← 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

Generated variants — 11

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

Variant 1 easy answer: 3 notebooks

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?

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÷5=3⋯217 \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.
5×4=205 \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=320 - 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 answer: 1 notebooks

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?

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÷3=7⋯223 \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.
3×8=243 \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=124 - 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 answer: 3 notebooks

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?

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÷4=7⋯129 \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.
4×8=324 \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=332 - 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 answer: 7 notebooks

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?

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÷9=4⋯238 \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.
9×5=459 \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=745 - 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 answer: 2 notebooks

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?

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÷6=6⋯440 \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.
6×7=426 \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=242 - 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 answer: 6 notebooks

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?

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÷7=7⋯150 \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.
7×8=567 \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=656 - 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 answer: 1 notebooks

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?

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÷8=6⋯755 \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.
8×7=568 \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=156 - 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 answer: 2 notebooks

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?

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÷7=8⋯561 \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.
7×9=637 \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=263 - 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 answer: 2 notebooks

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?

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÷6=12⋯476 \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.
6×13=786 \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=278 - 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 answer: 7 notebooks

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?

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÷9=9⋯283 \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.
9×10=909 \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=790 - 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 answer: 2 notebooks

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?

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÷8=11⋯694 \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.
8×12=968 \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=296 - 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!