Evaluate the following mathematical expression: \frac{7}{8} - \frac{2}{3} \times 1\frac{1}… — Armed Services Vocational Aptitude Battery (ASVAB)

Evaluate the following mathematical expression:

\frac{7}{8} - \frac{2}{3} \times 1\frac{1}{4}

Which of the following is the correct result?

The correct result is

\frac{1}{24}

The correct answer is found by first performing the multiplication (resulting in

\frac{5}{6}

) and then subtracting this from

\frac{7}{8}

using a common denominator of 24.

Convert the mixed number to an improper fraction.

1\frac{1}{4} = \frac{5}{4}

Fractions must be in proper or improper form before multiplying.

Multiply the fractions according to the order of operations (PEMDAS).

\frac{2}{3} \times \frac{5}{4} = \frac{10}{12}

Multiplication must be performed before subtraction in mathematical expressions.

Simplify the resulting fraction.

\frac{10}{12} = \frac{5}{6}

Simplifying makes finding a common denominator easier in the next step.

Find a common denominator and subtract the fractions.

\frac{7}{8} - \frac{5}{6} = \frac{21}{24} - \frac{20}{24} = \frac{1}{24}

Fractions require a common denominator before they can be added or subtracted.

Order of Operations with Fractions

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