← Adjust the total to leave no remainder · Divisibility and Remainder Reasoning

Adjust the total to leave no remainder · 11 practice problems

3.OA.C.73.OA.A.3

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Generated variants — 11

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

Variant 1 easy

There are 17 notebooks to be shared equally among the 5 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 17 notebooks to split evenly among 5 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 5.

Givens

There are 17 notebooks.
They must be shared equally among 5 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 5.

Constraints

The new total must be evenly divisible by 5.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 17 by 5 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 5 above 17 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 17 by 5. The 5 members each get 3 notebooks, using 15, and 2 are left over.

17 \div 5 = 3 \cdots 2

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 5

#6 Guess and Check 3.OA.A.3

The next multiple of 5 above 17 is 5 times 4, which is 20. We need to reach 20.

5 \times 4 = 20

Counting up to the next multiple of 5 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 17 from the target 20 to get the extra notebooks needed.

20 - 17 = 3

Adding 3 turns the leftover of 2 into a complete share, so the split is exact.

Answer: 3 notebooks

4 · Reviewdoes it hold up?

With 20 notebooks, 20 divided by 5 equals 4 with no remainder, so each member gets 4 and none are left over. Adding only 3 is fewer than starting a whole new round of 5, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 2, and to reach a full group of 5 we need 5 minus 2, which is 3 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 17 by 5 to find the quotient 3 and remainder 2.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 5 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 2 easy

There are 23 notebooks to be shared equally among the 3 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 23 notebooks to split evenly among 3 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 3.

Givens

There are 23 notebooks.
They must be shared equally among 3 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 3.

Constraints

The new total must be evenly divisible by 3.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 23 by 3 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 3 above 23 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 23 by 3. The 3 members each get 7 notebooks, using 21, and 2 are left over.

23 \div 3 = 7 \cdots 2

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 3

#6 Guess and Check 3.OA.A.3

The next multiple of 3 above 23 is 3 times 8, which is 24. We need to reach 24.

3 \times 8 = 24

Counting up to the next multiple of 3 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 23 from the target 24 to get the extra notebooks needed.

24 - 23 = 1

Adding 1 turns the leftover of 2 into a complete share, so the split is exact.

Answer: 1 notebooks

4 · Reviewdoes it hold up?

With 24 notebooks, 24 divided by 3 equals 8 with no remainder, so each member gets 8 and none are left over. Adding only 1 is fewer than starting a whole new round of 3, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 2, and to reach a full group of 3 we need 3 minus 2, which is 1 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 23 by 3 to find the quotient 7 and remainder 2.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 3 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 3 easy

There are 29 notebooks to be shared equally among the 4 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 29 notebooks to split evenly among 4 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 4.

Givens

There are 29 notebooks.
They must be shared equally among 4 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 4.

Constraints

The new total must be evenly divisible by 4.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 29 by 4 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 4 above 29 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 29 by 4. The 4 members each get 7 notebooks, using 28, and 1 are left over.

29 \div 4 = 7 \cdots 1

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 4

#6 Guess and Check 3.OA.A.3

The next multiple of 4 above 29 is 4 times 8, which is 32. We need to reach 32.

4 \times 8 = 32

Counting up to the next multiple of 4 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 29 from the target 32 to get the extra notebooks needed.

32 - 29 = 3

Adding 3 turns the leftover of 1 into a complete share, so the split is exact.

Answer: 3 notebooks

4 · Reviewdoes it hold up?

With 32 notebooks, 32 divided by 4 equals 8 with no remainder, so each member gets 8 and none are left over. Adding only 3 is fewer than starting a whole new round of 4, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 1, and to reach a full group of 4 we need 4 minus 1, which is 3 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 29 by 4 to find the quotient 7 and remainder 1.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 4 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 4 medium

There are 38 notebooks to be shared equally among the 9 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 38 notebooks to split evenly among 9 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 9.

Givens

There are 38 notebooks.
They must be shared equally among 9 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 9.

Constraints

The new total must be evenly divisible by 9.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 38 by 9 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 9 above 38 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 38 by 9. The 9 members each get 4 notebooks, using 36, and 2 are left over.

38 \div 9 = 4 \cdots 2

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 9

#6 Guess and Check 3.OA.A.3

The next multiple of 9 above 38 is 9 times 5, which is 45. We need to reach 45.

9 \times 5 = 45

Counting up to the next multiple of 9 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 38 from the target 45 to get the extra notebooks needed.

45 - 38 = 7

Adding 7 turns the leftover of 2 into a complete share, so the split is exact.

Answer: 7 notebooks

4 · Reviewdoes it hold up?

With 45 notebooks, 45 divided by 9 equals 5 with no remainder, so each member gets 5 and none are left over. Adding only 7 is fewer than starting a whole new round of 9, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 2, and to reach a full group of 9 we need 9 minus 2, which is 7 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 38 by 9 to find the quotient 4 and remainder 2.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 9 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 5 medium

There are 40 notebooks to be shared equally among the 6 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 40 notebooks to split evenly among 6 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 6.

