A maintenance technician is preparing a chemical solvent for parts cleaning. The technical… — Armed Services Vocational Aptitude Battery (ASVAB)

A maintenance technician is preparing a chemical solvent for parts cleaning. The technical manual specifies that the active cleaning agent must make up $32.5\%$ of the total solution. What fraction of the total solution must be the active cleaning agent, expressed in simplest form?

$\frac{13}{40}$ Answer
B
$\frac{13}{27}$
C
$\frac{13}{400}$
D
$\frac{40}{13}$

Answer

The correct fraction in its simplest form is

\frac{13}{40}

To convert

32.5\%

to a fraction, it is first written as

\frac{32.5}{100}

. Multiplying by

10

to remove the decimal results in

\frac{325}{1000}

. Dividing both numbers by

25

yields the simplest form,

\frac{13}{40}

Step-by-Step Solution

Convert the percentage to a fraction over 100.

32.5\% = \frac{32.5}{100}

A percentage represents a part out of 100.

Eliminate the decimal in the numerator by multiplying both the numerator and the denominator by 10.

\frac{32.5 \times 10}{100 \times 10} = \frac{325}{1000}

Fractions must be expressed using whole numbers before they can be simplified properly.

Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 25.

325 \div 25 = 13

and

1000 \div 25 = 40

. The simplified fraction is

\frac{13}{40}

The question requires the final answer to be expressed in its simplest form.

Key Concept

Converting a percentage with a decimal to a fraction in simplest form requires creating a fraction out of 100, scaling the fraction to eliminate the decimal, and finding the greatest common divisor.

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