Find the total first, then divide

3.OA.D.83.OA.A.3 · take · grade 3

Archetype: Division as the Inverse of Multiplication · step in a 4-type progression

Some tangerines were packed equally, $12$ to a bag, making $3$ bags. If these same tangerines are repacked equally into $6$ bags, how many tangerines can be put in each bag?

Show solution

Understand

Tangerines were packed 12 to a bag into 3 bags. The same tangerines are then repacked equally into 6 bags. I need to find how many go in each of the new bags.

Givens

Each original bag holds 12 tangerines.
There are 3 original bags.
All the tangerines are repacked equally into 6 bags.

Unknowns

The number of tangerines in each of the 6 new bags.

Constraints

The tangerines are split equally with none left over.
The total number of tangerines stays the same when repacked.

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units

This is a two-step calculation: first find the total number of tangerines (a multiplication subproblem), then split that total equally into 6 bags (a division subproblem). Breaking it into these two smaller problems makes the path clear, and watching the units (tangerines per bag times bags = tangerines) keeps the setup honest.

Execute

#7 Identify Subproblems 3.OA.A.3

There are 3 bags with 12 tangerines each, so multiply to find how many tangerines there are altogether.

12 \times 3 = 36

Equal groups of objects are counted by multiplying the group size by the number of groups.

#8 Analyze the Units 3.OA.A.3

The same 36 tangerines are repacked equally into 6 bags, so divide the total by the number of new bags.

36 \div 6 = 6

Sharing a total equally into a known number of groups is exactly what division finds.

Answer: 6 tangerines

Review

Going from 3 bags to 6 bags doubles the number of bags, so each bag should hold half as many: half of 12 is 6, which matches. Also 6 tangerines per bag times 6 bags equals 36, the same total we started with.

Look for a pattern (tool 5): doubling the number of bags from 3 to 6 halves the count per bag, so 12 becomes 6 without computing the total at all.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Multiplying to get the total, then dividing the total equally among the new bags.
3.OA.D.8 Solve two-step word problems using four operations within 100 — Combining the multiply-then-divide steps into one two-step word problem.

💡 Find the whole pile first, then share it out: that's all this Grade 3 problem needs!