Problem
Dividing by a whole number is multiplying by its reciprocal
Three bottles each hold the same fractional amount of juice, and seven people share all of it equally. We need one person's share in liters.
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
There is 24/5 L in all.
6.NS.A.1Identify Subproblems2STEP 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
Each person gets 24/35 L.
5.NF.B.7Analyze The UnitsEach person drinks .
Why?
Sharing equally among seven means the total is seven of whatever one person gets, so one share is the total cut into seven equal parts.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Cutting each of the five fifths into seven equal slices makes thirty-five slices in one whole, so a seventh of a fifth is one thirty-fifth.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Answer
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