A parachute rigger is inspecting and cutting suspension line for parachute maintenance. Th… — Armed Services Vocational Aptitude Battery (ASVAB)

A parachute rigger is inspecting and cutting suspension line for parachute maintenance. They start with a spool containing $25 \frac{1}{4}$ yards of nylon cord. They use $8 \frac{2}{3}$ yards to repair a main canopy and $6 \frac{5}{6}$ yards to repair a reserve parachute. How many yards of nylon cord remain on the spool?

A
$15 \frac{1}{2}$
B
$14 \frac{7}{9}$
$9 \frac{3}{4}$ Answer
D
$10 \frac{1}{4}$

Answer

The correct answer is

9 \frac{3}{4}

yards.

To find the remaining cord, first determine the total amount used by adding

8 \frac{2}{3}

and

6 \frac{5}{6}

. Using a common denominator of

6

, this is

8 \frac{4}{6} + 6 \frac{5}{6} = 14 \frac{9}{6}

, which simplifies to

15 \frac{1}{2}

. Next, subtract this total from the initial amount:

25 \frac{1}{4} - 15 \frac{1}{2}

. Find a common denominator of

4

, making it

25 \frac{1}{4} - 15 \frac{2}{4}

. Since

\frac{1}{4}

is smaller than

\frac{2}{4}

, borrow

1

from the

25

to get

24 \frac{5}{4}

. Finally,

24 \frac{5}{4} - 15 \frac{2}{4} = 9 \frac{3}{4}

Step-by-Step Solution

Calculate the total amount of nylon cord used for both repairs by finding a common denominator.

8 \frac{2}{3} + 6 \frac{5}{6} = 8 \frac{4}{6} + 6 \frac{5}{6} = 14 \frac{9}{6}

To find the total amount removed from the spool, the two individual parts must be added together using a common denominator of 6.

Simplify the total amount used.

14 \frac{9}{6} = 15 \frac{3}{6} = 15 \frac{1}{2}

yards.

Converting the improper fraction part to a mixed number and reducing it to simplest form makes the next calculation easier.

Set up the subtraction to find the remaining cord, finding a common denominator for the total length and the used length.

25 \frac{1}{4} - 15 \frac{1}{2} = 25 \frac{1}{4} - 15 \frac{2}{4}

To find what is left, the used amount must be subtracted from the initial amount on the spool. A common denominator of 4 is required.

Regroup the initial mixed number to perform the subtraction.

24 \frac{5}{4} - 15 \frac{2}{4} = 9 \frac{3}{4}

yards.

Since

\frac{1}{4}

is smaller than

\frac{2}{4}

, one whole unit (

\frac{4}{4}

) must be borrowed from the whole number

25

to make the subtraction possible.

Key Concept

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

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic