Class 8 Rational Numbers — practice questions with answers

Rational Numbers · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Which property is illustrated:

\frac{1}{3}

\frac{2}{5}

\frac{2}{5}

\frac{1}{3}

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Answer: A) Commutative addition

Order of two added numbers swapped — that's commutativity for addition.

2. Between any two distinct rational numbers, how many rational numbers lie?

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Answer: A) Infinitely many

By the density property, between any two distinct rationals there are infinitely many rationals.

3. Compute

\frac{4}{5} \times (\frac{3}{8} - \frac{1}{4})

using the distributive idea.

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Answer: A)

\frac{1}{10}

Inside:

\frac{3}{8} - \frac{1}{4} = \frac{3}{8} - \frac{2}{8} = \frac{1}{8}

. Then

\frac{4}{5} \times \frac{1}{8} = \frac{4}{40} = \frac{1}{10}

4. How many rational numbers with denominator 63 lie strictly between

\frac{2}{7}

and

\frac{3}{7}

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Answer: A) 8

\frac{2}{7} = \frac{18}{63}

and

\frac{3}{7} = \frac{27}{63}

. The numerators strictly between 18 and 27 are 19, 20, …, 26, which is

26 - 19 + 1 = 8

numbers. The trap is computing

27 - 18 = 9

, which quietly counts one of the endpoints.

5. Find a rational number lying between

- \frac{3}{4}

and

- \frac{2}{3}

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Answer: C)

- \frac{17}{24}

Average the two:

\frac{1}{2} (- \frac{3}{4} + (- \frac{2}{3})) = \frac{1}{2} (- \frac{9}{12} - \frac{8}{12}) = \frac{1}{2} \times (- \frac{17}{12}) = - \frac{17}{24}

, and −0.708 does sit between −0.75 and −0.667. ✓ Traps:

- \frac{17}{12}

skips the halving and lands outside, while

- \frac{1}{24}

comes from subtracting the two fractions instead of adding them.

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