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NCERT Solutions for Class 6 Maths Chapter 7 Fractions

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NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Edited By Ramraj Saini | Updated on Nov 30, 2023 09:49 AM IST

NCERT Solutions for Class 6 Maths Chapter 7 Fractions are discussed here. Our Expert team designed these NCERT solutions kepping in mind lated syllabus of CBSE 2023. A fraction is a number representing part of a whole. The whole may be a single object or a group of the object and the parts have to be equal. In Class 4 and 5 NCERT, you have already learnt about the representation of fractions. In Fraction class 6, you will learn about the various operations and applications of fractions in mathematics. You can also refer to the NCERT Books for Class 6 Maths to solve the problems covered under NCERT solutions for Class 6.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions
NCERT Solutions for Class 6 Maths Chapter 7 Fractions

The subtopics covered under the NCERT Fraction class 6 are the representation of fractions on the number line, proper- improper and mixed fractions, the simplest form of the fractions, equivalent fractions, comparing fractions, comparing, unlike fractions, comparing like fractions, subtraction, and addition of fractions and adding or subtracting fractions. CBSE NCERT solutions for Class 6 Maths chapter 7 Fractions is covering the problems from each subtopic. In this chapter of NCERT Syllabus for Class 6 Maths, there are a total of 37 questions in 6 exercises. To help students in their preparation, we have designed NCERT solutions for class 6th math chapter 7. NCERT Solutions are also available class-wise and subject-wise.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions - Important Formulae

  1. A fraction can be represented as A/B, where A is called the numerator and B is called the denominator. The denominator cannot be zero.

  2. Mixed fraction =Quotient {Remainder/Divisor)

  3. Addition and subtraction of fraction with same denominator

A/B + C/B = (A+C)/B

A/B - C/B = (A-C)/B

  1. Addition and subtraction of fraction with different denominator

A/B + C/D = AD/BD + BC/BD = (AD + CB)/BD

A/B - C/D = AD/BD - BC/BD = (AD - CB)/BD

  1. Multiplication: Multiply numerator to numerator and denominator to denominator

(A/B)(C/D) = AC/BD

  1. Division: Flip the second fraction and then multiply with the first fraction.

(A/B) /(C/D) = (A/B)(D/C) = AD/BC

NCERT Solutions for Class 6 Maths Chapter 7 Fractions - Important Points

Fraction: A fraction represents a part of a whole or a part of a group. It is expressed as a/b, where 'a' is called the numerator and 'b' is called the denominator.

Types of Fractions: Fractions can be classified as proper fractions, improper fractions, and mixed fractions. In a proper fraction, the numerator is smaller than the denominator. In an improper fraction, the numerator is equal to or greater than the denominator. A mixed fraction is a combination of a whole number and a proper fraction.

Equivalent Fractions: Fractions that represent the same value are called equivalent fractions. They have different numerators and denominators but represent the same part of a whole.

Simplification of Fractions: Fractions can be simplified by dividing both the numerator and the denominator by their common factors. The simplified fraction is the one in which the numerator and the denominator have no common factors other than 1.

Comparing Fractions: Fractions can be compared by cross-multiplication. If the product of the numerator of one fraction and the denominator of the other fraction is greater, then the first fraction is larger. If the product is smaller, then the second fraction is larger.

Addition and Subtraction of Fractions: For adding or subtracting fractions, the denominators must be the same. If they are different, the fractions need to be converted to equivalent fractions with the same denominator before performing the operation.

Multiplication of Fractions: To multiply fractions, multiply the numerators and multiply the denominators. The product is the numerator of the resulting fraction, and the product is the denominator.

Division of Fractions: To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction. In other words, multiply by the numerator of the second fraction and divide by the denominator of the second fraction.

Representation of Fractions on a Number Line: Fractions can be represented on a number line by dividing the line segment between 0 and 1 into equal parts based on the denominator of the fraction.

Operations on Fractions and Whole Numbers: To perform operations involving fractions and whole numbers, convert the whole number into a fraction by giving it a denominator of 1, and then proceed with the operation

Free download NCERT Solutions for Class 6 Maths Chapter 7 Fractions PDF for CBSE Exam.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

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NCERT Solutions for Class 6 Maths Chapter 7 Fractions (Intext Questions and Exercise)

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.1

Q1 Write the fraction representing the shaded portion.

1643038507901

Answer: (i) \frac{2}{4}\ =\ \frac{1}{2}

(ii) \frac{8}{9}

(iii) \frac{4}{8}\ =\ \frac{1}{2}

(iv) \frac{1}{4}

(v) \frac{3}{7}

(vi) \frac{9}{12}\ =\ \frac{3}{4}


(vii) \frac{10}{10}\ =\ 1

(viii) \frac{4}{9}

(ix) \frac{4}{8}\ =\ \frac{1}{2}

(x) \frac{1}{2}


Q2 Colour the part according to the given fraction.

1643038548278

Answer: The coloured parts are shown below :-

1643038564328

Q3 Identify the error if any

1643038594802 This is \frac{1}{2}

1643038605008 This is \frac{1}{4}

1643038615474 This is \frac{3}{4}

Answer: Yes, the above fractions are wrong. For these fractions to be correct areas of each part should be same. But clearly, in the given figure, the areas are not the same.

Q4 What fraction of a day is 8 hours?

Answer: Total hours in 1 day =\ 24

Thus the required fraction is :-

=\ \frac{8}{24}\ =\ \frac{1}{3}


Q5 What fraction of an hour is 40 minutes?

Answer: We know that 1 hour has 60 minutes.

Thus fraction of 40 minutes is :-

=\ \frac{40}{60}\ =\ \frac{4}{6}\ =\ \frac{2}{3}


Q8 Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Answer: We have :- 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

Prime number :- 2, 3, 5, 7, 11.

Thus the fraction of prime numbers is:- \frac{5}{11}


Q9 Write the natural numbers from 102 to 113 . What fraction of them are prime numbers?

Answer: The natural numbers are :- 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113.

Prime numbers are :- 103, 107, 109, 113.

Thus fraction is :- =\ \frac{4}{12}\ =\ \frac{1}{3}

Q10 What fraction of these circles have X ’s in them?

1643038649229

Answer: The number of boxes with X in them = 4

Total number of boxes = 8.

The required fraction is :

=\ \frac{4}{8}\ =\ \frac{1}{2}


Q11 Kristin received a CD player for her birthday. She bought 3

CDs and received 5 others as gifts. What fraction of her total

CDs did she buy and what fraction did she receive as gifts?

