\div 10

\; 272.23\div 10=27.223

(vi)\; 0.56\div 10

\; 0.56\div 10=0.056

(vii)\; 3.97\div 10

\; 3.97\div 10=0.397

3. Find:

(i)\; 2.7\div 100 (ii)\; 0.3\div 100 (iii)\; 0.78\div 100 (iv)\; 432.6\div 100

(v)\; 23.6\div 100 (vi)\; 98.53\div 100

Answer: As we know while dividing a decimal number by 100, the decimal point gets shifted to left by two digits.

So

(i)\; 2.7\div 100

\; 2.7\div 100=0.027

(ii)\; 0.3\div 100

\; 0.3\div 100=0.003

(iii)\; 0.78\div 100

\; 0.78\div 100=0.0078

(iv)\; 432.6\div 100

\; 432.6\div 100=4.326

(v)\; 23.6\div 100

\; 23.6\div 100=0.236

(vi)\; 98.53\div 100

\; 98.53\div 100=0.9853

4. Find:

(i)\; 7.9\div 1000 (ii)\; 26.3\div 1000 (iii)\; 38.53\div 1000 (iv)\; 128.9\div 1000

(v)\; 0.5\div 1000

Answer: As we know, while dividing a decimal number by 1000 we shift the decimal to left by 3 digits, So

(i)\; 7.9\div 1000

\; 7.9\div 1000=0.0079

(ii)\; 26.3\div 1000

\; 26.3\div 1000=0.0263

(iii)\; 38.53\div 1000

\; 38.53\div 1000=0.03853

(iv)\; 128.9\div 1000

\; 128.9\div 1000=0.1289

(v)\; 0.5\div 1000

5. Find:

(i)\; 7\div 3.5 (ii)\; 36\div 0.2 (iii)\; 3.25\div 0.5 (iv)\; 30.94\div 0.7

(v)\; 0.5\div 0.25 (vi)\; 7.75\div 0.25 (vii)\; 76.5\div 0.15 (viii)\; 37.8\div 1.4

(ix)\; 2.73\div 1.3

Answer: As we know, while dividing decimal, we first express the decimal in term of fraction and then divides it,

And

Dividing by a number is equivalent to multiplying by the reciprocal of that number.

So

(i)\; 7\div 3.5

\; 7\div 3.5=7\div \frac{35}{10}=7\times\frac{10}{35}=\frac{70}{35}=2

(ii)\; 36\div 0.2

\; 36\div 0.2=36\div\frac{2}{10}=36\times\frac{10}{2}=180

(iii)\; 3.25\div 0.5

\; 3.25\div 0.5=\frac{325}{100}\div\frac{5}{10}=\frac{325}{100}\times\frac{10}{5}=\frac{65}{10}=6.5

(iv)\; 30.94\div 0.7

\; 30.94\div 0.7=\frac{3094}{100}\div\frac{7}{10}=\frac{3094}{100}\times\frac{10}{7}=\frac{442}{10}=44.2

(v)\; 0.5\div 0.25

\; 0.5\div 0.25=\frac{5}{10}\div\frac{25}{100}=\frac{5}{10}\times\frac{100}{25}=\frac{10}{5}=2

(vi)\; 7.75\div 0.25

\; 7.75\div 0.25=\frac{775}{100}\div\frac{25}{100}=\frac{775}{100}\times\frac{100}{25}=31

(vii)\; 76.5\div 0.15

\; 76.5\div 0.15=\frac{765}{10}\div\frac{15}{100}=\frac{765}{10}\times\frac{100}{15}=510

(viii)\; 37.8\div 1.4

\; 37.8\div 1.4=\frac{378}{10}\div\frac{14}{10}=\frac{378}{10}\times\frac{10}{14}=27

(ix)\; 2.73\div 1.3

\; 2.73\div 1.3=\frac{273}{100}\div\frac{13}{10}=\frac{273}{100}\times\frac{10}{13}=\frac{21}{10}=2.1

6. A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre of petrol?

Answer: Distance travelled by vehicle in 2.4 litres of petrol = 43.2 km

Distance travelled by vehicle in 1 litre of petrol:

=\frac{43.2}{2.4}=\frac{432}{24}\times\frac{10}{10}=18

Hence Distance travelled by vehicle in 1 litre is 18 km.

Fractions and Decimals Class 7 Maths Chapter 2-Topics

Here students can find all the topics which are discussed in this chapter, fractions and decimals class 7.

  • How Well Have You Learnt About Fractions?
  • Multiplication Of Fractions
  • Division Of Fractions
  • How Well Have You Learnt About Decimal Numbers
  • Multiplication Of Decimal Numbers
  • Division Of Decimal Numbers

NCERT Solutions for Class 7 Maths Chapter Wise

Chapter No.

Chapter Name

Chapter 1

Integers

Chapter 2

Fractions and Decimals

Chapter 3

Data Handling

Chapter 4

Simple Equations

Chapter 5

Lines and Angles

Chapter 6

The Triangle and its Properties

Chapter 7

Congruence of Triangles

Chapter 8

Chapter 9

Rational Numbers

Chapter 10

Practical Geometry

Chapter 11

Perimeter and Area

Chapter 12

Algebraic Expressions

Chapter 13

Exponents and Powers

Chapter 14

Symmetry

Chapter 15

NCERT Solutions for Class 7 Subject Wise

Importance of NCERT Solutions for Class 7 Chapter 2 Fractions and Decimals

  • Now homework of the chapter becomes an easy breezy thing with CBSE NCERT solutions for Class 7 chapter 2 Fractions and Decimals in hand.
  • Solutions of NCERT Class 7 chapter 2 Fractions and Decimals in hand helps students in self-evaluation
  • The NCERT solutions for Class 7 Maths chapter 2 Fractions and Decimals are helpful in preparation for the exam. A similar type of question can be expected for the class exams.

