Problem
Adjust the total to leave no remainder
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.
Operations
Your answer
Watch out You need the amount that completes the next group, not the leftover 4 itself.
How to solve
Strategy Solve an Easier Related Problem — 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.
1STEP 1
Divide to see the leftover
Divide 76 by 6. Six members each get 12 notebooks, using 72, and 4 are left over.
76 ÷ 6 = 12 remainder 4
A simple division within 100 shows exactly how many notebooks cannot be shared evenly.
3.OA.C.7Solve An Easier Related Problem2STEP 2
Find the next multiple of 6
The next multiple of 6 above 76 is 6 times 13, which is 78. We need to reach 78.
6 × 13 = 78
Counting up to the next multiple of 6 is the smallest total that splits evenly.
3.OA.A.3Guess And CheckThe smallest total of at least 76 notebooks that all 6 members can share with none left over is 78.
Why?
Sharing a total among 6 members with nothing left over means the total is 6 equal shares put together, so the total has to be a multiple of 6.
Why?
Six equal shares put together is six groups of one share, and six groups of a number is exactly what six times that number means, so the total is six times the share.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
76 sits 4 past the multiple 72 = 6 x 12, and the very next multiple of 6 is 78, so counting up without removing any notebooks the first total that shares evenly is 78.
Why?
The next multiple after 6 x 12 is 6 x 13, and 6 x 13 is 6 x 12 with one more 6 added, so stepping from one multiple of 6 to the next always adds exactly 6.
Why?
Six groups of 13 is six groups of (12 and 1), which is six groups of 12 plus six groups of 1, so 78 is just 72 with one more 6.
🧱Distributive propertya groups of (b and c) is a groups of b plus a groups of c — you can split the group.
Why?
76 breaks with no gap or overlap into 72 and 4, so once 72 is six full groups the leftover 4 sits between the multiples 72 and 78.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
3STEP 3
Compute how many more are needed
Subtract the current 76 from the target 78: just 2 more notebooks are needed.
78 - 76 = 2
Adding 2 turns the leftover of 4 into a complete sixth share, so the split is exact.
3.OA.A.3Guess And CheckAnswer
2
78 - 76 = 2
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.
Takeaway
This only needs Grade 3 division sense: find the leftover, then add just enough to finish the group!
- Divide to see the leftover
- Find the next multiple of 6
- Compute how many more are needed
Where next?
Level upsuggested
Another one like thissuggested
Same look, different logicsuggested
Step back and solidifysuggested