CBSE Class 8 Mathematics Rational Numbers Assignment Set 03

Rational Numbers

Question : 1 Find the reciprocal of -2.

Question : 2 The sum of two numbers is 5\9. If one of the numbers is 1\3, find the other.

Question : 3 Write the additive inverse of 2\3 and show that their sum is zero.

Question : 4 Simplify 7\6 x -3\28 and find its reciprocal.

Question : 5 The product of two rational numbers is 15. If one of the numbers is –10, find the other.

Question : 6 Write any three rational numbers between –5 and 0.

Question : 7 True of False: 1 is the only rational number that is equal to its reciprocal.

Multiply:

Question. \( \frac{7}{11} \) by \( \frac{5}{4} \)
Answer: \( \frac{35}{44} \)

Question. \( \frac{5}{7} \) by \( \frac{-3}{4} \)
Answer: \( -\frac{15}{28} \)

Question. \( \frac{-2}{9} \) by \( \frac{5}{11} \)
Answer: \( -\frac{10}{99} \)

Question. \( \frac{-3}{17} \) by \( \frac{-5}{-4} \)
Answer: \( -\frac{15}{68} \)

Question. \( \frac{9}{-7} \) by \( \frac{36}{-11} \)
Answer: \( \frac{324}{77} \)

Question. \( \frac{-11}{13} \) by \( \frac{-21}{7} \)
Answer: \( \frac{33}{13} \)

Question. \( \frac{3}{-5} \) by \( -\frac{4}{7} \)
Answer: \( \frac{12}{35} \)

Question. \( \frac{15}{-11} \) by 7
Answer: \( -\frac{105}{11} \)

Multiply:

Question. \( \frac{-5}{17} \) by \( \frac{51}{-60} \)
Answer: \( \frac{1}{4} \)

Question. \( \frac{-6}{11} \) by \( \frac{-55}{36} \)
Answer: \( \frac{5}{6} \)

Question. \( \frac{-8}{25} \) by \( \frac{-5}{16} \)
Answer: \( \frac{1}{10} \)

Question. \( \frac{6}{7} \) by \( \frac{-49}{36} \)
Answer: \( -\frac{7}{6} \)

Question. \( \frac{8}{-9} \) by \( \frac{-7}{-16} \)
Answer: \( -\frac{7}{18} \)

Question. \( \frac{-8}{9} \) by \( \frac{3}{64} \)
Answer: \( -\frac{1}{24} \)

Simplify each of the following and express the result as a rational number in standard form:

Question. \( \frac{-16}{21} \times \frac{14}{5} \)
Answer: \( -\frac{32}{15} \)

Question. \( \frac{7}{6} \times \frac{-3}{28} \)
Answer: \( -\frac{1}{8} \)

Question. \( \frac{-19}{36} \times 16 \)
Answer: \( -\frac{76}{9} \)

Question. \( \frac{-13}{9} \times \frac{27}{-26} \)
Answer: \( \frac{3}{2} \)

Question. \( \frac{-9}{16} \times \frac{-64}{-27} \)
Answer: \( -\frac{4}{3} \)

Question. \( \frac{-50}{7} \times \frac{14}{3} \)
Answer: \( -\frac{100}{3} \)

Question. \( \frac{-11}{9} \times \frac{-81}{-88} \)
Answer: \( -\frac{9}{8} \)

Question. \( \frac{-5}{9} \times \frac{72}{-25} \)
Answer: \( \frac{8}{5} \)

Simplify:

Question. \( \left( \frac{25}{8} \times \frac{2}{5} \right) - \left( \frac{3}{5} \times \frac{-10}{9} \right) \)
Answer: \( \frac{5}{4} - \left( -\frac{2}{3} \right) = \frac{5}{4} + \frac{2}{3} = \frac{15+8}{12} = \frac{23}{12} \)

Question. \( \left( \frac{1}{2} \times \frac{1}{4} \right) + \left( \frac{1}{2} \times 6 \right) \)
Answer: \( \frac{1}{8} + 3 = \frac{25}{8} \)

Question. \( \left( -5 \times \frac{2}{15} \right) - \left( -6 \times \frac{2}{9} \right) \)
Answer: \( -\frac{2}{3} - \left( -\frac{4}{3} \right) = \frac{2}{3} \)

Question. \( \left( \frac{-9}{4} \times \frac{5}{3} \right) + \left( \frac{13}{2} \times \frac{5}{6} \right) \)
Answer: \( -\frac{15}{4} + \frac{65}{12} = \frac{-45+65}{12} = \frac{20}{12} = \frac{5}{3} \)

Question. \( \left( \frac{-4}{3} \times \frac{12}{-5} \right) + \left( \frac{3}{7} \times \frac{21}{15} \right) \)
Answer: \( \frac{16}{5} + \frac{3}{5} = \frac{19}{5} \)

Question. \( \left( \frac{13}{5} \times \frac{8}{3} \right) - \left( \frac{-5}{2} \times \frac{11}{3} \right) \)
Answer: \( \frac{104}{15} - \left( -\frac{55}{6} \right) = \frac{104}{15} + \frac{55}{6} = \frac{208+275}{30} = \frac{483}{30} = \frac{161}{10} \)

Question. \( \left( \frac{13}{7} \times \frac{11}{26} \right) - \left( \frac{-4}{3} \times \frac{5}{6} \right) \)
Answer: \( \frac{11}{14} - \left( -\frac{10}{9} \right) = \frac{11}{14} + \frac{10}{9} = \frac{99+140}{126} = \frac{239}{126} \)

Question. \( \left( \frac{8}{5} \times \frac{-3}{2} \right) + \left( \frac{-3}{10} \times \frac{11}{16} \right) \)
Answer: \( -\frac{12}{5} + \left( -\frac{33}{160} \right) = \frac{-384-33}{160} = -\frac{417}{160} \)

EXERCISE # 2

Give examples of:

Question. The rational number that does not have a reciprocal.
Answer: 0

Question. The rational numbers that are equal to their reciprocals.
Answer: 1 and – 1

Question. The rational number that is equal to its negative.
Answer: 0

Fill in the blanks.

Question. Zero has ______ reciprocal.
Answer: No

Question. The numbers______ and _____ are their own reciprocals.
Answer: 1, – 1

Question. The reciprocal of – 5 is _______.
Answer: \( -\frac{1}{5} \)

Question. Reciprocal of \( \frac{1}{x} \), where x ≠ 0 is______.
Answer: x

Question. The product of two rational numbers is always a______.
Answer: Rational Number

Question. The reciprocal of a positive rational number is ________.
Answer: positive

Question. Represent \( \frac{7}{4} \) and \( \frac{-5}{6} \) on the number line.
Answer: Refer to diagram in key.

Question. Represent \( \frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11} \) on the number line.
Answer: Refer to diagram in key.

Question. Write five rational numbers which are smaller than 2.
Answer: Some of these are 1, \( \frac{1}{2} \), 0, –1, \( -\frac{1}{2} \)

Question. Find ten rational numbers between \( \frac{-2}{5} \) and \( \frac{1}{2} \).
Answer: \( -\frac{7}{20}, -\frac{6}{20}, -\frac{5}{20}, -\frac{4}{20}, -\frac{3}{20}, -\frac{2}{20}, -\frac{1}{20}, 0, ..., \frac{1}{20}, \frac{2}{20} \)

Click on link below to download CBSE Class 8 Mathematics Rational Numbers Assignment Set C