Year 6AC9M6A02

Brackets and Order of Operations

Find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations.

Read this first

Brackets go first. Then times and divide. Then add and subtract.

Change the order and you change the answer.

Words you need

Brackets: Symbols that say do this part first.
Operation: Adding, subtracting, multiplying or dividing.
Order: Which part you do first.

Worked example

e.g. Work out 4 + 2 x 5 and then (4 + 2) x 5.

In the first sum there are no brackets. Do times first.
2 x 5 = 10. Then 4 + 10 = 14.
In the second sum, the brackets come first.
4 + 2 = 6. Then 6 x 5 = 30.
Same numbers, different answers. The order matters.

If there are brackets, they always go first. No exceptions.

Practice

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

1What is 3 + 4 x 2?with a picture

Answer11. Times first.

2What is (3 + 4) x 2?with a picture

Answer14. Brackets first.

3What is 20 - 6 / 2?with a hint

Need a hint?

Divide before you subtract.

Answer17.

4Find the missing number: 3 x (? + 2) = 15with a hint

Need a hint?

What must the bracket equal?

Answer3.

5What is 10 - 2 x 3?on your own

Answer4.

6What is (10 - 2) x 3?on your own

Answer24.

7Add brackets to make 2 + 3 x 4 equal 20.on your own

Answer(2 + 3) x 4.

Think about it

Why do we need an agreed order?

One good answerSo everyone gets the same answer from the same sum.

What do brackets really do?

One good answerThey change which part happens first.

Common mistakes

Working from left to right always.

Times and divide come before add and subtract.

Ignoring the brackets.

They are an instruction, not decoration.