Answer: The fraction of the CDs she bought is :

=\ \frac{3}{8}

And the fraction of CDs received as gifts is :

=\ \frac{5}{8}

NCERT Solutions for Class 6 Maths Topic: Fractions on the Number Line

Q1 Show \frac{3}{5} on a number line.

Answer: First we write 1 as \frac{5}{5} and divide the number line into 5 equal parts.

3-batta-5


Q2 Show \frac{1}{10},\frac{0}{10},\frac{5}{10} and \frac{10}{10} on a number line.

Answer:

First, we write 1 as \frac{10}{10} and divide the number line in 10 equal parts.

1-batta-10

Q3 Can you show any other fraction between 0 and 1 ?Write five more fractions that you can show.

Answer:

Yes. There are infinite number of fraction between 0 and 1 (Numerator is less than denominator)

Five more fractions are: \frac{4}{5}, \frac{6}{11}, \frac{4}{7}, \frac{3}{8}, \frac{11}{25}

Q4 How many fractions lie between 0 and 1 ? Think, discuss and write your answer?

Answer: There are infinite number of fractions between 0 and 1 .

A fraction is of form \frac{a}{b} and for a number lying between 0 and 1 , the numerator has to be less than the denominator.

NCERT Solutions for Class 6 Maths Topic: Proper Fractions

Q1 Give a proper fraction : (a) whose numerator is 5 and the denominator is 7.
(b) whose denominator is 9 and the numerator is 5.

(c) whose numerator and denominator add up to 10 . How many fractions of this kind can you make?

(d) whose denominator is 4 more than the numerator.

(Give any five. How many more can you make?)

Answer: A proper fraction whose:

(a) the numerator is 5 and the denominator is 7. = \frac{5}{7}

(b) denominator is 9 and numerator is 5. = \frac{5}{9}

(c) numerator and denominator add up to 10 .

Pairs of numbers having sum 10 = (1,9),(2,8),(3,7),(4,6)(5,5)

Therefore, the proper fractions are \frac{1}{9}, \frac{2}{8}, \frac{3}{7}, \frac{4}{6}

(d) denominator is 4 more than the numerator. = \frac{1}{5}, \frac{2}{6}, \frac{15}{19}, \frac{105}{109}, \frac{199}{203},

Q2 A fraction is given. How will you decide, by just looking at it, whether, the fraction is

(a) less than 1 ?

(b) equal to 1 ?

Answer: (a) If the numerator is smaller than the denominator, then the fraction will be less than 1 .

(b) If the numerator is equal to the denominator, then the fraction will be equal to 1 .

Q3 Fill up using one of these: ‘ > ’, ‘ < ’ or ‘ =

(a) \frac{1}{2}\square 1

(b) \frac{3}{5}\square 1

(c) 1\square \frac{7}{8}

(d) \frac{4}{4}\square 1

(e) \frac{2005}{2005}\square 1

Answer: (a)

\frac{1}{2}< 1

(b)

\frac{3}{5}< 1

(c)

1> \frac{7}{8}

(d)

\frac{4}{4}=1

(e)

\frac{2005}{2005}= 1

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.2

Q1 (a) Draw number lines and locate the points on them : \frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}

Answer: The number line is given below:-

1643038680325


Q1 (b) Draw number lines and locate the points on them : \frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}

Answer: The number line is shown below with the required points marked.

1643038705799


Q1 (c) Draw number lines and locate the points on them : \frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}

Answer: The number line locating the given fraction is shown below:-

1643038731961


Q2 Express the following as mixed fractions :

(a) \frac{20}{3}

(b) \frac{11}{5}

(c) \frac{17}{7}

(d) \frac{28}{5}

(e) \frac{19}{6}

(f) \frac{35}{9}

Answer: (a) \frac{20}{3}\ =\ \frac{18\ +\ 2}{3}\ =\ 6\frac{2}{3}

(b) \frac{11}{5}\ =\ \frac{10\ +\ 1}{5}\ =\ 2\frac{1}{5}

(c) \frac{17}{7}\ =\ \frac{14\ +\ 3}{7}\ =\ 2\frac{3}{7}

(d) \frac{28}{5}\ =\ \frac{25\ +\ 3}{5}\ =\ 5\frac{3}{5}

(e) \frac{19}{6}\ =\ \frac{18\ +\ 1}{6}\ =\ 3\frac{1}{6}

(f) \frac{35}{9}\ =\ \frac{27\ +\ 8}{9}\ =\ 3\frac{8}{9}


Q3 Express the following as improper fractions :

(a) 7\frac{3}{4}

(b) 5\frac{6}{7}

(c) 2\frac{5}{6}

(d) 10\frac{3}{5}

(e) 9\frac{3}{7}

(f) 8\frac{4}{9}

Answer: The improper fractions of the mixed fractions are given below :-

(a) 7\frac{3}{4}\ =\ \frac{28\ +\ 3}{4}\ =\ \frac{31}{4}

(b) 5\frac{6}{7}\ =\ \frac{35\ +\ 6}{7}\ =\ \frac{41}{7}

(c) 2\frac{5}{6}\ =\ \frac{12\ +\ 5}{6}\ =\ \frac{17}{6}

(d) 10\frac{3}{5}\ =\ \frac{50\ +\ 3}{5}\ =\ \frac{53}{5}

(e) 9\frac{3}{7}\ =\ \frac{63\ +\ 3}{7}\ =\ \frac{66}{7}

(f) 8\frac{4}{9}\ =\ \frac{72\ +\ 4}{9}\ =\ \frac{76}{9}


NCERT Solutions for Class 6 Maths Topic: Simplest Form of a Fraction

Q1 Write the simplest form of :

(i) \frac{15}{75}

(ii) \frac{16}{72}

(iii) \frac{17}{51}

(iv) \frac{42}{28}

(v) \frac{80}{24}

Answer: (i) \frac{15}{75}=\frac{5}{25}=\frac{1}{5}

(ii) \frac{16}{72}=\frac{8}{36}=\frac{4}{18}=\frac{2}{9}

(iii) \frac{17}{51}=\frac{1}{3}

(iv) \frac{42}{28}=\frac{21}{14}=\frac{3}{2}

(v) \frac{80}{24}=\frac{40}{12}=\frac{20}{6}=\frac{10}{3}



Q2 Is \frac{49}{64} in its simplest form?

