A plumber is installing copper piping and starts with a full pipe that measures 14 \frac{1… — Armed Services Vocational Aptitude Battery (ASVAB)

A plumber is installing copper piping and starts with a full pipe that measures $14 \frac{1}{8}$ feet in length. For the installation, he cuts off one section measuring $3 \frac{1}{2}$ feet and another section measuring $5 \frac{3}{8}$ feet. Assuming no material is lost to the saw blade during the cuts, what is the length of the remaining pipe? Enter your answer as a decimal.

Answer: 5.25 feet

Answer

The length of the remaining pipe is 5.25 feet.

First, the total length of the cut sections is found by getting a common denominator (

3 \frac{4}{8} + 5 \frac{3}{8} = 8 \frac{7}{8}

feet). To find the remaining pipe, this total is subtracted from the original length. Since

\frac{7}{8}

is larger than

\frac{1}{8}

, regrouping is necessary:

14 \frac{1}{8}

becomes

13 \frac{9}{8}

. Subtracting yields

5 \frac{2}{8}

, which simplifies to

5 \frac{1}{4}

. The decimal equivalent of

5 \frac{1}{4}

is 5.25.

Step-by-Step Solution

Find a common denominator for the two sections that were cut.

3 \frac{1}{2} = 3 \frac{4}{8}

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

Add the lengths of the two cut sections together.

3 \frac{4}{8} + 5 \frac{3}{8} = 8 \frac{7}{8}

feet

This determines the total amount of pipe removed from the original length.

Set up the subtraction to find the remaining pipe.

14 \frac{1}{8} - 8 \frac{7}{8}

Subtracting the removed amount from the original total gives the remaining balance.

Regroup the initial total to allow for fraction subtraction.

14 \frac{1}{8} = 13 + 1 \frac{1}{8} = 13 \frac{9}{8}

You cannot subtract

\frac{7}{8}

from

\frac{1}{8}

without borrowing a whole number (1 =

\frac{8}{8}

Subtract the whole numbers and the fractions.

13 \frac{9}{8} - 8 \frac{7}{8} = 5 \frac{2}{8}

feet, which simplifies to

5 \frac{1}{4}

feet.

This isolates the precise length of the pipe that is left.

Convert the simplified fraction into a decimal format.

5 \frac{1}{4} = 5.25

The question specifically requests the final answer to be entered as a decimal.

Key Concept

Fraction Addition and Subtraction in Context

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