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{(1/3)−3−(1/2)−3} ÷ (1/4)−3 ?
- a)19/64
- b)64/19
- c)27/16
- d)16/27
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
{(1/3)−3−(1/2)−3} ÷ (1/4)−3?a)19/64b)64...
{(1/3)−3−(1/2)−3} ÷ (1/4)−3 = {(3)3−(2)3} ÷ (4)3 = {27−8} ÷ 64 = 19/64
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{(1/3)−3−(1/2)−3} ÷ (1/4)−3?a)19/64b)64...
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{(1/3)−3−(1/2)−3} ÷ (1/4)−3?a)19/64b)64...
To evaluate this expression, we need to follow the order of operations (PEMDAS):
1. Evaluate expressions inside parentheses:
{(1/3) - 3 - (1/2) - 3} + (1/4) - 3
= (-3 - 3 - 1/2 + 1/3) + 1/4 - 3
= (-6 - 1/2 + 1/3) + 1/4 - 3
2. Find common denominators and combine fractions:
= (-6 - 3/6 + 2/6) + 1/4 - 3
= (-6 - 1/6) + 1/4 - 3
= (-6 - 1/6) + 3/12 - 3
= (-6 - 2/12) + 3/12 - 3
= -6 - 2/12 + 3/12 - 3
= -9 - 1/12 + 1/4
= -9 - 1/12 + 3/12
= -9 - 2/12 + 3/12
= -9 + 1/12
3. Simplify:
= -9 + 1/12
= -108/12 + 1/12
= -107/12
So, {(1/3) - 3 - (1/2) - 3} + (1/4) - 3 = -107/12.
1. Evaluate expressions inside parentheses:
{(1/3) - 3 - (1/2) - 3} + (1/4) - 3
= (-3 - 3 - 1/2 + 1/3) + 1/4 - 3
= (-6 - 1/2 + 1/3) + 1/4 - 3
2. Find common denominators and combine fractions:
= (-6 - 3/6 + 2/6) + 1/4 - 3
= (-6 - 1/6) + 1/4 - 3
= (-6 - 1/6) + 3/12 - 3
= (-6 - 2/12) + 3/12 - 3
= -6 - 2/12 + 3/12 - 3
= -9 - 1/12 + 1/4
= -9 - 1/12 + 3/12
= -9 - 2/12 + 3/12
= -9 + 1/12
3. Simplify:
= -9 + 1/12
= -108/12 + 1/12
= -107/12
So, {(1/3) - 3 - (1/2) - 3} + (1/4) - 3 = -107/12.
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{(1/3)−3−(1/2)−3} ÷ (1/4)−3?a)19/64b)64/19c)27/16d)16/27Correct answer is option 'A'. Can you explain this answer?
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