Answer: Yes, \frac{49}{64} is in its simplest form because 49 and 64 has no common divisor.

NCERT Solutions for Class 6 Maths Topic: Equivalent Fractions

Q1 Are \frac{1}{3} and \frac{2}{7} ; \frac{2}{5} and \frac{2}{7} ; \frac{2}{9} and \frac{6}{27} and equivalent? Give reason

Answer: \frac{1}{3} and \frac{2}{7} ; \frac{2}{5} and \frac{2}{7} are not equivalent because

\frac{1}{3}> \frac{2}{7} and

\frac{2}{5}> \frac{2}{7}

but

\frac{2}{9}= \frac{6}{27}=0.222


Q2 Give example of four equivalent fractions.

Answer: Four example of equivalent fractions are :

\frac{2}{4}=\frac{4}{8};\frac{1}{3}=\frac{3}{9};\frac{8}{4}=\frac{12}{6};\frac{1}{5}=\frac{5}{25}


Q3 Identify the fractions in each. Are these fractions equivalent?

seema

Answer:

seema

(i) \frac{6}{8} (ii) \frac{9}{12} (iii) \frac{12}{16} (iv) \frac{15}{20}

all fractions in it simplest form is

\frac{3}{4}

So all fractions are equivalent


Q1 Find five equivalent fractions of each of the following:

(i) \frac{2}{3}

(ii) \frac{1}{5}

(iii) \frac{3}{5}

(iv) \frac{5}{9}

Answer: (i) \frac{2}{3}=\frac{8}{12}

(ii) \frac{1}{5}=\frac{5}{25}

(iii) \frac{3}{5}=\frac{15}{25}

(iv) \frac{5}{9}=\frac{50}{90}

NCERT Solutions for Class 6 Maths Exercise: 7.3

Q1 Write the fractions. Are all these fractions equivalent?

1643038760286

1643038770006

Answer: In the case of (a), we have:-

(i) f_1\ =\ \frac{1}{2}

(ii) f_2\ =\ \frac{2}{4} =\ \frac{1}{2}

(iii) f_3\ =\ \frac{3}{6} =\ \frac{1}{2}

(iv) f_4\ =\ \frac{4}{8} =\ \frac{1}{2}

Hence all fractions are equal in this case.

In the case of (b), we have:-

(i) f_1\ =\ \frac{4}{12}\ =\ \frac{1}{3}

(ii) f_2\ =\ \frac{3}{9} =\ \frac{1}{3}

(iii) f_3\ =\ \frac{2}{6} =\ \frac{1}{3}

(iv) f_4\ =\ \frac{1}{3}

(v) f_5\ =\ \frac{6}{15}\ =\ \frac{2}{5}


Q2 Write the fractions and pair up the equivalent fractions from each row.

1643038839251

Answer: The fractions of each are given below :-

(a) f_a\ =\ \frac{1}{2}

(b) f_b\ =\ \frac{4}{6}\ =\ \frac{2}{3}

(c) f_c\ =\ \frac{3}{9}\ =\ \frac{1}{3}

(d) f_d\ =\ \frac{2}{8}\ =\ \frac{1}{4}

(e) f_e\ =\ \frac{3}{4}

Similarly,

(i) f_1\ =\ \frac{6}{18}\ =\ \frac{1}{3}

(ii) f_2\ =\ \frac{4}{8}\ =\ \frac{1}{2}

(iii) f_3\ =\ \frac{12}{16}\ =\ \frac{3}{4}

(iv) f_4\ =\ \frac{8}{12}\ =\ \frac{2}{3}

(v) f_5\ =\ \frac{4}{16}\ =\ \frac{1}{4}



Q3 (a) Replace box in each of the following by the correct number : \frac{2}{7}=\frac{8}{\square }

Answer: The correct number is 28.

\frac{2}{7}\times \frac{4}{4} =\ \frac{8}{28}\ =\frac{8}{\square }

Thus \square\ =\ 28 .

Q3 (b) Replace \square in each of the following by the correct number : \frac{5}{8}=\frac{10}{\square }

Answer: (b) The correct answer is 16.

\frac{5}{8}\times \frac{2}{2}=\frac{10}{16}


Q3 (c) Replace \square in each of the following by the correct number : \frac{3}{5}=\frac{\square }{20}

Answer: The required value is 12.

\frac{3}{5}\times \frac{4}{4}=\frac{12 }{20}



Q3 (d) Replace in each of the following by the correct number : \frac{45}{60}=\frac{15}{\square }

Answer: The required value is 20.

\frac{45}{60}\times \frac{\frac{1}{3}}{\frac{1}{3}}=\frac{15}{20 }


Q3 (e) Replace \square in each of the following by the correct number : \frac{18}{24}=\frac{4}{\square }

Answer: The correct number is \frac{48}{9} .

Multiplying numerator and denomenator by \frac{4}{18} .

We have :- \frac{18}{24}\times \frac {\frac{4}{18}}{\frac{4}{18}}\ =\ \frac{4}{\frac{96}{18}}\ =\ \frac{4}{\frac{48}{9}}

Hence \square\ =\ \frac{48}{9}



Q4 Find the equivalent fraction of \frac{3}{5} having

(a) denominator 20

(b) numerator 9

(c) denominator 30

(d) numerator 27

Answer: (a) Multiply numerator and denominator by 4, we have :

\frac{3}{5}\times \frac{4}{4}\ =\ \frac{12}{20}

(b) Multiply numerator and denominator by 3, we have :

\frac{3}{5}\times \frac{3}{3}\ =\ \frac{9}{15}

(c) Multiply numerator and denominator by 6, we have :

\frac{3}{5}\times \frac{6}{6}\ =\ \frac{18}{30}

(d) Multiply numerator and denominator by 9, we have :

\frac{3}{5}\times \frac{9}{9}\ =\ \frac{27}{45}


Q5 Find the equivalent fraction of \frac{36}{48} with

(a) numerator 9

(b) denominator 4

Answer: The required equivalent fractions are given below :-

(a) Divide both numerator and denomenator by 4.

\frac{36}{48}\times \frac{\frac{1}{4}}{\frac{1}{4}}\ =\ \frac{9}{12}

(b) Divide both numerator and denomenator by 12.

\frac{36}{48}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{3}{4}

Q6 (a) Check whether the given fractions are equivalent : \frac{5}{9},\frac{30}{35}

Answer: Multiply both numerator and denominator by 6.

