Class 8 Properties of Rational Numbers — practice questions with answers

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

1. Which number is the additive identity for rational numbers?

Show answer

Answer: A) 0

Adding 0 to any rational number leaves it unchanged: a + 0 = a. So 0 is the additive identity.

2. Find the sum of

\frac{3}{4}

and its additive inverse.

Show answer

Answer: D) 0

The additive inverse of

\frac{3}{4}

- \frac{3}{4}

, and

\frac{3}{4} + (- \frac{3}{4}) = 0

3. What number must you add to

\frac{5}{6}

to get the additive identity?

Show answer

Answer: A)

- \frac{5}{6}

The additive identity is 0, and

\frac{5}{6} + (- \frac{5}{6}) = 0

, so you must add

- \frac{5}{6}

4. Dev claims division is associative because

(12 \div 4) \div 1 = 12 \div (4 \div 1)

.
Test with a = 16, b = 4, c = 2 instead. Which conclusion is correct?

Show answer

Answer: A) False:

(16 \div 4) \div 2 = 2

but

16 \div (4 \div 2) = 8

(16 \div 4) \div 2 = 4 \div 2 = 2

, while

16 \div (4 \div 2) = 16 \div 2 = 8

. Since 2 is not 8, division is not associative.

5. A rational number x equals its own reciprocal, and x is also a rational number (

x = \frac{1}{x}

).
How many such rational numbers exist, and what are they?

Show answer

Answer: A) Two: 1 and -1

x = 1/x gives x² = 1, so x = 1 or x = -1. Both are rational, so there are exactly two such numbers.

10 free questions a day without an account — unlimited with a free account.