# USING PROPERTIES WITH RATIONAL NUMBERS

Example 1 :

Verify the distributive property a(b + c) = ab + ac for the rational numbers a = ⁻¹⁄₂, b =  and c = ⁻⁵⁄₆.

Solution :

For a = ⁻¹⁄₂, b =  and c = ⁻⁵⁄₆

a(b + c) :

ab + ac :

From (1) and (2),

a(b + c) = ab + bc

Example 2 :

Verify the commutative property of addition a + b = b + a for the rational numbers a = ¾ and b = .

Solution :

For a = ¾ and b = ,

a + b :

b + a :

From (1) and (2),

a + b = b + a

Example 3 :

Verify the a + (b + c) = (a + b) + c for the rational numbers a = ¼, b = ¾ and c = ⁵⁄₄.

Solution :

For a = ¾ and b = ,

a + (b + c) :

(a + b) + c :

## Evaluating Expressions with Rational Numbers

Example 4 :

Evaluate :

Solution :

Example 5 :

Evaluate :

Solution :

Least common multiple of (18, 9, 6) = 18.

So, make each denominator as 18, multiplying by appropriate numbers.

Example 6 :

Evaluate :

Solution :

Least common multiple of (8, 32, 20) = 160.

So, make each denominator as 160, multiplying by appropriate numbers.

Example 7 :

Evaluate :

Solution :

Least common multiple of (10, 32, 20) = 160.

So, make each denominator as 160, multiplying by appropriate numbers.

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