\frac{5}{9}\times \frac{6}{6}\ =\ \frac{30}{54}\ \neq \frac{30}{35}

Q6 (b) Check whether the given fractions are equivalent : \frac{3}{10},\frac{12}{50}

Answer:

Multiply both numerator and denominator by 4, we get :

\frac{3}{10}\times \frac{4}{4}\ =\ \frac{12}{40}\ \neq \ \frac{12}{50}

Q6 (c) Check whether the given fractions are equivalent : \frac{7}{13},\frac{5}{11}

Answer: Multiply both numerator and denominator by \frac{5}{7} , we get :

\frac{7}{13}\times \frac{\frac{5}{7}}{\frac{5}{7}}\ =\ \frac{5}{\frac{65}{7}}\ \neq \ \frac{5}{11}

Hence these two fractions are not the same.

Q7 Reduce the following fractions to simplest form :

(a) \frac{48}{60}

(b) \frac{150}{60}

(c) \frac{84}{98}

(d) \frac{12}{52}

(e) \frac{7}{28}

Answer: (a) \frac{48}{60}\ =\ \frac{24}{30}\ =\ \frac{12}{15}\ =\frac{4}{5}

(b) \frac{150}{60}\ =\ \frac{15}{6}\ =\ \frac{5}{2}

(c) \frac{84}{98}\ =\ \frac{42}{49}\ =\ \frac{6}{7}

(d) \frac{12}{52}\ =\ \frac{6}{26}\ =\ \frac{3}{13}

(e) \frac{7}{28}\ =\ \frac{1}{4}

Q8 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Answer: The fraction of pencils used by Ramesh is:-

=\ \frac{10}{20}\ =\ \frac{1}{2}

The fraction of pencils used by Sheelu is:-

=\ \frac{25}{50}\ =\ \frac{1}{2}

The fraction of pencils used by Jamaal is:-

=\ \frac{40}{80}\ =\ \frac{1}{2}

Thus, the fractions of pencils used by each are the same.

Q9 Match the equivalent fractions and write two more for each.

(i) \frac{250}{400} (a) \frac{2}{3}

(ii) \frac{180}{200} (b) \frac{2}{5}

(iii) \frac{660}{990} (c) \frac{1}{2}

(iv) \frac{180}{360} (d) \frac{5}{8}

(v) \frac{220}{550} (e) \frac{9}{10}

Answer: (i) \frac{250}{400}\ =\ \frac{25}{40}\ =\ \frac{5}{8}

(ii) \frac{180}{200}\ =\ \frac{18}{20}\ =\ \frac{9}{10}

(iii) \frac{660}{990}\ =\ \frac{66}{99}\ =\ \frac{22}{33}\ =\ \frac{2}{3}

(iv) \frac{180}{360}\ =\ \frac{18}{36}\ =\ \frac{2}{4}\ =\ \frac{1}{2}

(v) \frac{220}{550}\ =\ \frac{22}{55}\ =\ \frac{2}{5}


NCERT Solutions for Class 6 Maths Topic: Comparing Fractions

Q1 You get one-fifth of a bottle of juice and your sister gets one-third of the same size of a bottle of juice. Who gets more?

Answer: My sister gets more because \frac{1}{3}> \frac{1}{5}

NCERT Solutions for Class Maths Topic: Comparing Like Fractions

Q1 Which is the larger fraction?

(i) \frac{7}{10} or \frac{8}{10}

(ii) \frac{11}{24} or \frac{13}{24}

(iii) \frac{17}{102} or \frac{12}{102}

Answer: The fractions are shown below using greater than or less than sign

(i) \frac{7}{10} < \frac{8}{10}

(ii) \frac{11}{24} < \frac{13}{24}

(iii) \frac{17}{102} > \frac{12}{102}


NCERT Class 6 Maths Chapter 7 Fractions Topic: Arrangement of Fractions

Q1 (1) Arrange the following in ascending and descending order :

\frac{1}{12},\frac{1}{23},\frac{1}{5},\frac{1}{7},\frac{1}{50},\frac{1}{9},\frac{1}{17}


Answer: (a) \frac{1}{5}> \frac{1}{7}> \frac{1}{9}> \frac{1}{12}> \frac{1}{17}> \frac{1}{23}> \frac{1}{50}

and \frac{1}{50}< \frac{1}{23}< \frac{1}{17}< \frac{1}{12}< \frac{1}{9}< \frac{1}{7}< \frac{1}{5}

Q1 (b) Arrange the following in ascending and descending order :

\frac{3}{7},\frac{3}{11},\frac{3}{5},\frac{3}{2},\frac{3}{13},\frac{3}{4},\frac{3}{17}

Answer: The following in ascending and descending order are :

(b) \frac{3}{2}>\frac{3}{4}> \frac{3}{5}>\frac{3}{7}>\frac{3}{11}>\frac{3}{13}>\frac{3}{17}

\frac{3}{17}<\frac{3}{13}<\frac{3}{11}<\frac{3}{7}<\frac{3}{5}<\frac{3}{2}<\frac{3}{3}

Q1 (c) Arrange the following in ascending and descending order :

Write 3 more similar examples and arrange them in ascending and descending order.

Answer: The following in ascending and descending order are:

(i) \frac{3}{5},\frac{7}{5},\frac{4}{5}

\frac{3}{5}<\frac{4}{5}<\frac{7}{5}

and \frac{7}{5}>\frac{4}{5}>\frac{3}{5}

(ii) \frac{3}{11},\frac{7}{11},\frac{4}{11}

\frac{3}{11}<\frac{4}{11}<\frac{7}{11}

and \frac{7}{11}>\frac{4}{11}>\frac{3}{11}

(iii) \frac{3}{11},\frac{3}{7},\frac{3}{5}

\frac{3}{11}<\frac{3}{7}<\frac{3}{5}

and \frac{3}{5}>\frac{3}{7}>\frac{3}{11}

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.4

Q1 Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign '<'\; '='\; '> ' between the fractions:

1643038920076

1643038930022 (c) Show \frac{2}{6},\frac{4}{6},\frac{8}{6}\; and\; \frac{6}{6} on the number line. Put appropriate signs between the fractions given

\frac{5}{6}\square \frac{2}{6}, \frac{3}{6}\square 0, \frac{1}{6}\square \frac{6}{6}, \frac{8}{6}\square \frac{5}{6},


Answer: (a) f_1\ =\ \frac{3}{8}

f_2\ =\ \frac{6}{8}\ =\ \frac{3}{4}

f_3\ =\ \frac{4}{8}\ =\ \frac{1}{2}

f_4\ =\ \frac{1}{8}

f_2\ >\ f_3\ >\ f_1\ >\ f_4


(b) f_1\ =\ \frac{8}{9}

f_2\ =\ \frac{4}{9}

f_3\ =\ \frac{3}{9}\ =\ \frac{1}{3}

f_4\ =\ \frac{6}{9}\ =\ \frac{2}{3}


(c)

1643038946291

From the above number line we can compare the given numbers easily.

