What is the value of the following expression? \frac{2}{3} - \frac{1}{4} \times 1\frac{1}{… — Armed Services Vocational Aptitude Battery (ASVAB)

What is the value of the following expression?

\frac{2}{3} - \frac{1}{4} \times 1\frac{1}{2} + \frac{5}{8}

The correct value of the expression is

\frac{11}{12}

The correct answer is found by rigorously applying the order of operations. The multiplication

\frac{1}{4} \times 1\frac{1}{2}

must be done first. After converting

1\frac{1}{2}

\frac{3}{2}

, the product is

\frac{3}{8}

. Substituting this back gives

\frac{2}{3} - \frac{3}{8} + \frac{5}{8}

. By combining the terms with eighths, we get

-\frac{3}{8} + \frac{5}{8} = \frac{2}{8}

, or

\frac{1}{4}

. Adding this to the initial term requires a common denominator of 12:

\frac{8}{12} + \frac{3}{12} = \frac{11}{12}

Convert the mixed number to an improper fraction.

1\frac{1}{2} = \frac{3}{2}

Fraction multiplication requires all terms to be expressed as proper or improper fractions.

Perform the multiplication operation.

\frac{1}{4} \times \frac{3}{2} = \frac{3}{8}

According to the order of operations (PEMDAS), multiplication must be performed before addition and subtraction.

Substitute the multiplication result back into the expression.

\frac{2}{3} - \frac{3}{8} + \frac{5}{8}

This updates the expression for the remaining addition and subtraction operations.

Combine the fractions that already share a common denominator.

-\frac{3}{8} + \frac{5}{8} = \frac{2}{8}

, which simplifies to

\frac{1}{4}

Grouping terms with the same denominator makes the calculation faster and simpler.

Find a common denominator for the remaining terms and add.

\frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}

Fractions must have a common denominator (in this case, 12) before their numerators can be added.

Order of Operations with Fractions

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