A Navy Seabee is framing a new barracks and starts with a wooden board that is 16 \frac{3}… — Armed Services Vocational Aptitude Battery (ASVAB)

A Navy Seabee is framing a new barracks and starts with a wooden board that is $16 \frac{3}{8}$ feet long. For the first section of the frame, a piece measuring $4 \frac{3}{4}$ feet is cut from the board. For the second section, another piece measuring $5 \frac{5}{6}$ feet is cut. Assuming there is no waste from the saw cuts, what is the remaining length of the wooden board?

A
$6 \frac{23}{40}$
$5 \frac{19}{24}$ Answer
C
$10 \frac{7}{12}$
D
$6 \frac{5}{24}$

Answer

The remaining length of the wooden board is

5 \frac{19}{24}

feet.

To find the remaining length, the lengths of the two cut pieces must first be added together. Finding a common denominator of 24, the cuts are

4 \frac{18}{24}

and

5 \frac{20}{24}

. Their sum is

9 \frac{38}{24}

, which regroups to

10 \frac{14}{24}

. Next, subtract this total from the original board length:

16 \frac{9}{24} - 10 \frac{14}{24}

. Since

\frac{9}{24}

is smaller than

\frac{14}{24}

, borrowing from the whole number is required:

15 \frac{33}{24} - 10 \frac{14}{24} = 5 \frac{19}{24}

Step-by-Step Solution

Calculate the total length of the wooden board that was cut off.

4 \frac{3}{4} + 5 \frac{5}{6} = 4 \frac{18}{24} + 5 \frac{20}{24} = 9 \frac{38}{24} = 10 \frac{14}{24}

feet.

Adding the removed sections determines the total amount to subtract from the original board.

Set up the subtraction of the total cut length from the original length.

16 \frac{3}{8} - 10 \frac{14}{24} = 16 \frac{9}{24} - 10 \frac{14}{24}

A common denominator is needed to subtract the fractions.

Borrow from the whole number to subtract the fractions.

15 \frac{33}{24} - 10 \frac{14}{24} = 5 \frac{19}{24}

feet.

Since

\frac{9}{24}

is less than

\frac{14}{24}

, borrowing

1

(or

\frac{24}{24}

) from the whole number

16

makes the subtraction possible.

Key Concept

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

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