# Division with Remainders

Ensure nothing is left-over in your revision schedule by completing division with remainders at KS3 level.

Here, we’ll show you how to get to grips with the topic’s basics whilst highlighting worked examples that show methodology alongside set questions.

The content will suit KS3 Maths pupils/classes and we’ve included a few tasks – direct questions and word problems – at the bottom of the page for learners to try out.

Pupils should have prior knowledge of the times tables in order to gain the most from this tutorial-style post.

You can check out the full Division with Remainders worksheet pack here

### Division with Remainders Methodology

When you divide a number by another number, you are sharing out that number into equal-sized groups.

Example 1:

12 ÷ 4

You can think of this as 12 lines:

As we are dividing by 4, we split up the lines into groups of 4:

This gives us 3 groups, so 12 ÷ 4 = 3

Example 2:

11 ÷ 3

We’re dividing by 3 so we split our lines up into groups of 3:

This time, we have divided 11 into groups of 3. We have 3 groups with 2 left over. These 2 are our remainder. We can say:

11 ÷ 3 = 3 remainder 2, or 3r2.

Once you get used to this, you can try it without writing lines, by using your times tables.

Example 3:

17 ÷ 5

From your 5 times table, you know that 3 × 5 = 15 but 15 isn’t the number we’re looking for. You also know that 4 × 5 = 20, but this is too big.

If we know 3 × 5 = 15, we can then count on to the number we want, 17. To get from 15 to 17, we have to count on 2, so that is our remainder.

17 ÷ 5 = 3r2

Sometimes, you are asked to divide a smaller number by a bigger number.

Example 4:

5 ÷ 6

In this example, you can imagine you have 5 lines. The question is asking you how many groups of 6 you can make with those 5 lines, or how many times 6 fits into 5. The answer to this is 0. However, we haven’t divided up any of our 5 lines, so we have a remainder of 5.

5 ÷ 6 = 0r5

Be very careful with this type of question. Sometimes people change the order of the division, and work out 6 ÷ 5 = 1r1. This is the answer to a different question! Unfortunately, you cannot swap the numbers in a division.

1a) 18 ÷ 3

b) 48 ÷ 6

2a) 13 ÷ 5

b) 25 ÷ 6

c) 70 ÷ 8

d) 130 ÷ 12

### Word Problems

1. Jamie has 19 sweets and wants to share them between 5 friends so each friend gets the same amount. How many sweets will be left over?
2. Sam has 26 bricks and wants to make them into 4 equal-height towers. How many bricks will be left over?
3. There are 23 pupils in a class. Each table can hold 4 pupils. How many tables will the teacher need?

1a) 18 ÷ 3 = 6

1b) 48 ÷ 6 = 8

2a) 13 ÷ 5 = 2r3

2b) 25 ÷ 6 = 4r1

2c) 70 ÷ 8 = 8r6

2d) 130 ÷ 12 = 10r10

1. Jamie has 19 sweets and wants to share them between 5 friends so each friend gets the same amount. How many sweets will be left over?
19 ÷ 5 = 3r4, so 4 sweets will be left over.
2. Sam has 26 bricks and wants to make them into 4 equal-height towers. How many bricks will be left over?
26 ÷ 4 = 6r2, so 2 bricks will be left over.
3. There are 23 pupils in a class. Each table can hold 4 pupils. How many tables will the teacher need?
23 ÷ 4 = 5r3. As you can’t have “remainder 3” of a table, the teacher will need 6 tables.

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