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) \(\frac{5}{16}\), \(\frac{3}{4}\)