Givens

There are 40 notebooks.
They must be shared equally among 6 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 6.

Constraints

The new total must be evenly divisible by 6.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 40 by 6 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 6 above 40 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 40 by 6. The 6 members each get 6 notebooks, using 36, and 4 are left over.

40 \div 6 = 6 \cdots 4

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 6

#6 Guess and Check 3.OA.A.3

The next multiple of 6 above 40 is 6 times 7, which is 42. We need to reach 42.

6 \times 7 = 42

Counting up to the next multiple of 6 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 40 from the target 42 to get the extra notebooks needed.

42 - 40 = 2

Adding 2 turns the leftover of 4 into a complete share, so the split is exact.

Answer: 2 notebooks

4 · Reviewdoes it hold up?

With 42 notebooks, 42 divided by 6 equals 7 with no remainder, so each member gets 7 and none are left over. Adding only 2 is fewer than starting a whole new round of 6, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 4, and to reach a full group of 6 we need 6 minus 4, which is 2 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 40 by 6 to find the quotient 6 and remainder 4.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 6 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 6 medium

There are 50 notebooks to be shared equally among the 7 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 50 notebooks to split evenly among 7 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 7.

Givens

There are 50 notebooks.
They must be shared equally among 7 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 7.

Constraints

The new total must be evenly divisible by 7.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 50 by 7 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 7 above 50 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 50 by 7. The 7 members each get 7 notebooks, using 49, and 1 are left over.

50 \div 7 = 7 \cdots 1

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 7

#6 Guess and Check 3.OA.A.3

The next multiple of 7 above 50 is 7 times 8, which is 56. We need to reach 56.

7 \times 8 = 56

Counting up to the next multiple of 7 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 50 from the target 56 to get the extra notebooks needed.

56 - 50 = 6

Adding 6 turns the leftover of 1 into a complete share, so the split is exact.

Answer: 6 notebooks

4 · Reviewdoes it hold up?

With 56 notebooks, 56 divided by 7 equals 8 with no remainder, so each member gets 8 and none are left over. Adding only 6 is fewer than starting a whole new round of 7, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 1, and to reach a full group of 7 we need 7 minus 1, which is 6 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 50 by 7 to find the quotient 7 and remainder 1.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 7 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 7 medium

There are 55 notebooks to be shared equally among the 8 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 55 notebooks to split evenly among 8 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 8.

Givens

There are 55 notebooks.
They must be shared equally among 8 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 8.

Constraints

The new total must be evenly divisible by 8.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 55 by 8 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 8 above 55 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 55 by 8. The 8 members each get 6 notebooks, using 48, and 7 are left over.

55 \div 8 = 6 \cdots 7

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 8

#6 Guess and Check 3.OA.A.3

The next multiple of 8 above 55 is 8 times 7, which is 56. We need to reach 56.

8 \times 7 = 56

Counting up to the next multiple of 8 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 55 from the target 56 to get the extra notebooks needed.

56 - 55 = 1

Adding 1 turns the leftover of 7 into a complete share, so the split is exact.

Answer: 1 notebooks

4 · Reviewdoes it hold up?

With 56 notebooks, 56 divided by 8 equals 7 with no remainder, so each member gets 7 and none are left over. Adding only 1 is fewer than starting a whole new round of 8, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 7, and to reach a full group of 8 we need 8 minus 7, which is 1 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 55 by 8 to find the quotient 6 and remainder 7.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 8 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 8 medium

There are 61 notebooks to be shared equally among the 7 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 61 notebooks to split evenly among 7 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 7.

Givens

There are 61 notebooks.
They must be shared equally among 7 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 7.

Constraints

The new total must be evenly divisible by 7.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 61 by 7 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 7 above 61 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 61 by 7. The 7 members each get 8 notebooks, using 56, and 5 are left over.

61 \div 7 = 8 \cdots 5

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 7

#6 Guess and Check 3.OA.A.3

The next multiple of 7 above 61 is 7 times 9, which is 63. We need to reach 63.

7 \times 9 = 63

Counting up to the next multiple of 7 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 61 from the target 63 to get the extra notebooks needed.

63 - 61 = 2

Adding 2 turns the leftover of 5 into a complete share, so the split is exact.

Answer: 2 notebooks

4 · Reviewdoes it hold up?

With 63 notebooks, 63 divided by 7 equals 9 with no remainder, so each member gets 9 and none are left over. Adding only 2 is fewer than starting a whole new round of 7, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 5, and to reach a full group of 7 we need 7 minus 5, which is 2 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 61 by 7 to find the quotient 8 and remainder 5.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 7 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 9 hard

There are 76 notebooks to be shared equally among the 6 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 76 notebooks to split evenly among 6 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 6.

