A combat engineer is preparing a concrete mixture for a runway repair. The project require… — Armed Services Vocational Aptitude Battery (ASVAB)

A combat engineer is preparing a concrete mixture for a runway repair. The project requires a total of $18 \frac{1}{4}$ cubic feet of sand. The engineer has two available piles of sand: one containing $7 \frac{4}{5}$ cubic feet and another containing $5 \frac{1}{2}$ cubic feet. If both piles are combined, how many more cubic feet of sand are needed to meet the total requirement?

A
$5 \frac{15}{28}$
B
$5 \frac{1}{20}$
$4 \frac{19}{20}$ Answer
D
$5 \frac{19}{20}$

Answer

The correct amount of additional sand needed is

4 \frac{19}{20}

cubic feet.

The correct calculation requires first summing the available resources (

7 \frac{4}{5} + 5 \frac{1}{2} = 13 \frac{3}{10}

) and then subtracting this from the target amount (

18 \frac{1}{4} - 13 \frac{3}{10}

). Converting to a common denominator of

20

and regrouping the whole number correctly yields exactly

4 \frac{19}{20}

Step-by-Step Solution

Calculate the total volume of available sand by adding the two piles together.

7 \frac{4}{5} + 5 \frac{1}{2} = 7 \frac{8}{10} + 5 \frac{5}{10} = 12 \frac{13}{10}

. Since

\frac{13}{10}

is an improper fraction (

1 \frac{3}{10}

), this simplifies to

13 \frac{3}{10}

cubic feet.

You must first determine how much sand is already on hand before calculating the remaining amount needed.

Find a common denominator to subtract the available sand from the total required sand.

The least common denominator for

4

and

10

20

. Convert the fractions:

18 \frac{1}{4}

becomes

18 \frac{5}{20}

, and

13 \frac{3}{10}

becomes

13 \frac{6}{20}

Fractions must have equivalent denominators before they can be added or subtracted.

Subtract the available sand from the required total by regrouping (borrowing).

Subtract

13 \frac{6}{20}

from

18 \frac{5}{20}

. Since

5

is less than

6

, borrow

1

from the whole number

18

to get

17 \frac{25}{20}

. Then,

17 \frac{25}{20} - 13 \frac{6}{20} = 4 \frac{19}{20}

cubic feet.

Regrouping is necessary when the fraction being subtracted is larger than the fraction it is being subtracted from.

Key Concept

Adding and subtracting mixed numbers with unlike denominators, including regrouping (borrowing).

Question

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Key Concept

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