\frac{5}{6}\ >\ \frac{2}{6}, \frac{3}{6}\ >\ 0, \frac{1}{6}\ <\ \frac{6}{6}, \frac{8}{6}\ >\ \frac{5}{6}


Q2 Compare the fractions and put an appropriate sign.

(a) \frac{3}{6}\square \frac{2}{6}

(b) \frac{1}{7}\square \frac{1}{4}

(c) \frac{4}{5}\square \frac{5}{5}

(d) \frac{3}{5}\square \frac{3}{7}


Answer: The comparison is given below :-

(a) \frac{3}{6}\ >\ \frac{2}{6}

(b) \frac{1}{7}\ <\ \frac{1}{4}

(c) \frac{4}{5}\ <\ \frac{5}{5}

(d) \frac{3}{5}\ >\ \frac{3}{7}

Q3 Make five more such pairs and put appropriate signs.

Answer: The five pairs can be :-

\frac{2}{3}\ > \frac{1}{3} , \frac{5}{3}\ > \frac{2}{3} \frac{5}{9}\ < \frac{4}{3} \frac{2}{7}\ < \frac{5}{7} \frac{1}{2}\ >\ \frac{1}{3}


Q4 (a) Look at the figures and write '< ' or '> ','=' between the given pairs of fractions.

1643038973885

(a) \frac{1}{6}\square \frac{1}{3}


Answer: With the help of given diagram :

\frac{1}{6}\ <\ \frac{2}{6}

Thus \frac{1}{6}\ <\ \frac{1}{3}


Q4 (b) Look at the figures and write '< ' or '> ','=' between the given pairs of fractions.

1643038997226

(b) \frac{3}{4}\square \frac{2}{6}

Answer: From the diagram it is cleat that :

\frac{3}{4}\ >\ \frac{2}{6}


Q4 (c) Look at the figures and write '< ' or '> ','=' between the given pairs of fractions.

1643039020469

(c) \frac{2}{3}\square \frac{2}{4}

Answer: From the given diagram, we can clearly say that :-

\frac{2}{3}\ >\ \frac{2}{4}


Q5 How quickly can you do this? Fill appropriate sign.

(a) \frac{1}{2}\square \frac{1}{5}

(b) \frac{2}{4}\square \frac{3}{6}

(c) \frac{3}{5}\square \frac{2}{3}

(d) \frac{3}{4}\square \frac{2}{8}

(e) \frac{3}{5}\square \frac{6}{5}

(f) \frac{7}{9}\square \frac{3}{9}

(g) \frac{1}{4}\square \frac{2}{8}

(h) \frac{6}{10}\square \frac{4}{5}

(i) \frac{3}{4}\square \frac{7}{8}

(j) \frac{6}{10}\square \frac{3}{5}

(k) \frac{5}{7}\square \frac{15}{21}

Answer: (a) \frac{1}{2}\ >\ \frac{1}{5}

(b) \frac{2}{4}\ =\ \frac{3}{6}

(c) \frac{3}{5}\ <\ \frac{2}{3}

(d) \frac{3}{4}\ >\ \frac{2}{8}

(e) \frac{3}{5}\ <\ \frac{6}{5}

(f) \frac{7}{9}\ >\ \frac{3}{9}

(g) \frac{1}{4}\ =\ \frac{2}{8}

(h) \frac{6}{10}\ <\ \frac{4}{5}

(i) \frac{3}{4}\ <\ \frac{7}{8}

(j) \frac{6}{10}\ =\ \frac{3}{5}

(k) \frac{5}{7}\ =\ \frac{15}{21}


Q6 The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

(a) \frac{2}{12}

(b) \frac{3}{15}

(c) \frac{8}{50}

(d) \frac{16}{100}

(e) \frac{10}{16}

(f) \frac{15}{75}

(g) \frac{12}{60}

(h) \frac{16}{96}

(i) \frac{12}{75}

( j) \frac{12}{72}

(k) \frac{3}{18}

(l) \frac{4}{25}

Answer: (i) \frac{2}{12}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{1}{6}

(ii) \frac{3}{15}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{1}{5}

(iii) \frac{8}{50}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{4}{25}

(iv) \frac{16}{100}\times \frac{\frac{1}{4}}{\frac{1}{4}}\ =\ \frac{4}{25}

(v) \frac{10}{16}\times \frac{\frac{1}{2}}{\frac{1}{2}}\ =\ \frac{5}{8}

(vi) \frac{15}{75}\times \frac{\frac{1}{15}}{\frac{1}{15}}\ =\ \frac{1}{5}

(vii) \frac{12}{60}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{1}{5}

(viii) \frac{16}{96}\times \frac{\frac{1}{16}}{\frac{1}{16}}\ =\ \frac{1}{6}

(ix) \frac{12}{75}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{4}{25}

(x) \frac{12}{72}\times \frac{\frac{1}{12}}{\frac{1}{12}}\ =\ \frac{1}{6}

(xi) \frac{3}{18}\times \frac{\frac{1}{3}}{\frac{1}{3}}\ =\ \frac{1}{6}

(xii) \frac{4}{25}


Q7 (a) Find answers to the following. Write and indicate how you solved them.

Is \frac{5}{9} equal to \frac{4}{5}?

Answer: No.

Multiply numerator and denomenator by \frac{4}{5} .

We have : \frac{5}{9}\times \frac{\frac{4}{5}}{\frac{4}{5}}\ =\ \frac{4}{\frac{36}{5}}

Hence \frac{5}{9}\ \neq \ \frac{4}{5}



Q7 (c) Find answers to the following. Write and indicate how you solved them.

Is \frac{4}{5} equal to \frac{16}{20}?

Answer: Yes.

By multiplying numerator and denominator by 5, we get :

\frac{4}{5}\times \frac{5}{5}\ =\ \frac{16}{20}


Q7 (d) Find answers to the following. Write and indicate how you solved them.

Is \frac{1}{15} equal to \frac{4}{30} ?

Answer: No.

