A fuel tank is initially \frac{1}{4} full. A driver adds fuel until the tank is exactly \f… — Armed Services Vocational Aptitude Battery (ASVAB)

A fuel tank is initially $\frac{1}{4}$ full. A driver adds fuel until the tank is exactly $\frac{2}{3}$ full. What fraction of the tank's total capacity was added?

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

Answer

\frac{5}{12}

To find out how much fuel was added, you must subtract the initial amount (

\frac{1}{4}

) from the final amount (

\frac{2}{3}

). Since the denominators

3

and

4

are different, you first find the lowest common denominator, which is

12

. Converting the fractions gives

\frac{8}{12}

and

\frac{3}{12}

. Subtracting

\frac{3}{12}

from

\frac{8}{12}

results in the correct answer of

\frac{5}{12}

Step-by-Step Solution

Set up a subtraction equation to find the difference between the final amount and the initial amount.

\frac{2}{3} - \frac{1}{4}

The fuel added is the difference between the ending capacity and the starting capacity.

Find a common denominator for

3

and

4

12

Fractions must have the same denominator before they can be added or subtracted.

Convert both fractions to have the common denominator of

12

and subtract.

\frac{8}{12} - \frac{3}{12} = \frac{5}{12}

\frac{2}{3} = \frac{8}{12}

and \frac{1}{4} = \frac{3}{12}$. Subtracting the numerators yields the final answer.

Key Concept

Subtracting fractions with unlike denominators in a real-world context.

Estimated Time:1m 0s

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