If p = -4/9 q = 2/3 and r = -8/11 , then verify the following :
• p× ( q+ r) = p× q + p× r
• p× q = q×p
Answers
Answer:
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Concept
The commutative property is concerned with how certain mathematical operations are performed in sequence. It can be written as a + b = b + a for a binary operation. An expression of the form A (B + C) can be solved as A (B + C) = AB + AC according to the distributive property. The formula for this distributive property, which also holds true for subtraction, is A (B - C) = AB - AC. The distribution of operand A among the other two operands is indicated by this.
Given
p = ₋4/9
q = 2/3
r = ₋8/11
Find
we are asked to verify the following expression.
- p × (q ₊ r) = p × q ₊ p × r
- p × q = q × p
Solution
p × (q ₊ r) = p × q ₊ p × r represents the distributive property.
L.H.S = p × (q ₊ r)
∴ p × (q ₊ r) = ₋ 4/9 × [(2/3) ₊ (₋8/11)]
= ₋ 4/9 × [2/3 ₋ 8/11]
= ₋ 4/9 × [22 ₋ 24/33]
= ₋ 4/9 × [₋2/33]
= 8/297
R.H.S = p × q ₊ p × r
= ₋ 4/9 × 2/3 ₊ [₋ 4/9 × ₋8/11]
= ₋ 4/9 × 2/3 ₋ [4/9 × ₋8/11]
= ₋ 4/9 [2/3 ₋ 8/11]
= ₋ 4/9 × [22 ₋ 24/33]
= 8/297
∴ L.H.S = R.H.S
hence proved p × (q ₊ r) = p × q ₊ p × r
p × q = q × p represents commutative property.
L.H.S = p × q
p × q = ₋ 4/9 × 2/3
= ₋8/27
R.H.S = q × p
q × p = 2/3 × ₋ 4/9
= ₋8/27
∴ L.H.S = R.H.S
hence proved p × q = q × p
The property rules so confirm the given expressions.
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