Givens

There are 76 notebooks.
They must be shared equally among 6 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 6.

Constraints

The new total must be evenly divisible by 6.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 76 by 6 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 6 above 76 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 76 by 6. The 6 members each get 12 notebooks, using 72, and 4 are left over.

76 \div 6 = 12 \cdots 4

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 6

#6 Guess and Check 3.OA.A.3

The next multiple of 6 above 76 is 6 times 13, which is 78. We need to reach 78.

6 \times 13 = 78

Counting up to the next multiple of 6 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 76 from the target 78 to get the extra notebooks needed.

78 - 76 = 2

Adding 2 turns the leftover of 4 into a complete share, so the split is exact.

Answer: 2 notebooks

4 · Reviewdoes it hold up?

With 78 notebooks, 78 divided by 6 equals 13 with no remainder, so each member gets 13 and none are left over. Adding only 2 is fewer than starting a whole new round of 6, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 4, and to reach a full group of 6 we need 6 minus 4, which is 2 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 76 by 6 to find the quotient 12 and remainder 4.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 6 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 10 hard

There are 83 notebooks to be shared equally among the 9 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 83 notebooks to split evenly among 9 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 9.

Givens

There are 83 notebooks.
They must be shared equally among 9 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 9.

Constraints

The new total must be evenly divisible by 9.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 83 by 9 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 9 above 83 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 83 by 9. The 9 members each get 9 notebooks, using 81, and 2 are left over.

83 \div 9 = 9 \cdots 2

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 9

#6 Guess and Check 3.OA.A.3

The next multiple of 9 above 83 is 9 times 10, which is 90. We need to reach 90.

9 \times 10 = 90

Counting up to the next multiple of 9 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 83 from the target 90 to get the extra notebooks needed.

90 - 83 = 7

Adding 7 turns the leftover of 2 into a complete share, so the split is exact.

Answer: 7 notebooks

4 · Reviewdoes it hold up?

With 90 notebooks, 90 divided by 9 equals 10 with no remainder, so each member gets 10 and none are left over. Adding only 7 is fewer than starting a whole new round of 9, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 2, and to reach a full group of 9 we need 9 minus 2, which is 7 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 83 by 9 to find the quotient 9 and remainder 2.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 9 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Variant 11 hard

There are 94 notebooks to be shared equally among the 8 members of a group, with none left over. At least how many more notebooks are needed?

Your answer

Show solution

1 · Understandwhat's really being asked

We have 94 notebooks to split evenly among 8 group members with nothing left over. We need the smallest number of extra notebooks to add so the total divides exactly by 8.

Givens

There are 94 notebooks.
They must be shared equally among 8 members.
No notebooks may be left over.

Unknowns

The least number of additional notebooks needed so the total is a multiple of 8.

Constraints

The new total must be evenly divisible by 8.
We add the fewest notebooks possible (we cannot remove any).

2 · Planchoose the strategy

#9 Solve an Easier Related Problem · also uses: #6 Guess and Check

First do the plain division 94 by 8 to see what is left over; the remainder tells us how far we are from a clean split. Then find the next multiple of 8 above 94 and check the gap.

3 · Execute3 carry out the plan

1Divide to see the leftover

#9 Solve an Easier Related Problem 3.OA.C.7

Divide 94 by 8. The 8 members each get 11 notebooks, using 88, and 6 are left over.

94 \div 8 = 11 \cdots 6

A simple division within 100 shows exactly how many notebooks cannot be shared evenly.

2Find the next multiple of 8

#6 Guess and Check 3.OA.A.3

The next multiple of 8 above 94 is 8 times 12, which is 96. We need to reach 96.

8 \times 12 = 96

Counting up to the next multiple of 8 is the smallest total that splits evenly.

3Compute how many more are needed

#6 Guess and Check 3.OA.A.3

Subtract the current 94 from the target 96 to get the extra notebooks needed.

96 - 94 = 2

Adding 2 turns the leftover of 6 into a complete share, so the split is exact.

Answer: 2 notebooks

4 · Reviewdoes it hold up?

With 96 notebooks, 96 divided by 8 equals 12 with no remainder, so each member gets 12 and none are left over. Adding only 2 is fewer than starting a whole new round of 8, so it is the least possible.

Another way: Use Work Backwards (tool 11): the remainder is 6, and to reach a full group of 8 we need 8 minus 6, which is 2 more notebooks.

Standardsmin grade 3

3.OA.C.7 Fluently multiply and divide within 100 — Dividing 94 by 8 to find the quotient 11 and remainder 6.
3.OA.A.3 Solve multiplication and division word problems within 100 — Finding the next multiple of 8 and the number of extra notebooks needed.

💡Takeaway. This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!

Where next?

← Back to the problem: Adjust the total to leave no remainder