Multiply both numerator and denomenator by 2, we get :-

\frac{1}{15}\times \frac{2}{2}\ =\ \frac{2}{30}\ \neq\ \frac{4}{30}


Q8 Ila read 25 pages of a book containing 100 pages. Lalita read \frac{2}{5} of the same book. Who read less?

Answer: The fraction of the book read by Ila is:-

=\ \frac{25}{100}\ =\ \frac{1}{4}

So we can compare the fraction now:-

\frac{1}{4}\ <\ \frac{2}{5}

Hence Ila reads less.

Q9 Rafiq exercised for \frac{3}{6} of an hour, while Rohit exercised for \frac{3}{4} of an hour. Who exercised for a longer time?

Answer: Who exercised for a longer time can be found by comparing the fraction of their work time.

\frac{3}{6}\ <\ \frac{3}{4}

Hence Rohit exercised for a longer time.

Q10 In a class A of 25 students, 20 passed with 60^{o}/_{o} or more marks; in another class B of 30 students, 24 passed with 60^{o}/_{o} or more marks. In which class was a greater fraction of students getting with 60^{o}/_{o} or more marks?

Answer: In class A, the fraction of students passed with 60 \% or above marks :

=\ \frac{20}{25}\ =\ \frac{4}{5}

And, in class B, the fraction is :

=\ \frac{24}{30}\ =\ \frac{4}{5}

Hence the required fraction is same in both the classes.

NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions

Q1 My mother divided an apple into 4 equal parts. She gave me two parts and my brother one part. How much apple did she give to both of us together?

Answer: mother gave to me \frac{1}{2} part

mother gave to my brother \frac{1}{4} part

She gave both off us

\frac{1}{2}+\frac{1}{4}=\frac{3}{4} part

Q3 Sohan was putting covers on his note books. He put one fourth of the covers on Monday. He put another one fourth on Tuesday and the remaining on Wednesday. What fraction of the covers did he put on Wednesday?

Answer: He put covers on Monday= \frac{1}{4}

He put the cover on Tuesday = \frac{1}{4}

and the remaining on Wednesday.

Thus, the fraction of the covers he put on Wednesday = 1-(\frac{1}{4}+\frac{1}{4})

=1-(\frac{1}{2})

=\frac{1}{2}

NCERT Class 6 Maths Chapter 7 Fractions Topic: Adding or Substracting like Fractions

Q1 Find the difference between \frac{7}{8} and \frac{3}{8} .

Answer: The difference between \frac{7}{8} and \frac{3}{8} is given by

\frac{7}{8}-\frac{3}{8}=\frac{4}{8}=\frac{1}{2}


NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.5

Q1 Write these fractions appropriately as additions or subtractions :

1643039073930

1643039101975 1643039087324

1643039121480

Answer: In case (a) - Addition

case (b) - Subtraction

case (c) - Addition

1643039131177

Q2 Solve :

(a) \frac{1}{18} +\frac{1}{18}

(b) \frac{8}{15} +\frac{3}{15}

(c) \frac{7}{7} -\frac{5}{7}

(d) \frac{1}{22} +\frac{21}{22}

(e) \frac{12}{15} -\frac{7}{15}

(f) \frac{5}{8} +\frac{3}{8}

(g) 1-\frac{2}{3}\left ( 1=\frac{3}{3} \right )

( h) \frac{1}{4}+\frac{0}{4}

(i) 3-\frac{12}{5}

Answer: (a) \frac{1}{18} +\frac{1}{18}\ =\ \frac{1+1}{18}\ =\ \frac{2}{18}\ =\ \frac{1}{9}

(b) \frac{8}{15} +\frac{3}{15}\ =\ \frac{8+3}{15}\ =\ \frac{11}{15}

(c) \frac{7}{7} -\frac{5}{7}\ =\ \frac{7-5}{7}\ =\ \frac{2}{7}

(d) \frac{1}{22} +\frac{21}{22}\ =\ \frac{1+21}{22}\ =\ \frac{22}{22}\ =\ 1

(e) \frac{12}{15} -\frac{7}{15}\ =\ \frac{12-7}{15}\ =\ \frac{5}{15}\ =\ \frac{1}{ 3}

(f) \frac{5}{8} +\frac{3}{8}\ =\ \frac{5+3}{8}\ =\ \frac{8}{8}\ =\ 1

(g) 1-\frac{2}{3}\ =\ \frac{3}{3}\ -\ \frac{2}{3}\ =\ \frac{3-2}{3}\ =\ \frac{1}{3}

( h) \frac{1}{4}+\frac{0}{4}\ =\ \frac{1+0}{4}\ =\ \frac{1}{4}

(i) 3-\frac{12}{5}\ =\ \frac{15}{5}\ -\ \frac{12}{5}\ =\ \frac{15-12}{5}\ =\ \frac{3}{5}


Q3 Shubham painted \frac{2}{3} of the wall space in his room. His sister Madhavi helped and painted \frac{1}{3} of the wall space. How much did they paint together?

Answer: Total wall painted = Wall painted by Subham + Wall pained by Madhavi

=\ \frac{2}{3}\ +\ \frac{1}{3}\ =\ \frac{3}{3}\ =\ 1

Hence the whole wall is painted by them.

Q4 Fill in the missing fractions.

(a) \frac{7}{10}-\square =\frac{3}{10}

(b) -\square \frac{3}{21}=\frac{5}{21}

(c) \square- \frac{3}{6}=\frac{3}{6}

(d) \square+ \frac{5}{27}=\frac{12}{27}

Answer: (a) \frac{7}{10}-\square =\frac{3}{10}

\square\ =\ \frac{7}{10}\ -\ \frac{3}{10}

or \square\ =\ \frac{5}{10}\ =\ \frac{1}{2}


(b) -\square \frac{3}{21}=\frac{5}{21}

-\square =\frac{5}{3}

or \square\ =\ -\ \frac{5}{3}


(c) \square- \frac{3}{6}=\frac{3}{6}

\square\ =\ \frac{3}{6}\ +\ \frac{3}{6}\ =\ \frac{6}{6}\ =\ 1


(d) \square+ \frac{5}{27}=\frac{12}{27}

\square\ =\ \frac{12}{27}\ -\ \frac{5}{27}

or =\ \frac{7}{27}


Q5 Javed was given \frac{5}{7} of a basket of oranges. What fraction of oranges was left in the basket?

Answer: The total fraction of oranges in the basket are \frac{7}{7} .

Thus the fraction of oranges left is :

\frac{7}{7}\ -\ \frac{5}{7}\ =\ \frac{2}{7}

NCERT Class 6 Maths Chapter 7 Fractions Topic: Addition and Subtraction of Fractions

Q1 Add \frac{2}{5} and \frac{3}{7} .

Answer: Addition of \frac{2}{5} and \frac{3}{7} is given by

\frac{2}{5}+\frac{3}{7}=\frac{14+15}{35}=\frac{29}{35}


Q2 Subtract \frac{2}{5} from \frac{5}{7} .

Answer: Subtraction of \frac{2}{5} from \frac{5}{7} is given by

\frac{5}{7}-\frac{2}{5}=\frac{25-14}{35}=\frac{11}{35}

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise: 7.6

Q1 Solve

(a) \frac{2}{3}+\frac{1}{7} (b) \frac{3}{10}+\frac{7}{15} (c) \frac{4}{9}+\frac{2}{7}

(d) \frac{5}{7}+\frac{1}{3} (e) \frac{2}{5}+\frac{1}{6} (f) \frac{4}{5}+\frac{2}{3}

Answer: (a) \frac{2}{3}+\frac{1}{7}\ =\ \frac{2\times 7\ +\ 1\times 3}{21}\ =\ \frac{17}{21}

(b) \frac{3}{10}+\frac{7}{15}\ =\ \frac{3\times 15\ +\ 7\times 10}{150}\ =\ \frac{115}{150}\ =\ \frac{23}{30}

(c) \frac{4}{9}+\frac{2}{7}\ =\ \frac{4\times 3\ +\ 2\times 9}{63}\ =\ \frac{46}{63}

(d) \frac{5}{7}+\frac{1}{3}\ =\ \frac{5\times 3\ +\ 1\times 7}{21}\ =\ \frac{22}{21}

(e) \frac{2}{5}+\frac{1}{6}\ =\ \frac{2\times 6\ +\ 1\times 5}{30}\ =\ \frac{17}{30}

(f) \frac{4}{5}+\frac{2}{3}\ =\ \frac{4\times 3\ +\ 2\times 5}{15}\ =\ \frac{22}{15}


Q1 Solve

(g) \frac{3}{4}-\frac{1}{3} (h) \frac{5}{5}-\frac{1}{3} (i) \frac{2}{3}+\frac{3}{4}+\frac{1}{2}

(j) \frac{1}{2}+\frac{1}{3}+\frac{1}{6} (k) 1\frac{1}{3}+3\frac{2}{3} (l) 4\frac{2}{3}+3\frac{1}{4}

(m) \frac{16}{5}-\frac{7}{5} (n) \frac{4}{3}-\frac{1}{2}


Answer: (g) \frac{3}{4}-\frac{1}{3}\ =\ \frac{3\times 3\ -\ 1\times 4}{12}\ =\ \frac{5}{12}

(h) \frac{5}{5}-\frac{1}{3}\ =\ \frac{5\times 3\ -\ 1\times 5}{15}\ =\ \frac{10}{15}\ =\ \frac{2}{3}

(i) \frac{2}{3}+\frac{3}{4}+\frac{1}{2}\ =\ \frac{2\times 4\ +\ 3\times 3}{12}\ +\ \frac{1}{2}\ =\ \frac{17}{12}\ +\ \frac{1}{2}\ =\ \frac{17\times 2\ +\ 1\times 12}{24}

=\ \frac{46}{24}\ =\ \frac{23}{12}

(j) \frac{1}{2}+\frac{1}{3}+\frac{1}{6}\ =\ \frac{1\times 3\ +\ 1\times 2}{6}\ +\ \frac{1}{6}\ =\ \frac{5}{6}\ +\ \frac{1}{6}\ =\ \frac{6}{6}\ =\ 1

(k) 1\frac{1}{3}+3\frac{2}{3}\ =\ \frac{4}{3}\ +\ \frac{11}{3}\ =\ \frac{15}{3}\ =\ 5

(l) 4\frac{2}{3}+3\frac{1}{4}\ =\ \frac{14}{3}\ +\ \frac{13}{4}\ =\ \frac{14\times 4\ +\ 13\times 3}{12}\ =\ \frac{95}{12} \

(m) \frac{16}{5}-\frac{7}{5}\ =\ \frac{16\ -\ 7}{5}\ =\ \frac{9}{5}

(n) \frac{4}{3}-\frac{1}{2}\ =\ \frac{4\times2\ -\ 1\times3}{6}\ =\ \frac{5}{6}


Q2 Sarita bought \frac{2}{5} metre of ribbon and Lalita \frac{3}{4} metre of ribbon. What is the total length of the ribbon they bought?

Answer: The total length of ribbon is given :-

=\ \frac{2}{5}\ +\ \frac{3}{4}\ =\ \frac{2\times 4\ +\ 3\times 5}{20}\ =\ \frac{23}{20}

Thus total length of ribbon is \frac{23}{20}\ m .

Q3 Naina was given 1\frac{1}{2} piece of cake and Najma was given 1\frac{1}{3} piece of cake. Find the total amount of cake was given to both of them.

Answer: Total amount of cake given to both = Cake given to Naina + Cake given to Najma

=\ 1\frac{1}{2}\ +\ 1\frac{1}{3}

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

=\ \frac{3\times 3\ +\ 4\times 2 }{6}

=\ \frac{17 }{6}


Q4 Fill in the boxes :

(a) \square-\frac{5}{8}=\frac{1}{4}

(b) \square-\frac{1}{5}=\frac{1}{2}

(c) \frac{1}{2}-\square =\frac{1}{6}

Answer: (a) \square-\frac{5}{8}=\frac{1}{4} :-

\square\ =\ \frac{1}{4}\ +\ \frac{5}{8}\ =\ \frac{1\times 8\ +\ 5\times 4}{32}\ =\ \frac{28}{32}\ =\ \frac{7}{8}

(b) \square-\frac{1}{5}=\frac{1}{2} :-

\square\ =\ \frac{1}{2}\ +\ \frac{1}{5}\ =\ \frac{1\times 5\ +\ 1\times 2}{10}\ =\ \frac{7}{10}

(c) \frac{1}{2}-\square =\frac{1}{6} :-

\square\ =\ \frac{1}{2}\ -\ \frac{1}{6}\ =\ \frac{1\times 6\ -\ 1\times 2}{12}\ =\ \frac{4}{12}\ =\ \frac{1}{3}


Q5 Complete the addition-subtraction box.

