A military supply depot has a stockpile of 26 \frac{2}{3} gallons of synthetic transmissio… — Armed Services Vocational Aptitude Battery (ASVAB)

A military supply depot has a stockpile of $26 \frac{2}{3}$ gallons of synthetic transmission fluid. If each transport vehicle requires exactly $1 \frac{1}{3}$ gallons of this fluid for a complete routine service, how many vehicles can be fully serviced using the entire stockpile?

20Cevap
B
28
C
$35 \frac{5}{9}$
D
$25 \frac{1}{3}$

Cevap

To determine how many vehicles can be serviced, the total amount of fluid (

26 \frac{2}{3}

gallons) must be divided by the amount required per vehicle (

1 \frac{1}{3}

gallons). First, convert both amounts to improper fractions:

\frac{80}{3} \div \frac{4}{3}

. Next, multiply by the reciprocal of the second fraction:

\frac{80}{3} \times \frac{3}{4}

. The 3s in the numerator and denominator cancel out, leaving

80 \div 4

, which equals exactly 20.

Adım Adım Çözüm

Convert both mixed numbers to improper fractions.

26 \frac{2}{3} = \frac{80}{3}

and

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

Mixed numbers must be written as improper fractions before they can be multiplied or divided.

Set up the division equation.

\frac{80}{3} \div \frac{4}{3}

To find how many times the vehicle requirement fits into the total stockpile, divide the total fluid by the fluid needed per vehicle.

Multiply by the reciprocal of the divisor to solve.

\frac{80}{3} \times \frac{3}{4} = \frac{240}{12} = 20

Dividing by a fraction is mathematically identical to multiplying by its reciprocal. The 3s cross-cancel, leaving 80 divided by 4.

Anahtar Kavram

Dividing mixed numbers by converting them to improper fractions and multiplying by the reciprocal.

Tahmini Süre:1m 30s

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