Grade 5 Long Division: Interpreting Remainders

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   A library is packing 982 books into boxes. Each box holds 20 books. How many boxes are needed to pack all of the books?

   1. We know the total (982) and how many fit in one group (20), and we want how many groups. That is division: 982 ÷ 20.
   2. 982 ÷ 20: take away 20 × 40 = 800 (182 left), 20 × 9 = 180 (2 left). 40 + 9 = 49, so 982 ÷ 20 = 49 R2.
   3. 49 boxes hold 980, but 2 more still need a place, so one more is needed: 49 + 1 = 50.
   4. So the answer is 50 boxes.

   Answer: 50

2. Example 2

   1397 students are going on a field trip. Each bus holds 52 students. How many buses are needed so every student has a seat?

   1. We know the total (1397) and how many fit in one group (52), and we want how many groups. That is division: 1397 ÷ 52.
   2. 1397 ÷ 52: take away 52 × 20 = 1040 (357 left), 52 × 6 = 312 (45 left). 20 + 6 = 26, so 1397 ÷ 52 = 26 R45.
   3. 26 buses hold 1352, but 45 more still need a place, so one more is needed: 26 + 1 = 27.
   4. So the answer is 27 buses.

   Answer: 27

3. Example 3

   A school needs 2181 muffins. Muffins are sold in trays of 36. How many trays must the school buy to have enough muffins?

   1. We know the total (2181) and how many fit in one group (36), and we want how many groups. That is division: 2181 ÷ 36.
   2. 2181 ÷ 36: take away 36 × 60 = 2160 (21 left). 2181 ÷ 36 = 60 R21.
   3. 60 trays hold 2160, but 21 more still need a place, so one more is needed: 60 + 1 = 61.
   4. So the answer is 61 trays.

   Answer: 61