Rational Numbers MCQ Test — Class 8 ICSE

Solution:

A rational number is any number that can be written as a fraction p/q, where p and q are integers and q ≠ 0.

3/7 is already in the form p/q with p = 3, q = 7.

√2, √5, and π are irrational numbers — they cannot be expressed as fractions.

Solution:

The additive inverse of a number a is -a, because a + (-a) = 0.

Additive inverse of -5/8: — -(-5/8) = 5/8

Check: — -5/8 + 5/8 = 0 ✓

Solution:

The multiplicative inverse of a number is the number that when multiplied gives 1.

Reciprocal of 3/4: — 4/3

Check: — 3/4 × 4/3 = 12/12 = 1 ✓

Solution:

Same denominator, so add the numerators: — 2/5 + 3/5 = (2+3)/5 = 5/5

Simplify: — 5/5 = 1

Solution:

The additive inverse property states: a + (-a) = 0 for every rational number a.

Here: — 3/7 + (-3/7) = 0

This shows that -3/7 is the additive inverse of 3/7.

Solution:

For any rational number a: — a + 0 = a

Since adding 0 leaves the number unchanged, 0 is called the additive identity.

Solution:

Multiply numerators: — (-2) × 5 = -10

Multiply denominators: — 3 × 7 = 21

Result: — (-2/3) × (5/7) = -10/21

Solution:

The commutative property of multiplication states: — a × b = b × a

The order of the numbers can be swapped without changing the result.

Solution:

Same denominator: — 7/12 - 3/12 = (7-3)/12 = 4/12

Simplify by dividing numerator and denominator by 4: — 4/12 = 1/3

Solution:

For any rational number a: — a × 1 = a

Since multiplying by 1 leaves any number unchanged, 1 is the multiplicative identity.