Year 5AC9M5N07

Division with Remainders

Solve problems involving division, choosing efficient strategies; interpret any remainder according to the context and express results as a whole number, decimal or fraction.

Read this first

Dividing shares an amount into equal groups. Sometimes there is a bit left over. That bit is the remainder.

17 shared into rows of 5 fills 3 rows, with 2 left over. So $17 \div 5 = 3$ remainder 2.

Words you need

Remainder: What is left over when the sharing will not come out even.
Divisor: The number you are dividing by.
Quotient: How many whole groups you made.

Worked example

e.g. Work out

58 \div 4

Ask how many 4s fit into 5. Just one, with 1 left over.
Carry that 1 across to make 18. Now ask how many 4s fit into 18. Four of them, and $4 \times 4 = 16$ .
$18 - 16 = 2$ . So 2 is left over.
So $58 \div 4 = 14$ remainder 2.
Check it. $14 \times 4 = 56$ , and $56 + 2 = 58$ . ✓

Always check by multiplying back and adding the remainder. It should give you the number you started with.

Practice

The pictures fade as you go. By the last few you are on your own.

1Share 14 counters into groups of 4. How many groups, and how many left over?with a picture

Answer3 groups with 2 left over.

14 \div 4 = 3

remainder 2.

2Work out

37 \div 5

.with a hint

Need a hint?

How many 5s fit into 37? Count up in fives.

Answer7 remainder 2.

7 \times 5 = 35

, and

37 - 35 = 2

3Work out

92 \div 7

.with a hint

Need a hint?

How many 7s in 9? Then carry what is left across to the 2.

Answer13 remainder 1.

13 \times 7 = 91

, and

91 + 1 = 92

46 \div 3

on your own

Answer15 remainder 1

75 \div 8

on your own

Answer9 remainder 3

100 \div 6

on your own

Answer16 remainder 4

729 children go on a trip. Each car holds 4 children. How many cars are needed?on your own

Answer8 cars.

29 \div 4 = 7

remainder 1, but that last child still needs a car, so round up to 8.

8You have 50 stickers to share evenly between 6 friends. How many each, and how many left?on your own

Answer8 each, with 2 left over.

Think about it

Why does the car question need 8 cars when

29 \div 4

is 7 remainder 1?

One good answerThe remainder is a real child who still needs a seat. When the leftover still needs a group, round up. Read what the question is actually asking.

Can a remainder ever be bigger than the number you divided by?

One good answerNo. If it were, you could fit another whole group in. A remainder is always smaller than the divisor.

How can you check a division answer without dividing again?

One good answerMultiply your answer by the divisor, then add the remainder. You should get back to the number you started with.

Common mistakes

Leaving a remainder that is bigger than the divisor.

That means another whole group fits. Keep going.

Always rounding down in word problems.

Sometimes the leftover still needs a group, like children needing a car. Think about what the question is really asking.

Forgetting to carry the leftover across.

58 \div 4

, the 1 left from the 5 becomes part of 18. Miss it and the answer comes out far too small.