Solve the following word problem and enter your final answer as a simplified mixed number … — Armed Services Vocational Aptitude Battery (ASVAB)

Solve the following word problem and enter your final answer as a simplified mixed number or improper fraction (e.g., 2 3/4 or 11/4).

Answer:An electrician starts a project with a spool containing

20 \frac{4}{5}

meters of copper wire. They use

6 \frac{1}{3}

meters for the kitchen circuits and

8 \frac{1}{2}

meters for the living room outlets. After these installations, there are 【5 29/30】 meters of wire remaining on the spool.

Answer

5 29/30

To find the remaining wire, the total length used must be subtracted from the original length. First, the used lengths (

6 \frac{1}{3}

and

8 \frac{1}{2}

) are added by finding a common denominator of 6, totaling

14 \frac{5}{6}

meters. Next, this total is subtracted from the original

20 \frac{4}{5}

meters. A common denominator of 30 is used, converting the expression to

20 \frac{24}{30} - 14 \frac{25}{30}

. Because

\frac{24}{30}

is smaller than

\frac{25}{30}

, regrouping is required:

20 \frac{24}{30}

becomes

19 \frac{54}{30}

. Subtracting

14 \frac{25}{30}

leaves exactly

5 \frac{29}{30}

meters.

Step-by-Step Solution

Find the total amount of wire used by adding the lengths used for the kitchen and living room.

6 \frac{1}{3} + 8 \frac{1}{2} = 14 \frac{5}{6}

To determine how much wire is left, we first need to know the total amount taken from the spool. This requires finding a common denominator (6) for the fractions

\frac{1}{3}

and

\frac{1}{2}

Set up the subtraction to find the remaining wire on the spool.

20 \frac{4}{5} - 14 \frac{5}{6}

Subtracting the total used from the initial amount will give the remaining balance.

Find a common denominator to perform the subtraction.

The common denominator for 5 and 6 is 30. We convert the fractions:

20 \frac{24}{30} - 14 \frac{25}{30}

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

Borrow from the whole number to allow subtraction of the fractions.

Borrow 1 from 20 to get 19, and add

\frac{30}{30}

\frac{24}{30}

, resulting in

19 \frac{54}{30}

. Then subtract:

19 \frac{54}{30} - 14 \frac{25}{30} = 5 \frac{29}{30}

Since

\frac{24}{30}

is smaller than

\frac{25}{30}

, regrouping is required to complete the subtraction.

Key Concept

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

Question

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Step-by-Step Solution

Key Concept

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