1643039159028

Answer: The required table is shown below:-

1643039168790

Q5 Complete the addition-subtraction box.

1643039199627

Answer: The required box is given below :-

1643039209377

Q6 A piece of wire \frac{7}{8} metre long broke into two pieces. One piece was \frac{1}{4} metre long. How long is the other piece?

Answer: Let the length of another piece of wire be x.

Thus, x\ +\ \frac{1}{4}\ =\ \frac{7}{8}

x\ =\ \frac{7}{8}\ -\ \frac{1}{4}

=\ \frac{7\times 4\ -\ 1\times 8}{32}\ =\ \frac{20}{32}

=\ \frac{10}{16}\ =\ \frac{5}{8}

Hence the length of other part is \frac{5}{8}\ m .

Q8 Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is \frac{5}{6}th full and Samuel’s shelf is \frac{2}{5}th full. Whose bookshelf is more full? By what fraction?

Answer: If we compare the bookshelves of both, we obtain that :

\frac{5}{6}\ >\ \frac{2}{5}

Also, \frac{5}{6}\ -\ \frac{2}{5}\ =\ \frac{25-12}{30}\ =\ \frac{13}{30}

Hence the bookshelf of Asha is more full and by \frac{13}{30} fraction.

Q9 Jaidev takes 2\frac{1}{5} minutes to walk across the school ground. Rahul takes \frac{7}{4} minutes to do the same. Who takes less time and by what fraction?

Answer: Firstly, let us convert the time taken by Jaidev in the improper fraction from mixed fraction.

2\frac{1}{5}\ =\ \frac{10\ +\ 1}{5}\ =\ \frac{11}{5}

Now, comparing both, we have :

\frac{11}{5}\ >\ \frac{7}{4}

Also, \frac{11}{5}\ -\ \frac{7}{4}\ =\ \frac{11\times 4\ -\ 7\times 5}{20}\ =\ \frac{9}{20}

Hence Rahul takes less time as compared to Jaidev by \frac{9}{20}\ minute a fraction.


Fractions Class 6 Maths Chapter 7-Topics

  • A Fraction
  • Fraction of the Number Line
  • Proper Fraction
  • Improper and Mixed Fractions
  • Equivalent Fractions

NCERT Solutions for Class 6 Mathematics Chapter Wise

Chapters No. Chapters Name
Chapter - 1 Knowing Our Numbers
Chapter - 2 Whole Numbers
Chapter - 3 Playing with Numbers
Chapter - 4 Basic Geometrical Ideas
Chapter - 5 Understanding Elementary Shapes
Chapter - 6 Integers
Chapter - 7 Fractions
Chapter - 8 Decimals
Chapter - 9 Data Handling
Chapter -10 Mensuration
Chapter -11 Algebra
Chapter -12 Ratio and Proportion
Chapter -13 Symmetry
Chapter -14 Practical Geometry

Key features of NCERT Solutions for Class 6 Maths chapter 7

Extensive Topic Coverage: The solutions for maths class 6 chapter 7 encompass all the important topics and subtopics of the chapter, ensuring that students have a thorough understanding of the content.

Focus on Exam Readiness: The NCERT Class 6 Maths Chapter 7 solutions adopt an exam-focused approach, equipping students with the necessary skills and strategies to approach exam questions effectively and perform well.

Interactive Learning: The NCERT class 6 maths chapter 7 promote interactive learning by incorporating illustrations, diagrams, and practical examples, making the learning process engaging and enjoyable for students.

Step-by-Step Solutions: Each problem in the fraction questions for class 6 is accompanied by a detailed step-by-step solution, enabling students to follow the logical thought process and learn problem-solving techniques.

NCERT Solutions for Class 6 Subject wise

How to Use NCERT Solutions for Class 6 Maths Chapter 7 Fractions?

  • Learn the representation of fractions using the equal part concept.
  • Go through the text given in the textbook to learn various applications and concepts.
  • Have a glance through some examples to understand the answering of a particular kind of question with the help of NCERT Solutions for Class 6 .
  • Now you can jump to the practice problems.
  • While practicing you can use NCERT solutions for Class 6 Maths chapter 7 Fractions as a helping tool.

Keep learning and working hard!

Also Check NCERT Books and NCERT Syllabus here:

Frequently Asked Question (FAQs)

1. What is fraction according to class 6 chapter 7 maths?

A fraction is a number representing part of a whole.

Example-1/2, 3/4...

Students we get detailed discussion about the concepts related to fraction above in this article.

2. What topics are covered in Chapter 7 of Class 6 Maths NCERT Solutions?

In maths class 6 chapter 7 NCERT Solutions, you will learn about the following important topics:

  • Introduction to fractions
  • Understanding fractions on the number line
  • Types of fractions: proper fractions, improper fractions, and mixed fractions
  • Equivalent fractions
  • Expressing fractions in the simplest form
  • Like fractions and how to compare them
  • Addition and subtraction of fractions
3. How many exercise are solved in NCERT Solutions for Class 6 Maths Chapter 7 Fractions

A total of 6 exercise are discussed in the chapter 7 maths class 6. After practicing these exercises, Students get command on the concepts which ultimately lead to confidence during the exam and finaly able to score well in the exam.

4. How are fractions defined in Chapter 7 of Class 6 Maths NCERT Solutions?

Fractions, in Chapter 7 of Class 6 Maths NCERT Solutions, are defined as parts of a whole number. They are expressed as a ratio between two integers, one written above the other and separated by a line. The number above the line is called the numerator, and the number below the line is called the denominator.

5. Can I get the NCERT Solutions for Class 6 Maths Chapter 7 in PDF format?

Yes, you can download the NCERT Solutions for Class 6 Maths Chapter 7 in PDF format from Careers360. These solutions have been prepared by highly experienced faculty, following the latest CBSE board syllabus. You can use the PDF to cross-check your answers and understand different methods of solving complex problems with ease.

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0.34\; J

Option 2)

0.16\; J

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1.00\; J

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0.67\; J

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Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

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2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

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K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

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Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

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2.5 × 10-2

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Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

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be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

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Molality

Option 2)

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Fraction of solute present in water

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Mole fraction.

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Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

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more than 6 but less than 9

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Data Administrator

Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.

4 Jobs Available
Ethical Hacker

A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.

3 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
Geothermal Engineer

Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.

3 Jobs Available
Remote Sensing Technician

Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive. 

Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.

3 Jobs Available
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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