Q.1 Using appropriate properties find.

  (i)\:\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}

Q.1  Using appropriate properties find.

          (ii)\frac{2}{5}\times \frac{-3}{7}- \frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}

 Write the additive inverse of each of the following:

(i) \frac{2}{8}                           (ii)\frac{-5}{9}                    (iii) \frac{-6}{-5}               (iv) \frac{2}{-9}              (v)\frac{19}{-6}              

3.  Verify that – (– x) = x for 

      (i) x = \frac{11}{15}          (ii) x = \frac{-13}{17}

4. Find the multiplicative inverse of the following.

    (i)  - 13               (ii) \frac{-13}{19}           (iii) \frac{1}{5}            (iv) \frac{-5}{8}\times \frac{-3}{7}          (v)  -1\times \frac{-2}{5}         (vi)  - 1

Q5. Name the property under multiplication used in each of the following.

    (i) \frac{-4}{5}\times 1= 1\times \frac{-4}{5} = \frac{-4}{5}            (ii) -\frac{13}{17}\times \frac{-2}{7} = \frac{-2}{7}\times \frac{-13}{17}       (iii) \frac{-19}{29}\times \frac{29}{-19} = 1

Q6. Multiply  \frac{6}{13}  by the reciprocal of  \frac{-7}{16} .

Q7. Tell what property allows you to compute  \frac{1}{3}\times \left ( 6\times \frac{4}{3} \right )  as \left ( \frac{1}{3}\times 6 \right )\times \frac{4}{3}.

8. Is  \frac{8}{9}  the multiplicative inverse of -1\frac{1}{8} ? Why or why not?

9. Is 0.3 the multiplicative inverse of  3\frac{1}{3} ? Why or why not?

Q10.Write.

(i) The rational number that does not have a reciprocal.

(ii) The rational numbers that are equal to their reciprocals.

(iii) The rational number that is equal to its negative.

Q11. Fill in the blanks.

(i) Zero has ________ reciprocal.

(ii) The numbers ________ and ________ are their own reciprocals.

(iii) The reciprocal of – 5 is ________.

(iv) Reciprocal of  \frac{1}{x} , where x ≠ 0 is ________.

(v) The product of two rational numbers is always a _______.

(vi) The reciprocal of a positive rational number is ________.

1. Represent these numbers on the number line.   (i) \frac{7}{4}         (ii) \frac{-5}{6}

Q2. Represent  \frac{-2}{11},\frac{-5}{11},\frac{-9}{11}  on the number line.

Q3. Write five rational numbers which are smaller than 2.

4. Find ten rational numbers between  \frac{-2}{5} and \frac{1}{2} .

5. Find five rational numbers between.

(i)  \frac{2}{3}  and  \frac{4}{5}              (ii)  \frac{-3}{2} and  \frac{5}{3}             (iii)  \frac{1}{4} and  \frac{1}{2}

6. Write five rational numbers greater than –2.

7. Find ten rational numbers between  \frac{3}{5} and \frac{3}{4}.

Fill in the blanks in the following table.

  Addition Substraction Multiplication Division
Rational Numbers Yes Yes ... No
Integers ... Yes ... No
Whole Numbers ... ... Yes ...
Natural Numbers ... No ... ...

 

Complete the following table:

Commutative for
  Addition Subtraction multiplication division
Rational Numbers Yes ... ... ...
Integers ... No ... ...
Whole numbers ... ... Yes ...
Natural numbers ... ... ... No

 

Complete the following table:

Associative for
  Addition Subtraction Multiplication Division
Rational Numbers ... ... ... No
Integers ... ... Yes ...
Whole Numbers Yes ... ... ...
Natural Numbers ... Yes ... ...

 

 

Find using distributivity:

(i) \left \{ \frac{7}{5}\times \left ( \frac{-3}{12} \right ) \right \}+\left \{ \frac{7}{5}\times \frac{5}{12} \right \}                  (ii) \left \{ \frac{9}{16}\times \frac{4}{12} \right \}+\left \{ \frac{9}{16}\times \frac{-3}{9} \right \}

Write the rational number for each point labelled with a letter:

 

Solve the following equations.

Q.1  x – 2 = 7                               

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