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Difficulty: MediumFraction Multiplication and Division in Context

A military mess hall receives a shipment of 13114131 \frac{1}{4} pounds of ground beef. The kitchen staff uses 37\frac{3}{7} of the shipment to prepare lunch. The remaining ground beef is portioned into smaller storage bags that each hold 3343 \frac{3}{4} pounds for dinner recipes. How many storage bags can be completely filled with the remaining ground beef?

Answer: 20 bags

Answer

20
First, the remaining fraction of beef is determined to be 4/7. Multiplying the total initial weight of 131 1/4 pounds (or 525/4) by 4/7 yields exactly 75 pounds of remaining ground beef. Finally, dividing these 75 pounds by the capacity of each bag, which is 3 3/4 pounds (or 15/4), gives exactly 20 completely filled storage bags.

Step-by-Step Solution

1
Calculate the fraction of the ground beef that remains after lunch.
1−37=471 - \frac{3}{7} = \frac{4}{7}
The kitchen staff used 3/7 of the shipment, so 4/7 of the shipment is left for the dinner recipes.
2
Convert the total shipment weight from a mixed number to an improper fraction.
13114=5254131 \frac{1}{4} = \frac{525}{4}
Converting to an improper fraction makes it easier to multiply by the remaining fraction.
3
Multiply the total weight by the remaining fraction to find the remaining weight.
47×5254=5257=75\frac{4}{7} \times \frac{525}{4} = \frac{525}{7} = 75 pounds
This calculation yields the exact weight of the ground beef available to be portioned into storage bags. Notice that the 4 in the numerator and denominator cancel out.
4
Convert the storage bag capacity from a mixed number to an improper fraction.
334=1543 \frac{3}{4} = \frac{15}{4}
This prepares the divisor for the fraction division step.
5
Divide the remaining weight by the capacity of each storage bag.
75÷154=75×415=30015=2075 \div \frac{15}{4} = 75 \times \frac{4}{15} = \frac{300}{15} = 20 bags
Dividing the total available weight by the weight per bag yields the exact number of bags that can be completely filled.

Key Concept

Fraction Multiplication and Division in Context
Estimated Time:1m 30s
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Topics

Fraction Multiplication and Division in Context

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