Bihar School Examination Board (BSEB) Class 8 Mathematics: Rational Numbers

Instructions. Answer all questions. Fill exactly one bubble per question on the OMR sheet.

1. Rational Numbers

   1.

   What is the additive inverse of $\frac{-7}{19}$?

   1. (A)

      $\frac{19}{7}$

   2. (B)

      $\frac{7}{19}$

   3. (C)

      $\frac{-19}{7}$

   4. (D)

      $0$

   Show answerHide answer

   Answer: (B)

   $\frac{7}{19}$

   The additive inverse of a rational number is the number that, when added to it, results in zero. For $\frac{-7}{19}$, the additive inverse is $\frac{7}{19}$ because $\frac{-7}{19} + \frac{7}{19} = 0$.

   Rational Numbers · Easy

2. 2.

   Which property is illustrated by the equation $\frac{2}{3} \times (\frac{1}{2} + \frac{3}{4}) = (\frac{2}{3} \times \frac{1}{2}) + (\frac{2}{3} \times \frac{3}{4})$?

   1. (A)

      Commutative property

   2. (B)

      Associative property

   3. (C)

      Identity property

   4. (D)

      Distributive property

   Show answerHide answer

   Answer: (D)

   Distributive property

   This equation demonstrates the distributive property of multiplication over addition, where a number outside the parenthesis is distributed to each term inside.

   Rational Numbers · Medium

3. 3.

   The product of two rational numbers is $\frac{-18}{5}$. If one of the numbers is $\frac{9}{10}$, what is the other number?

   1. (A)

      $-4$

   2. (B)

      $\frac{-81}{50}$

   3. (C)

      $\frac{4}{5}$

   4. (D)

      $\frac{-4}{5}$

   Show answerHide answer

   Answer: (A)

   $-4$

   Let the other number be $x$. Then $\frac{9}{10} \times x = \frac{-18}{5}$. Solving for $x$, we get $x = \frac{-18}{5} \times \frac{10}{9} = \frac{-2 \times 2}{1} = -4$.

   Rational Numbers · Medium

4. 4.

   Which of the following rational numbers lies between $\frac{1}{4}$ and $\frac{1}{2}$?

   1. (A)

      $\frac{1}{3}$

   2. (B)

      $\frac{5}{8}$

   3. (C)

      $\frac{3}{8}$

   4. (D)

      $\frac{1}{8}$

   Show answerHide answer

   Answer: (A)

   $\frac{1}{3}$

   To compare, convert to a common denominator. $\frac{1}{4} = \frac{2}{8}$ and $\frac{1}{2} = \frac{4}{8}$. Only $\frac{1}{3} \approx 0.333$ lies between $0.25$ and $0.5$. $\frac{1}{3} = \frac{8}{24}$ which is between $\frac{6}{24}$ and $\frac{12}{24}$.

   Rational Numbers · Hard

5. 5.

   What is the reciprocal of $(\frac{2}{3} \times \frac{6}{5})$?

   1. (A)

      $\frac{4}{5}$

   2. (B)

      $\frac{15}{12}$

   3. (C)

      $\frac{5}{4}$

   4. (D)

      $\frac{12}{15}$

   Show answerHide answer

   Answer: (C)

   $\frac{5}{4}$

   First, calculate the product: $\frac{2}{3} \times \frac{6}{5} = \frac{12}{15} = \frac{4}{5}$. The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$.

   Rational Numbers · Easy

— End of the paper · updated 14 October 2026 —