Order of operations and expressions (grade 5) · lesson

Multiply and divide before you add and subtract

💡 Do times and divide before plus and minus.

In 7 + 2 × 4, do 2 × 4 first. That is 8. Then 7 + 8 = 15.

If you added first, you would get 36. That is not right.

🧠 Let's work it out

Find the value of 9 − 3 × 2.

What do you think comes next?

💡 Do what is inside parentheses before anything else.

Parentheses ( ) say: do this part first.

(6 + 3) × 2: add first to get 9. Then 9 × 2 = 18.

🧠 Let's work it out

Find the value of (7 + 1) × 3.

What do you think comes next?

💡 With parentheses inside brackets, start with the innermost group and work out.

Brackets [ ] group things just like parentheses. They often hold parentheses inside them.

Do the parentheses first. Then finish the brackets. Then do the rest.

🧠 Let's work it out

Find the value of 4 × [10 − (3 + 2)].

What do you think comes next?

💡 Times and divide are a tie, so do them in order from left to right.

Times and divide have the same rank. So do whichever comes first as you read left to right.

24 ÷ 4 × 2: divide first because it comes first. 6 × 2 = 12. Then do any plus or minus last.

🧠 Let's work it out

Find the value of 30 ÷ 5 × 2 − 4.

What do you think comes next?

💡 Put parentheses around the step that has to happen first.

"Add 4 and 5, then times by 2" has the adding first. But times usually goes first.

So put the adding in parentheses: (4 + 5) × 2.

🧠 Let's work it out

Write "take 3 from 8, then times by 6."

What do you think comes next?