← Larger dividend gives larger quotient · Division as the Inverse of Multiplication

Larger dividend gives larger quotient · 10 practice problems

3.OA.A.23.OA.A.3

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Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy

There are $8$ erasers and $20$ clips. The erasers and the clips are each shared equally among $4$ children. How many more clips than erasers does each child get?

Your answer

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1 · Understandwhat's really being asked

There are 8 erasers and 20 clips. Each type is shared equally among 4 children. I need to find how many more clips than erasers each child gets.

Givens

There are 8 erasers.
There are 20 clips.
Each kind of treat is shared equally among 4 children.

Unknowns

The difference between clips per child and erasers per child.

Constraints

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

2 · Planchoose the strategy

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

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

3 · Execute3 carry out the plan

1Erasers per child

#7 Identify Subproblems 3.OA.A.2

Share 8 erasers equally among 4 children by dividing.

8 \div 4 = 2

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

2Clips per child

#7 Identify Subproblems 3.OA.A.2

Share 20 clips equally among the same 4 children by dividing.

20 \div 4 = 5

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

3Compare the two shares

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

Subtract the erasers-per-child from the clips-per-child to find how many more clips each child gets.

5 - 2 = 3

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

Answer: 3 more clips

4 · Reviewdoes it hold up?

Each child gets 2 erasers and 5 clips; 5 is indeed 3 more than 2. Checking totals: 2 times 4 is 8 and 5 times 4 is 20, both correct.

Another way: Use the difference first: there are 20 - 8 = 12 more clips than erasers in all, and those extras shared among 4 children give 3 extra clips per child.

Standardsmin 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.

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

Variant 2 easy

There are $14$ cards and $21$ coins. The cards and the coins are each shared equally among $7$ children. How many more coins than cards does each child get?

Your answer

Show solution

1 · Understandwhat's really being asked

There are 14 cards and 21 coins. Each type is shared equally among 7 children. I need to find how many more coins than cards each child gets.

Givens

There are 14 cards.
There are 21 coins.
Each kind of treat is shared equally among 7 children.

Unknowns

The difference between coins per child and cards per child.

Constraints

Both the cards and the coins are divided equally with none left over.
The number of children (7) is the same for both shares.

2 · Planchoose the strategy

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

Find each child's share of cards and of coins as two separate division subproblems, then compare them. Because the same 7 children share both, the larger total gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Cards per child

#7 Identify Subproblems 3.OA.A.2

Share 14 cards equally among 7 children by dividing.

14 \div 7 = 2

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

2Coins per child

#7 Identify Subproblems 3.OA.A.2

Share 21 coins equally among the same 7 children by dividing.

21 \div 7 = 3

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

3Compare the two shares

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

Subtract the cards-per-child from the coins-per-child to find how many more coins each child gets.

3 - 2 = 1

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

Answer: 1 more coins

4 · Reviewdoes it hold up?

Each child gets 2 cards and 3 coins; 3 is indeed 1 more than 2. Checking totals: 2 times 7 is 14 and 3 times 7 is 21, both correct.

Another way: Use the difference first: there are 21 - 14 = 7 more coins than cards in all, and those extras shared among 7 children give 1 extra coins per child.

Standardsmin grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 7 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.

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

Variant 3 easy

There are $12$ apples and $24$ oranges. The apples and the oranges are each shared equally among $6$ children. How many more oranges than apples does each child get?

Your answer

Show solution

1 · Understandwhat's really being asked

There are 12 apples and 24 oranges. Each type is shared equally among 6 children. I need to find how many more oranges than apples each child gets.

Givens

There are 12 apples.
There are 24 oranges.
Each kind of treat is shared equally among 6 children.

Unknowns

The difference between oranges per child and apples per child.

Constraints

Both the apples and the oranges are divided equally with none left over.
The number of children (6) is the same for both shares.