Also Check NCERT Books and NCERT Syllabus here:

Frequently Asked Question (FAQs)

1. Do I need to acquire knowledge of all the topics covered in the NCERT Solutions for Class 7 Maths Chapter 2?

Absolutely, it is crucial to thoroughly grasp all the topics presented in the NCERT Solutions for Class 7 Maths Chapter 2 in order to achieve high marks in the Class 7 board exams. These solutions are meticulously crafted by subject matter experts who have compiled model questions encompassing all the exercise questions from the textbook. Emphasis is placed on elucidating the solutions in a manner that is easily comprehensible for students, thereby aiding their understanding.

2. Can I rely solely on the NCERT Solutions for Class 7 Maths Chapter 2 to confidently tackle all the questions in the board exam?

Indeed, the NCERT Solutions for Class 7 Maths Chapter 2 are sufficient to solve all the questions that appear in the board exam. Thoroughly practicing this chapter enables students to grasp the concepts flawlessly. These questions have been meticulously designed in accordance with the NCERT syllabus and guidelines, ensuring that students can achieve good marks in their final exams. To study both online and offline, students can download class 7 maths chapter 2 pdf.

3. List the topics included in the NCERT Solutions for class 7 chapter 2 maths.

The main topics covered in the NCERT Solutions for class 7 chapter 2 maths include:

  1. Addition and subtraction of fractions
  2. Multiplication of fractions
  3. Multiplication of a fraction by a whole number
  4. Multiplication of a fraction by a fraction
  5. Division of fractions
  6. Division of a whole number by a fraction
  7. Reciprocal of a fraction
  8. Division of a fraction by a whole number
  9. Division of a fraction by another fraction
  10. Multiplication of decimal numbers
  11. Multiplication of decimal numbers by 10, 100, and 1000
  12. Division of decimal numbers
  13. Division of decimals by 10, 100, and 1000
  14. Division of a decimal number by a whole number
  15. Division of a decimal number by another decimal number.

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Geotechnical engineer

The role of geotechnical engineer starts with reviewing the projects needed to define the required material properties. The work responsibilities are followed by a site investigation of rock, soil, fault distribution and bedrock properties on and below an area of interest. The investigation is aimed to improve the ground engineering design and determine their engineering properties that include how they will interact with, on or in a proposed construction. 

The role of geotechnical engineer in mining includes designing and determining the type of foundations, earthworks, and or pavement subgrades required for the intended man-made structures to be made. Geotechnical engineering jobs are involved in earthen and concrete dam construction projects, working under a range of normal and extreme loading conditions. 

3 Jobs Available
Cartographer

How fascinating it is to represent the whole world on just a piece of paper or a sphere. With the help of maps, we are able to represent the real world on a much smaller scale. Individuals who opt for a career as a cartographer are those who make maps. But, cartography is not just limited to maps, it is about a mixture of art, science, and technology. As a cartographer, not only you will create maps but use various geodetic surveys and remote sensing systems to measure, analyse, and create different maps for political, cultural or educational purposes.

3 Jobs Available
Budget Analyst

Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.

4 Jobs Available
Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Investment Banker

An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.

3 Jobs Available
Underwriter

An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.

3 Jobs Available
Finance Executive
3 Jobs Available
Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
Plumber

An expert in plumbing is aware of building regulations and safety standards and works to make sure these standards are upheld. Testing pipes for leakage using air pressure and other gauges, and also the ability to construct new pipe systems by cutting, fitting, measuring and threading pipes are some of the other more involved aspects of plumbing. Individuals in the plumber career path are self-employed or work for a small business employing less than ten people, though some might find working for larger entities or the government more desirable.

2 Jobs Available
Construction Manager

Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.

2 Jobs Available
Urban Planner

Urban Planning careers revolve around the idea of developing a plan to use the land optimally, without affecting the environment. Urban planning jobs are offered to those candidates who are skilled in making the right use of land to distribute the growing population, to create various communities. 

Urban planning careers come with the opportunity to make changes to the existing cities and towns. They identify various community needs and make short and long-term plans accordingly.

2 Jobs Available
Highway Engineer

Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

2 Jobs Available
Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems. 

2 Jobs Available
Naval Architect

A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability. 

2 Jobs Available
Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
Veterinary Doctor
5 Jobs Available
Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
Speech Therapist
4 Jobs Available
Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth. 

4 Jobs Available
Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

3 Jobs Available
Hospital Administrator

The hospital Administrator is in charge of organising and supervising the daily operations of medical services and facilities. This organising includes managing of organisation’s staff and its members in service, budgets, service reports, departmental reporting and taking reminders of patient care and services.

2 Jobs Available
Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

4 Jobs Available
Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
Videographer
2 Jobs Available
Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

2 Jobs Available
Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

5 Jobs Available
Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

3 Jobs Available
Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
Linguist

Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning). 

Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian

2 Jobs Available
Public Relation Executive
2 Jobs Available
Travel Journalist

The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
QA Manager
4 Jobs Available
Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Production Manager
3 Jobs Available
Merchandiser
2 Jobs Available
QA Lead

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans. 

2 Jobs Available
Metallurgical Engineer

A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment. 

2 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
QA Manager
4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
ITSM Manager
3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
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