Rational Numbers Quiz - ICSE Class 8 Mathematics

Free practice quiz: Rational Numbers (ICSE Class 8 Mathematics). 57 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 8 Mathematics practice quiz has 57 multiple-choice questions on Rational Numbers, and 57 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If $\frac{a}{b} = \frac{3}{5}$ and $\frac{b}{c} = \frac{10}{7}$, what is the value of $\frac{a}{c}$?

   1. $\frac{3}{7}$
   2. $\frac{6}{7}$
   3. $\frac{21}{50}$
   4. $\frac{7}{6}$
   Show answer

   Answer: B. $\frac{6}{7}$

   To find $\frac{a}{c}$, we can multiply the given ratios: $\frac{a}{c} = \frac{a}{b} \times \frac{b}{c} = \frac{3}{5} \times \frac{10}{7} = \frac{3 \times 10}{5 \times 7} = \frac{30}{35}$. Simplifying this fraction by dividing the numerator and denominator by their greatest common divisor, which is 5, we get $\frac{30 \div 5}{35 \div 5} = \frac{6}{7}$.

2. The sum of two rational numbers is $\frac{-7}{8}$. If one of the numbers is $\frac{1}{4}$, what is the other number?

   1. $\frac{-9}{8}$
   2. $\frac{-5}{8}$
   3. $\frac{-7}{32}$
   4. $\frac{-1}{8}$
   Show answer

   Answer: A. $\frac{-9}{8}$

   Let the other rational number be $x$. According to the problem, $\frac{1}{4} + x = \frac{-7}{8}$. To find $x$, we subtract $\frac{1}{4}$ from $\frac{-7}{8}$: $x = \frac{-7}{8} - \frac{1}{4}$. To perform the subtraction, we need a common denominator, which is 8. Convert $\frac{1}{4}$ to $\frac{2}{8}$: $x = \frac{-7}{8} - \frac{2}{8} = \frac{-7-2}{8} = \frac{-9}{8}$.

3. If $\frac{x}{y} = 2$ and $\frac{y}{z} = 3$, what is $\frac{x}{z}$?

   1. 6
   2. 5
   3. 3/2
   4. 2/3
   Show answer

   Answer: A. 6

   We are given $\frac{x}{y} = 2$ and $\frac{y}{z} = 3$. To find $\frac{x}{z}$, we can multiply these two ratios: $\frac{x}{z} = \frac{x}{y} \times \frac{y}{z} = 2 \times 3 = 6$.

4. What is the multiplicative inverse of $-\frac{2}{7}$?

   1. $\frac{2}{7}$
   2. $\frac{7}{2}$
   3. $-\frac{7}{2}$
   4. $\frac{-2}{7}$
   Show answer

   Answer: C. $-\frac{7}{2}$

   The multiplicative inverse (or reciprocal) of a rational number is the number that, when multiplied by the original number, results in 1. For a rational number $\frac{p}{q}$, its multiplicative inverse is $\frac{q}{p}$, provided $p \neq 0$ and $q \neq 0$. The multiplicative inverse of $-\frac{2}{7}$ is $\frac{7}{-2}$, which is equivalent to $-\frac{7}{2}$.

5. Simplify: $\frac{3}{5} \div \frac{6}{5}$

   1. $\frac{18}{25}$
   2. $\frac{1}{2}$
   3. 2
   4. $\frac{25}{18}$
   Show answer

