Simplify 2/3*|-5/8-1/4|

Problem

2/3⋅|−5/8−1/4|

Solution

1. Find a common denominator for the fractions inside the absolute value bars. The least common multiple of 8 and 4 is 8

1/4=2/8

2. Subtract the fractions inside the absolute value.

−5/8−2/8=−7/8

3. Apply the absolute value by taking the non-negative version of the result.

|−7/8|=7/8

4. Multiply the remaining fraction by the constant outside the absolute value.

2/3⋅7/8=14/24

5. Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2

14/24=7/12

Final Answer

2/3⋅|−5/8−1/4|=7/12

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