2 · Planchoose the strategy

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

Find each child's share of apples and of oranges as two separate division subproblems, then compare them. Because the same 6 children share both, the larger total gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Apples per child

#7 Identify Subproblems 3.OA.A.2

Share 12 apples equally among 6 children by dividing.

12 \div 6 = 2

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

2Oranges per child

#7 Identify Subproblems 3.OA.A.2

Share 24 oranges equally among the same 6 children by dividing.

24 \div 6 = 4

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

3Compare the two shares

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

Subtract the apples-per-child from the oranges-per-child to find how many more oranges each child gets.

4 - 2 = 2

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

Answer: 2 more oranges

4 · Reviewdoes it hold up?

Each child gets 2 apples and 4 oranges; 4 is indeed 2 more than 2. Checking totals: 2 times 6 is 12 and 4 times 6 is 24, both correct.

Another way: Use the difference first: there are 24 - 12 = 12 more oranges than apples in all, and those extras shared among 6 children give 2 extra oranges per child.

Standardsmin grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 6 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.

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

Variant 4 medium

There are $18$ stamps and $27$ stickers. The stamps and the stickers are each shared equally among $3$ children. How many more stickers than stamps does each child get?

Your answer

Show solution

1 · Understandwhat's really being asked

There are 18 stamps and 27 stickers. Each type is shared equally among 3 children. I need to find how many more stickers than stamps each child gets.

Givens

There are 18 stamps.
There are 27 stickers.
Each kind of treat is shared equally among 3 children.

Unknowns

The difference between stickers per child and stamps per child.

Constraints

Both the stamps and the stickers are divided equally with none left over.
The number of children (3) is the same for both shares.

2 · Planchoose the strategy

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

Find each child's share of stamps and of stickers as two separate division subproblems, then compare them. Because the same 3 children share both, the larger total gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Stamps per child

#7 Identify Subproblems 3.OA.A.2

Share 18 stamps equally among 3 children by dividing.

18 \div 3 = 6

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

2Stickers per child

#7 Identify Subproblems 3.OA.A.2

Share 27 stickers equally among the same 3 children by dividing.

27 \div 3 = 9

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

3Compare the two shares

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

Subtract the stamps-per-child from the stickers-per-child to find how many more stickers each child gets.

9 - 6 = 3

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

Answer: 3 more stickers

4 · Reviewdoes it hold up?

Each child gets 6 stamps and 9 stickers; 9 is indeed 3 more than 6. Checking totals: 6 times 3 is 18 and 9 times 3 is 27, both correct.

Another way: Use the difference first: there are 27 - 18 = 9 more stickers than stamps in all, and those extras shared among 3 children give 3 extra stickers per child.

Standardsmin grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 3 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.

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

Variant 5 medium

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?

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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 gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Crackers per child

#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.

2Candies per child

#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.

3Compare the two shares

#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

4 · Reviewdoes it hold up?

Each child gets 5 crackers and 7 candies; 7 is indeed 2 more than 5. Checking totals: 5 times 4 is 20 and 7 times 4 is 28, both correct.

Another way: Use the difference first: there are 28 - 20 = 8 more candies than crackers in all, and those extras shared among 4 children give 2 extra candies per child.

Standardsmin 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.

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

Variant 6 medium

There are $10$ buttons and $30$ blocks. The buttons and the blocks are each shared equally among $5$ children. How many more blocks than buttons does each child get?

Your answer

Show solution

1 · Understandwhat's really being asked

There are 10 buttons and 30 blocks. Each type is shared equally among 5 children. I need to find how many more blocks than buttons each child gets.

Givens

There are 10 buttons.
There are 30 blocks.
Each kind of treat is shared equally among 5 children.

Unknowns

The difference between blocks per child and buttons per child.

Constraints

Both the buttons and the blocks are divided equally with none left over.
The number of children (5) is the same for both shares.

2 · Planchoose the strategy

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

Find each child's share of buttons and of blocks as two separate division subproblems, then compare them. Because the same 5 children share both, the larger total gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Buttons per child

#7 Identify Subproblems 3.OA.A.2

Share 10 buttons equally among 5 children by dividing.

10 \div 5 = 2

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

2Blocks per child

#7 Identify Subproblems 3.OA.A.2

Share 30 blocks equally among the same 5 children by dividing.

30 \div 5 = 6

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

3Compare the two shares

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

Subtract the buttons-per-child from the blocks-per-child to find how many more blocks each child gets.

6 - 2 = 4

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

Answer: 4 more blocks

4 · Reviewdoes it hold up?

Each child gets 2 buttons and 6 blocks; 6 is indeed 4 more than 2. Checking totals: 2 times 5 is 10 and 6 times 5 is 30, both correct.

Another way: Use the difference first: there are 30 - 10 = 20 more blocks than buttons in all, and those extras shared among 5 children give 4 extra blocks per child.

Standardsmin grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 5 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.

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

Variant 7 medium

There are $15$ pens and $30$ pencils. The pens and the pencils are each shared equally among $5$ children. How many more pencils than pens does each child get?

Your answer

Show solution

1 · Understandwhat's really being asked

There are 15 pens and 30 pencils. Each type is shared equally among 5 children. I need to find how many more pencils than pens each child gets.

Givens

There are 15 pens.
There are 30 pencils.
Each kind of treat is shared equally among 5 children.

Unknowns

The difference between pencils per child and pens per child.

Constraints

Both the pens and the pencils are divided equally with none left over.
The number of children (5) is the same for both shares.

2 · Planchoose the strategy

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

Find each child's share of pens and of pencils as two separate division subproblems, then compare them. Because the same 5 children share both, the larger total gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Pens per child

#7 Identify Subproblems 3.OA.A.2

Share 15 pens equally among 5 children by dividing.

15 \div 5 = 3

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

2Pencils per child

#7 Identify Subproblems 3.OA.A.2

Share 30 pencils equally among the same 5 children by dividing.

30 \div 5 = 6

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

3Compare the two shares

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

Subtract the pens-per-child from the pencils-per-child to find how many more pencils each child gets.

6 - 3 = 3

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

Answer: 3 more pencils

4 · Reviewdoes it hold up?

Each child gets 3 pens and 6 pencils; 6 is indeed 3 more than 3. Checking totals: 3 times 5 is 15 and 6 times 5 is 30, both correct.

Another way: Use the difference first: there are 30 - 15 = 15 more pencils than pens in all, and those extras shared among 5 children give 3 extra pencils per child.

Standardsmin grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 5 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.

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

Variant 8 hard

There are $24$ grapes and $36$ cherries. The grapes and the cherries are each shared equally among $6$ children. How many more cherries than grapes does each child get?

Your answer

Show solution

1 · Understandwhat's really being asked

There are 24 grapes and 36 cherries. Each type is shared equally among 6 children. I need to find how many more cherries than grapes each child gets.

Givens

There are 24 grapes.
There are 36 cherries.
Each kind of treat is shared equally among 6 children.

Unknowns

The difference between cherries per child and grapes per child.

Constraints

Both the grapes and the cherries are divided equally with none left over.
The number of children (6) is the same for both shares.

2 · Planchoose the strategy

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

Find each child's share of grapes and of cherries as two separate division subproblems, then compare them. Because the same 6 children share both, the larger total gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Grapes per child

#7 Identify Subproblems 3.OA.A.2

Share 24 grapes equally among 6 children by dividing.

24 \div 6 = 4

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

2Cherries per child

#7 Identify Subproblems 3.OA.A.2

Share 36 cherries equally among the same 6 children by dividing.

36 \div 6 = 6

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

3Compare the two shares

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

Subtract the grapes-per-child from the cherries-per-child to find how many more cherries each child gets.

6 - 4 = 2

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

Answer: 2 more cherries

4 · Reviewdoes it hold up?

