A storage warehouse is currently filled to \frac{1}{4} of its total capacity. A new shipme… — Armed Services Vocational Aptitude Battery (ASVAB)

A storage warehouse is currently filled to $\frac{1}{4}$ of its total capacity. A new shipment arrives and is stored, bringing the warehouse to $\frac{5}{6}$ of its total capacity. What fraction of the warehouse's capacity was filled by the new shipment?

$\frac{7}{12}$ Answer
B
$\frac{3}{5}$
C
$\frac{2}{3}$
D
$\frac{1}{6}$

Answer

The new shipment filled

\frac{7}{12}

of the warehouse's capacity.

To find the amount of capacity added, subtract the initial capacity from the final capacity (

\frac{5}{6} - \frac{1}{4}

). Convert both fractions to a common denominator of 12, resulting in

\frac{10}{12}

and

\frac{3}{12}

. Subtracting these fractions gives

\frac{7}{12}

Step-by-Step Solution

Set up the subtraction expression to find the difference in capacity.

\frac{5}{6} - \frac{1}{4}

The fraction added is equal to the final capacity minus the initial capacity.

Find the lowest common denominator (LCD) for the fractions with denominators 6 and 4.

The LCD is 12.

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

Convert both fractions to equivalent fractions with a denominator of 12.

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

and

\frac{1}{4} = \frac{3}{12}

This standardizes the parts so they can be accurately subtracted.

Subtract the numerators and keep the common denominator.

\frac{10}{12} - \frac{3}{12} = \frac{7}{12}

The numerators represent the specific number of parts being subtracted from the whole.

Key Concept

Fraction Addition and Subtraction in Context

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