This page has been put together to help you practise and revisit some of the brilliant skills you’ve learned all through primary school.

It’s a great way to boost your confidence in maths and get you ready for the exciting next step into Year 8!

What do you do with your leftovers?

When a number doesn't divide perfectly, you get a remainder.

The real challenge isn't just finding the remainder, it's knowing what to do with it.

In this guide, you will learn:

• how to find a remainder using short division (eg 17 ÷ 4 = 4 r 1)

• the three ways to handle a remainder in a word problem

Case 1: When you must round up.

Case 2: When you must round down.

Case 3: When the remainder is the answer.

When you divide using the 'bus stop' method, the number left at the end that is too small to be divided is the remainder.

Example: 15 ÷ 6

1 ÷ 6 doesn't go.

Carry the 1 over to the 5, making 15.

How many 6s go into 15? 2 (because 2 x 6 = 12).

What is the 'leftover' amount? 15 - 12 = 3.

So, 15 ÷ 6 = 2 remainder 3.

But what does “2 r 3” mean? The answer could be 2, or 3. It all depends on the story.

Top tip: the golden rule

The calculation (eg 15 ÷ 6 = 2 r 3) is only the first step.

Before you answer, re-read the question and ask yourself:

Do I need another whole one to fit everyone/everything in? (Round up)

Does it ask for complete groups? (Round down)

Does it ask what is left over? (Remainder is the answer)

This happens when everyone or everything must be included.

Problem:‘A group of 40 pupils are going on a trip. A minibus can hold 6 pupils. How many minibuses are needed?’

Solution:

Sum: 40 ÷ 6 = 6 r 4

Thinking: 6 buses would only hold 36 pupils (6 x 6). You still have 4 pupils left on the pavement!

Context: To get all 40 pupils to the trip, you need another bus for those 4 leftovers.

Answer: You must round up. You need 7 minibuses.

This happens when the question asks for complete or full items.

Problem: ‘A teacher has 40 pupils. She wants to make complete teams of 6 for a game. How many full teams can she make?’

Solution:

Sum: 40 ÷ 6 = 6 r 4

Thinking: You can make 6 full teams (36 pupils). You have 4 pupils left over, which is not enough for another complete team.

Context: The question only wants to know about full teams. The remainder is ignored.

Answer: You must round down. She can make 6 full teams.

This happens when the question asks "how many are left?" or "how many are remaining?"

Problem: ‘A teacher has 40 sweets to share equally among 6 prize winners. How many sweets will be left over?’

Solution:

Sum: 40 ÷ 6 = 6 r 4

Thinking: Each pupil gets 6 sweets (6 x 6 = 36). The amount 'left over' is the remainder.

Context: The question is only asking about the leftover amount.

Answer: The remainder is the answer. There are 4 sweets left over.

You are now a master of remainders!

You know that a calculation like 17 ÷ 5 = 3 r 2 is just the start.

You also know how to read the context to decide if the true answer is 3 (rounding down), 4 (rounding up), or 2 (the remainder itself).

This is a top-level problem-solving skill.

Think about these questions to stretch your thinking and sharpen your skills!

• Describe a real-life situation where you would have to round up the answer to a division sum.

• Describe a real-life situation where you would have to round down and ignore the remainder.

• A school of 100 pupils is going to the cinema. The cinema seats are in rows of 8. A teacher says, "100 divided by 8 is 12 remainder 4." What three different questions could be asked that would give the answer 12, 13, or 4?

Have a chat about your answers with a parent, teacher or your class.