An interior communications electrician is wiring a new bulkhead and starts with a spool co… — Armed Services Vocational Aptitude Battery (ASVAB)

An interior communications electrician is wiring a new bulkhead and starts with a spool containing $50$ yards of specialized copper cabling. They use $14 \frac{2}{3}$ yards for the primary circuit and $21 \frac{3}{4}$ yards for a secondary circuit. What is the remaining length of cabling on the spool in yards?

Answer:The remaining length of cabling on the spool is 【13 7/12】 yards.

Answer

13 7/12

The total amount of cabling used is found by adding

14 \frac{2}{3}

and

21 \frac{3}{4}

, which equals

36 \frac{5}{12}

yards after finding a common denominator and regrouping. Subtracting this total from the initial

50

yards by borrowing (

49 \frac{12}{12} - 36 \frac{5}{12}

) yields the correct remaining length of

13 \frac{7}{12}

yards.

Step-by-Step Solution

Find a common denominator to add the lengths of cabling used for the primary and secondary circuits.

The least common multiple of 3 and 4 is 12. Convert the fractions:

14 \frac{2}{3} = 14 \frac{8}{12}

and

21 \frac{3}{4} = 21 \frac{9}{12}

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

Add the converted mixed numbers to find the total amount of cabling used.

14 \frac{8}{12} + 21 \frac{9}{12} = 35 \frac{17}{12}

. Since

\frac{17}{12}

is an improper fraction, regroup it as

1 \frac{5}{12}

. Adding this to 35 gives

36 \frac{5}{12}

yards used in total.

This step determines the combined amount of cabling taken from the spool.

Subtract the total amount used from the original amount on the spool.

Subtract

36 \frac{5}{12}

from

50

. To do this, borrow 1 from 50 to create a fraction:

50 = 49 \frac{12}{12}

. Then subtract:

49 \frac{12}{12} - 36 \frac{5}{12} = 13 \frac{7}{12}

yards.

Subtracting the part used from the whole determines the remaining length of cabling.

Key Concept

Adding mixed numbers with unlike denominators and subtracting a mixed number from a whole number.

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