Operations & Word Problems

Depth · one concept from first principles · step 2 of 4

Dividing by a whole number is multiplying by its reciprocal

Three bottles each holding 135 L1\frac{3}{5}\ \text{L} of juice are bought and shared equally among 77 people. How many liters does each person drink?

FractionsNumber system
Your answer
How to solve
Strategy Identify Subproblems — Do it in the order the story happens: first pour all the bottles together, then split that one total seven ways. Dividing by 7 is the same as taking one seventh, which keeps it to fraction multiplication.
1STEP 1

Find how much juice there is altogether

Three bottles of 1 3/5 L each: write the mixed number as 8/5 and multiply by 3.

8/5 × 3 = 24/5
2STEP 2

Share the total among seven people

Splitting equally among 7 means dividing by 7, which is the same as multiplying by 1/7.

24/5 ÷ 7 = 24/5 × 1/7 = 24/35
Answer
2435\frac{24}{35} L
Put it back together: 24/35 × 7 = 24/5, which is the total we started from.
Takeaway

Dividing by a whole number is the same as taking one of that many equal parts.

  • Find how much juice there is altogether
  • Share the total among seven people
Where next?
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