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

What is the value of the following expression?

\frac{3}{4} + \frac{1}{2} \div \frac{2}{3} - \frac{1}{8}

The correct answer is

1 \frac{3}{8}

The correct answer is found by first performing the division operation (which becomes

3/4

), then finding a common denominator (8) to add and subtract the remaining fractions. This yields

11/8

, which simplifies to

1 \frac{3}{8}

Evaluate the division portion of the expression first according to the order of operations.

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

The order of operations requires division to be performed before addition or subtraction.

Substitute the division result back into the original expression.

\frac{3}{4} + \frac{3}{4} - \frac{1}{8}

This updates the expression to contain only addition and subtraction operations.

Find the least common multiple (LCM) for the denominators to perform addition and subtraction.

The LCM of 4 and 8 is 8. Converting the fractions yields

\frac{6}{8} + \frac{6}{8} - \frac{1}{8}

Fractions must have a common denominator to be added or subtracted.

Perform the addition and subtraction sequentially from left to right.

\frac{6}{8} + \frac{6}{8} - \frac{1}{8} = \frac{12}{8} - \frac{1}{8} = \frac{11}{8}

Addition and subtraction carry the same precedence and are evaluated from left to right.

Convert the resulting improper fraction into a mixed number.

\frac{11}{8} = 1 \frac{3}{8}

The answer choices are presented as mixed numbers, requiring the improper fraction to be converted.

Applying the order of operations (PEMDAS) to compound fraction arithmetic.

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