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Zorluk: KolayFraction Multiplication and Division in Context

A supply clerk is distributing a 2020-pound bulk bag of coffee to different departments. If each department receives a standard ration of 1141 \frac{1}{4} pounds of coffee, how many departments can be supplied from this single bag?

  1. A
    4
  2. 16Cevap
  3. C
    25
  4. D
    5

Cevap

16
The correct answer is 16. To find how many equal portions can be made from a total amount, division must be used. Dividing the total 2020 pounds by the ration size of 1141 \frac{1}{4} (which is equivalent to the improper fraction 54\frac{5}{4}) pounds yields 20×4520 \times \frac{4}{5}. Multiplying this out gives 805\frac{80}{5}, which simplifies exactly to 1616.

Adım Adım Çözüm

1
Identify the operation needed by recognizing that a total amount is being divided into equal smaller portions.
20÷11420 \div 1 \frac{1}{4}
Dividing the total weight by the weight per ration gives the total number of rations (departments) that can be supplied.
2
Convert the mixed number to an improper fraction for easier calculation.
114=1×4+14=541 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4}
Mathematical operations with fractions require mixed numbers to be in improper fraction form before multiplying or dividing.
3
Divide the whole number by the improper fraction by multiplying by its reciprocal.
20÷54=20×45=805=1620 \div \frac{5}{4} = 20 \times \frac{4}{5} = \frac{80}{5} = 16
Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.

Anahtar Kavram

Dividing a whole number by a mixed number in a real-world distribution context.
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Konular

Fraction Multiplication and Division in Context

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