   Answer: B. $\frac{1}{2}$

   To divide by a rational number, multiply by its reciprocal. The reciprocal of $\frac{6}{5}$ is $\frac{5}{6}$. So, $\frac{3}{5} \div \frac{6}{5} = \frac{3}{5} \times \frac{5}{6} = \frac{3 \times 5}{5 \times 6} = \frac{15}{30}$. Simplify this fraction by dividing the numerator and denominator by their greatest common divisor, which is 15: $\frac{15 \div 15}{30 \div 15} = \frac{1}{2}$.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the additive inverse of $\frac{-7}{12}$?
2. The product of two rational numbers is -18. If one of the numbers is $-\frac{5}{6}$, what is the other number?
3. Which of the following rational numbers is the largest?
4. Simplify: $\frac{1}{2} + \frac{1}{3} - \frac{1}{6}$
5. What is the reciprocal of $\frac{-4}{9}$?
6. If $x = \frac{2}{3}$ and $y = \frac{1}{4}$, what is the value of $x - y$?
7. Which rational number lies between $\frac{2}{5}$ and $\frac{3}{5}$?
8. Evaluate: $(\frac{-3}{4}) \times (\frac{8}{-5})$
9. What is the value of $\frac{-2}{3} \div \frac{4}{9}$?
10. If $\frac{x}{y} = \frac{5}{7}$ and $\frac{y}{z} = \frac{14}{3}$, find $\frac{x}{z}$.
11. Which of the following is equivalent to $\frac{-5}{-6}$?
12. Simplify: $\frac{2}{3} \times \frac{9}{4} \div \frac{3}{2}$
13. The average of four rational numbers is $\frac{5}{8}$. If three of the numbers are $\frac{1}{2}$, $\frac{3}{4}$, and $\frac{1}{8}$, what is the fourth number?
14. Find the rational number that should be multiplied by $-\frac{3}{5}$ to get $\frac{6}{7}$.
15. Which of the following statements is true for all rational numbers $a$ and $b$?
16. Simplify: $\frac{3}{8} + \frac{5}{12} - \frac{1}{4}$
17. If $x = \frac{-2}{5}$ and $y = \frac{3}{10}$, what is $x \times y$?
18. Which rational number is the smallest?
19. Calculate: $(\frac{1}{2} + \frac{1}{3}) \div (\frac{1}{4} - \frac{1}{6})$
20. Find the additive inverse of the sum of $\frac{3}{4}$ and $\frac{-5}{6}$.
21. Which of the following rational numbers has the smallest value?
22. Simplify: $(\frac{2}{5})^2 - (\frac{1}{2})^2$
23. What is the sum of the largest and smallest rational numbers among $\frac{3}{4}$, $\frac{1}{2}$, $\frac{5}{6}$, $\frac{2}{3}$?
24. Evaluate: $\frac{3}{5} \times (\frac{-10}{9} \div \frac{2}{3})$
25. What is the reciprocal of $\frac{1}{1}$?
26. Simplify: $\frac{-1}{3} + \frac{2}{5} - \frac{1}{2}$
27. If $\frac{a}{b} = \frac{1}{2}$ and $\frac{b}{c} = \frac{3}{4}$, what is $\frac{a}{c}$?
28. What is the value of $0.75$ as a rational number in its simplest form?
29. If a number is multiplied by itself, and the result is $\frac{9}{16}$, what is the number if it is positive?
30. The sum of two rational numbers is $-3$. If one of the numbers is $\frac{1}{2}$, what is the other number?
31. Which rational number is equivalent to $0.\overline{3}$?
32. Simplify: $\frac{1}{5} \times \frac{10}{3} \div \frac{2}{3}$
33. If $\frac{a}{b} = \frac{2}{3}$ and $\frac{b}{c} = \frac{5}{7}$, find $\frac{a}{c}$ in simplest form.
34. Calculate the product of $\frac{-3}{7}$ and $\frac{14}{9}$.
35. The sum of two rational numbers is $\frac{1}{6}$. If one number is $\frac{1}{3}$, what is the other number?
36. Which of the following is the additive inverse of $\frac{1}{3}$?
37. Evaluate: $(\frac{-2}{5}) \div (\frac{3}{10})$
38. Which rational number is the largest?
39. If $\frac{x}{y} = 5$ and $\frac{y}{z} = \frac{2}{3}$, what is $\frac{x}{z}$?
40. Find the rational number that should be added to $\frac{2}{3}$ to get $\frac{1}{2}$.
41. Which of the following is equivalent to $\frac{-1}{2}$?
42. The product of two rational numbers is $-\frac{3}{4}$. If one of the numbers is $-\frac{9}{10}$, what is the other number?
43. What is the value of $0.\overline{6}$ as a rational number in simplest form?
44. Which of the following is equal to $\frac{-1}{4}$?
45. What is the rational number that when multiplied by itself gives $\frac{16}{25}$ and is negative?
46. Simplify: $\frac{7}{8} - \frac{2}{3}$
47. If $\frac{a}{b} = \frac{3}{4}$ and $\frac{b}{c} = \frac{8}{9}$, find $\frac{a}{c}$.
48. What is the sum of $\frac{1}{2}$ and its additive inverse?
49. Which of the following is equivalent to $1\frac{3}{5}$?
50. Simplify: $\frac{-3}{4} + \frac{1}{2} - \frac{1}{8}$
51. If $\frac{a}{b} = \frac{5}{6}$ and $\frac{b}{c} = \frac{3}{10}$, what is $\frac{a}{c}$?
52. What is the value of $0.125$ as a rational number in simplest form?

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