A military dining facility begins the week with 30 \frac{1}{2} gallons of cooking oil. On … — Armed Services Vocational Aptitude Battery (ASVAB)

A military dining facility begins the week with $30 \frac{1}{2}$ gallons of cooking oil. On Monday, the kitchen uses $12 \frac{3}{4}$ gallons of the oil. On Tuesday, the kitchen uses another $9 \frac{2}{3}$ gallons. How many gallons of cooking oil remain at the facility?

$8 \frac{1}{12}$ Answer
B
$8 \frac{11}{14}$
C
$9 \frac{1}{12}$
D
$22 \frac{5}{12}$

Answer

8 \frac{1}{12}

The correct answer is found by first calculating the total oil used by finding a common denominator of 12 and regrouping (

12 \frac{3}{4} + 9 \frac{2}{3} = 22 \frac{5}{12}

gallons). Then, this combined amount is subtracted from the initial inventory using the same common denominator (

30 \frac{1}{2} - 22 \frac{5}{12} = 30 \frac{6}{12} - 22 \frac{5}{12} = 8 \frac{1}{12}

gallons).

Step-by-Step Solution

Find the total amount of oil used by adding the amounts from Monday and Tuesday.

12 \frac{3}{4} + 9 \frac{2}{3}

To find out how much oil is left, we must first know the total volume that was removed from the initial inventory.

Convert the fractions to a common denominator to add them.

The least common multiple of

4

and

3

12

. The fractions become

\frac{9}{12}

and

\frac{8}{12}

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

Add the converted mixed numbers and regroup the improper fraction.

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

. Since

\frac{17}{12}

1 \frac{5}{12}

, the total used is

22 \frac{5}{12}

gallons.

Simplifying the combined total makes the final subtraction step accurate and easier to perform.

Subtract the total amount used from the initial inventory to find the remaining oil.

30 \frac{1}{2} - 22 \frac{5}{12}

Subtracting the part used from the whole gives the remaining balance.

Find a common denominator for the final subtraction.

The least common multiple of

2

and

12

12

. The initial amount becomes

30 \frac{6}{12}

Again, fractions require a common denominator for subtraction.

Perform the subtraction.

30 \frac{6}{12} - 22 \frac{5}{12} = 8 \frac{1}{12}

gallons.

This calculation yields the final volume of oil remaining in the facility.

Key Concept

Adding and subtracting mixed numbers with unlike denominators by finding the lowest common denominator and regrouping improper fractions.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic