A logistics specialist is calculating the total weight of cargo for a transport flight. Th… — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics specialist is calculating the total weight of cargo for a transport flight. The first crate weighs $45 \frac{1}{3}$ pounds, and the second crate weighs $32 \frac{1}{6}$ pounds. What is the total combined weight of both crates?

$77 \frac{1}{2}$ poundsAnswer
B
$77 \frac{2}{9}$ pounds
C
$77 \frac{1}{3}$ pounds
D
$13 \frac{1}{6}$ pounds

Answer

The total combined weight is

77 \frac{1}{2}

pounds.

The correct answer is found by identifying a common denominator of 6 for the fractions. The fraction 1/3 becomes 2/6. Adding 2/6 and 1/6 equals 3/6, which reduces to 1/2. Adding the whole numbers 45 and 32 gives 77. The combined weight is 77 1/2 pounds.

Step-by-Step Solution

Set up the addition problem for the two mixed numbers.

45 \frac{1}{3} + 32 \frac{1}{6}

The question asks for the total combined weight, requiring addition.

Find a common denominator for the fractional parts.

The lowest common multiple of

3

and

6

6

. Convert

\frac{1}{3}

by multiplying both numerator and denominator by 2 to get

\frac{2}{6}

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

Add the whole numbers and the fractions, then simplify.

Whole numbers:

45 + 32 = 77

. Fractions:

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

. Simplifying

\frac{3}{6}

yields

\frac{1}{2}

. The final result is

77 \frac{1}{2}

Combining the sums of the whole numbers and the simplified fraction gives the final total weight.

Key Concept

Adding Mixed Numbers with Unlike Denominators

Estimated Time:45s

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