Sensim Math · Depth 한국어

3-2 · Division

Adjust the total to leave no remainder

3.OA.A.33.OA.C.7 · take · grade 3

Archetype: Divisibility and Remainder Reasoning · step in a 8-type progression

▶ Practice — 11 problems

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

Understand

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).

Plan

#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.

Execute

#9 Solve an Easier Related Problem 3.OA.C.7
Divide 76 by 6. Six 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.
#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.
#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 sixth share, so the split is exact.
Answer: 2 notebooks

Review

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.

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.

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