Example 1 :
Verify the distributive property a(b + c) = ab + ac for the rational numbers a = ⁻¹⁄₂, b = ⅔ and c = ⁻⁵⁄₆.
Solution :
For a = ⁻¹⁄₂, b = ⅔ 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 = ⅝.
Solution :
For a = ¾ and b = ⅝,
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 = ⅝,
a + (b + c) :
(a + b) + c :
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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