Each child gets 4 grapes and 6 cherries; 6 is indeed 2 more than 4. Checking totals: 4 times 6 is 24 and 6 times 6 is 36, both correct.

Another way: Use the difference first: there are 36 - 24 = 12 more cherries than grapes in all, and those extras shared among 6 children give 2 extra cherries per child.

Standardsmin grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 6 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.

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

Variant 9 hard

There are $16$ marbles and $40$ beads. The marbles and the beads are each shared equally among $8$ children. How many more beads than marbles does each child get?

Your answer

Show solution

1 · Understandwhat's really being asked

There are 16 marbles and 40 beads. Each type is shared equally among 8 children. I need to find how many more beads than marbles each child gets.

Givens

There are 16 marbles.
There are 40 beads.
Each kind of treat is shared equally among 8 children.

Unknowns

The difference between beads per child and marbles per child.

Constraints

Both the marbles and the beads are divided equally with none left over.
The number of children (8) is the same for both shares.

2 · Planchoose the strategy

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

Find each child's share of marbles and of beads as two separate division subproblems, then compare them. Because the same 8 children share both, the larger total gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Marbles per child

#7 Identify Subproblems 3.OA.A.2

Share 16 marbles equally among 8 children by dividing.

16 \div 8 = 2

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

2Beads per child

#7 Identify Subproblems 3.OA.A.2

Share 40 beads equally among the same 8 children by dividing.

40 \div 8 = 5

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

3Compare the two shares

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

Subtract the marbles-per-child from the beads-per-child to find how many more beads each child gets.

5 - 2 = 3

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

Answer: 3 more beads

4 · Reviewdoes it hold up?

Each child gets 2 marbles and 5 beads; 5 is indeed 3 more than 2. Checking totals: 2 times 8 is 16 and 5 times 8 is 40, both correct.

Another way: Use the difference first: there are 40 - 16 = 24 more beads than marbles in all, and those extras shared among 8 children give 3 extra beads per child.

Standardsmin grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 8 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.

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

Variant 10 hard

There are $18$ nuts and $45$ raisins. The nuts and the raisins are each shared equally among $9$ children. How many more raisins than nuts does each child get?

Your answer

Show solution

1 · Understandwhat's really being asked

There are 18 nuts and 45 raisins. Each type is shared equally among 9 children. I need to find how many more raisins than nuts each child gets.

Givens

There are 18 nuts.
There are 45 raisins.
Each kind of treat is shared equally among 9 children.

Unknowns

The difference between raisins per child and nuts per child.

Constraints

Both the nuts and the raisins are divided equally with none left over.
The number of children (9) is the same for both shares.

2 · Planchoose the strategy

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

Find each child's share of nuts and of raisins as two separate division subproblems, then compare them. Because the same 9 children share both, the larger total gives the larger per-child amount, so the final step is a simple subtraction of the two shares.

3 · Execute3 carry out the plan

1Nuts per child

#7 Identify Subproblems 3.OA.A.2

Share 18 nuts equally among 9 children by dividing.

18 \div 9 = 2

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

2Raisins per child

#7 Identify Subproblems 3.OA.A.2

Share 45 raisins equally among the same 9 children by dividing.

45 \div 9 = 5

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

3Compare the two shares

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

Subtract the nuts-per-child from the raisins-per-child to find how many more raisins each child gets.

5 - 2 = 3

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

Answer: 3 more raisins

4 · Reviewdoes it hold up?

Each child gets 2 nuts and 5 raisins; 5 is indeed 3 more than 2. Checking totals: 2 times 9 is 18 and 5 times 9 is 45, both correct.

Another way: Use the difference first: there are 45 - 18 = 27 more raisins than nuts in all, and those extras shared among 9 children give 3 extra raisins per child.

Standardsmin grade 3

3.OA.A.2 Interpret whole-number quotients of whole numbers — Dividing each total equally among 9 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.

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

Where next?

← Back to the problem: Larger dividend gives larger quotient