# Class 08 - Chapter 01 - Rational Numbers (20)

Posted in Class VIII

Rational Numbers
Class VIII
Chapter 01

Q.1. Using the appropriate properties find.

a) $$- \frac{3}{5} \times \frac{1}{5} - \frac{1}{5} \times \frac{4}{5}$$

b) $$\frac{2}{7} \times (- \frac{2}{11} ) - \frac{3}{5} \times \frac{2}{11} + \frac{1}{9} \times \frac{2}{5}$$

Q.2. Write the additive inverse of the each of the following.

a) $$\frac{2}{7}$$ b) $$\frac{-3}{11}$$ c) $$\frac{-7}{-11}$$ d) $$\frac{6}{-14}$$ e) $$\frac{19}{-3}$$

Q.3. Find the multiplicative inverse of the following.

a) -11 b) $$\frac{1}{3}$$ c) $$\frac{-11}{13}$$ d) $$\frac{-5}{7} \times \frac{7}{-11}$$ e) $$-1 \times \frac{12}{-15}$$

Q.4. Given below are the pairs of two rational numbers. Multiply the first number by the reciprocal of the second number in each pair.

a) $$\frac{2}{7}$$, $$\frac{11}{2}$$

b) $$\frac{7}{11}$$, $$\frac{-7}{9}$$

c) $$\frac{11}{12}$$, $$\frac{13}{-7}$$

d) $$\frac{13}{-19}$$, $$\frac{-21}{-33}$$

Q.5. Name the property under multiplication used in each of the following:

a) $$\frac{-2}{3} \times 2$$ = $$2 \times \frac{-2}{3}$$

b) $$-\frac{11}{15} \times \frac{-3}{5}$$ = $$\frac{-3}{5} \times \frac{11}{-15}$$

c) $$\frac{3}{5} \times \frac{5}{3}$$ = 1

d) $$\frac{7}{-9} \times \frac{11}{21}$$ = $$\frac{11}{21} \times \frac{7}{-9}$$

e) $$3 \times \frac{-9}{-43}$$ = $$\frac{9}{43} \times 3$$

Q.6. Find the additive inverse of the following:

a) $$\frac{2}{3} + \frac{1}{3}$$

b) $$2 \times \frac{3}{6}$$

c) $$0 \times \frac{5}{9} \times \frac{7}{11}$$

d) $$1 \times \frac{-2}{3}$$

e) $$1 \times \frac{4}{5} + 1 \times \frac{-4}{5}$$

Q.7. State whether the following statements are true or false.

a) The additive inverse of 1 is -1.

b) The reciprocal of $$\frac{2}{-3}$$ is $$\frac{2}{3}$$

c) A rational number when multiplied by its reciprocal results in 0.

d) A rational number when multiplied by its reciprocal results in 1.

e) The reciprocal of $$\frac{7}{2000}$$ is $$\frac{2000}{-7}$$.

f) The reciprocal of $$\frac{21}{100}$$ is $$4\frac{16}{100}$$

g) The multiplicative inverse of $$\frac{19}{21}$$

h) Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well.

i) 1 is the multiplicative identity for rational numbers.

Q.8. Fill in the blanks.

a) The product of two rational numbers is always ________________________.

b) The product of rational number and its multiplicative inverse is _____________.

c) The multiplicative inverse of 1 is ________.

d) The multiplicative inverse of 4 is ________.

Q.9. Find five (5) rational numbers between the following pairs.

a) $$\frac{1}{9}$$, $$\frac{8}{9}$$

b) $$\frac{11}{21}$$, $$\frac{17}{21}$$

c) $$\frac{1}{3}$$, $$\frac{2}{3}$$

d) $$\frac{13}{17}$$, $$\frac{15}{17}$$

Q.10. Find five (5) rational numbers between the following pairs.

a) $$\frac{1}{5}$$, $$\frac{1}{3}$$

b) $$\frac{2}{3}$$, $$\frac{4}{5}$$

c) $$\frac{7}{13}$$, $$\frac{15}{17}$$

d) $$\frac{5}{16}$$, $$\frac{3}{4}$$