A heavy-duty diesel generator has a maximum fuel capacity of 120 gallons. The tank current… — Armed Services Vocational Aptitude Battery (ASVAB)

A heavy-duty diesel generator has a maximum fuel capacity of $120$ gallons. The tank currently contains $84 \frac{1}{3}$ gallons of diesel. If a technician adds $18 \frac{3}{5}$ gallons of fuel to the tank, how many more gallons are needed to completely fill the tank?

(Enter your answer as a mixed number in its simplest form, using a space between the whole number and the fraction, such as 5 1/2)

Cevap:The generator needs 【17 1/15】 more gallons of fuel.

Cevap

17 1/15

By finding a common denominator of 15, the total fuel currently in the tank is calculated as

102 \frac{14}{15}

gallons. Subtracting this from the

120

-gallon total capacity requires borrowing

1

from

120

to make it

119 \frac{15}{15}

. Subtracting

102 \frac{14}{15}

from

119 \frac{15}{15}

leaves

17 \frac{1}{15}

gallons.

Adım Adım Çözüm

Find a common denominator to add the current fuel and the added fuel together.

The lowest common multiple of 3 and 5 is 15.

84 \frac{1}{3} = 84 \frac{5}{15}

18 \frac{3}{5} = 18 \frac{9}{15}

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

Add the two mixed numbers to find the total amount of fuel currently in the tank.

84 \frac{5}{15} + 18 \frac{9}{15} = 102 \frac{14}{15}

gallons.

This establishes the current volume of fuel occupying the tank.

Subtract the total current fuel from the maximum capacity of the tank.

120 - 102 \frac{14}{15}

To subtract, borrow 1 from 120 to create a fraction:

119 \frac{15}{15}

119 \frac{15}{15} - 102 \frac{14}{15} = 17 \frac{1}{15}

gallons.

Subtracting the volume currently inside the tank from the maximum capacity gives the remaining space available.

Anahtar Kavram

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

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