A maintenance technician needs to cut a continuous length of electrical wire into smaller … — Armed Services Vocational Aptitude Battery (ASVAB)

A maintenance technician needs to cut a continuous length of electrical wire into smaller segments. If the technician has a piece of wire that is $45$ feet long and each segment must be $3 \frac{3}{4}$ feet long, how many full segments can be cut?

Answer: 12 segments

Answer

To find the total number of segments, the total length of wire (

45

feet) must be divided by the length of each individual segment (

3 \frac{3}{4}

feet). Converting

3 \frac{3}{4}

to the improper fraction

\frac{15}{4}

and multiplying

45

by its reciprocal (

\frac{4}{15}

) yields exactly

12

segments.

Step-by-Step Solution

Convert the mixed number to an improper fraction.

3 \frac{3}{4} = \frac{15}{4}

Division operations with mixed numbers require converting them to improper fractions first.

Set up the division equation.

45 \div \frac{15}{4}

To find how many smaller segments fit into the total length, you must divide the total wire length by the length of one individual segment.

Convert the division into multiplication.

45 \times \frac{4}{15}

Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.

Simplify the expression and calculate the final value.

3 \times 4 = 12

Cross-canceling

45

and

15

leaves a factor of

3

, which is then multiplied by

4

to reach the final whole number answer.

Key Concept

Dividing a whole quantity by a mixed number using improper fractions and reciprocals.

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