An Equipment Operator is laying a base layer of crushed rock for a new supply road. The pr… — Armed Services Vocational Aptitude Battery (ASVAB)

An Equipment Operator is laying a base layer of crushed rock for a new supply road. The project requires a total of $22 \frac{1}{4}$ tons of crushed rock. The first dump truck delivers $8 \frac{1}{2}$ tons, and the second dump truck delivers $7 \frac{1}{3}$ tons. How many more tons of crushed rock are needed to complete the base layer?

$6 \frac{5}{12}$ Answer
B
$6 \frac{17}{20}$
C
$7 \frac{7}{12}$
D
$38 \frac{1}{12}$

Answer

6 \frac{5}{12}

tons

To find the remaining amount needed, first calculate the total crushed rock delivered by adding the two truckloads. Convert the fractions to a common denominator of

6

8 \frac{1}{2} = 8 \frac{3}{6}

and

7 \frac{1}{3} = 7 \frac{2}{6}

. Adding these gives

15 \frac{5}{6}

tons delivered. Next, subtract this amount from the total required,

22 \frac{1}{4}

. Convert to a common denominator of

12

22 \frac{1}{4} = 22 \frac{3}{12}

and

15 \frac{5}{6} = 15 \frac{10}{12}

. Since

\frac{3}{12}

is less than

\frac{10}{12}

, borrow

1

(or

\frac{12}{12}

) from

22

to get

21 \frac{15}{12}

. Finally, subtract:

21 \frac{15}{12} - 15 \frac{10}{12} = 6 \frac{5}{12}

tons.

Step-by-Step Solution

Calculate the total amount of crushed rock delivered.

8 \frac{1}{2} + 7 \frac{1}{3} = 8 \frac{3}{6} + 7 \frac{2}{6} = 15 \frac{5}{6}

The total delivered is the sum of the two truckloads, requiring a common denominator of 6.

Set up the subtraction from the total required amount using a common denominator.

22 \frac{1}{4} - 15 \frac{5}{6} = 22 \frac{3}{12} - 15 \frac{10}{12}

To find the remaining amount, subtract the delivered total from the required total using the least common multiple of 4 and 6, which is 12.

Regroup (borrow) to perform the subtraction.

21 \frac{15}{12} - 15 \frac{10}{12} = 6 \frac{5}{12}

Since 3/12 is smaller than 10/12, borrow 1 (as 12/12) from the whole number 22 to make it 21 15/12, then subtract the whole numbers and numerators.

Key Concept

Adding and subtracting mixed numbers with unlike denominators, including regrouping.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic