Larger dividend gives larger quotient

3.OA.A.23.OA.A.3 · take · grade 3

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

There are $20$ crackers and $28$ candies. The crackers and the candies are each shared equally among $4$ children. How many more candies than crackers does each child get?

Show solution

Understand

There are 20 crackers and 28 candies. Each type is shared equally among 4 children. I need to find how many more candies than crackers each child gets.

Givens

There are 20 crackers.
There are 28 candies.
Each kind of treat is shared equally among 4 children.

Unknowns

The difference between candies per child and crackers per child.

Constraints

Both the crackers and the candies are divided equally with none left over.
The number of children (4) is the same for both shares.

Plan

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

Find each child's share of crackers and of candies as two separate division subproblems, then compare them. Because the same 4 children share both, the larger total (candies) must give the larger per-child amount, so the final step is a simple subtraction of the two shares.

Execute

#7 Identify Subproblems 3.OA.A.2

Share 20 crackers equally among 4 children by dividing.

20 \div 4 = 5

Dividing a total into equal groups tells how many each child receives.

#7 Identify Subproblems 3.OA.A.2

Share 28 candies equally among the same 4 children by dividing.

28 \div 4 = 7

The same equal-sharing idea applies; a bigger total split the same way gives a bigger share.

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

Subtract the crackers-per-child from the candies-per-child to find how many more candies each child gets.

7 - 5 = 2

"How many more" is found by subtracting the smaller amount from the larger one.

Answer: 2 more candies

Review

Each child gets 5 crackers and 7 candies; 7 is indeed 2 more than 5. Checking totals: 5 times 4 is 20 crackers and 7 times 4 is 28 candies, both correct. The larger pile (candies) gives the larger share, as expected.

Use the difference first (tool 11/15 idea): there are 28 - 20 = 8 more candies than crackers in all, and those 8 extra are shared among 4 children, so 8 divided by 4 is 2 extra candies per child.

Standards · min grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 4 children to find each child's share.
3.OA.A.3 Solve multiplication and division word problems within 100 — Comparing the two shares to answer the how-many-more question.

💡 Share each pile out, then compare the shares: Grade 3 division and subtraction is all it takes!