Rational and Irrational Numbers (परिमेय आणि अपरिमेय संख्या) MCQ Test — Class 8 Maharashtra SSC

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 p/q form with p = 3 and q = 7.

√2, √5, and π are irrational numbers.

Solution:

The additive identity is the number that, when added to any number, gives the same number.

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

Solution:

The multiplicative identity is 1.

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

Solution:

The additive inverse of a/b is -a/b.

Additive inverse of 3/5: — -(3/5) = -3/5

Verification: — 3/5 + (-3/5) = 0 ✓

Solution:

The reciprocal of a/b is b/a.

Reciprocal of 2/7: — 7/2

Verification: — 2/7 × 7/2 = 14/14 = 1 ✓

Solution:

The commutative property of addition states that changing the order of addends does not change the sum.

For rational numbers a and b: — a + b = b + a

Solution:

Since denominators are equal: — 2/3 + 1/3 = (2+1)/3 = 3/3 = 1

Solution:

These are additive inverses of each other: — -4/9 + 4/9 = 0

Solution:

Zero is a rational number, but 1/0 is undefined.

So not every rational number has a multiplicative inverse.

All other properties (closure, commutative, associative) hold for multiplication.

Solution:

Write -3 as a fraction: — -3 = -3/1

Multiply numerator and denominator by 5: — -3/1 = (-3 × 5)/(1 × 5) = -15/5