Steply

Order of operations

Foundations · 24 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Powers
  2. Times and divide
  3. Plus and minus

The steps for Calculate -2^2 + 3 × 4. Every solution names its steps, so you always know what comes next.

Worked examples

Calculate 5 + 4 × 2 Easy

The question

Question: work out 5 + 4 × 2.

5 + 4 × 2

1 Times and divide

Times comes before plus.

Order: ( ) → x² √ → × ÷ → + −

4 times 2 is 8.

= 5 + 8

2 Plus and minus

5 plus 8 is 13.

= 13

Careful!

Many people go from left to right and get 18.

But times and divide come before plus and minus.

Careful: not 5 + 4 × 2 = 18 ✗

So the answer is 13.

Let's look back.

First: times and divide.

Last: plus and minus.

Answer
= 13

▶ Watch it solved

Calculate 24 ÷ 4 × 3 Medium

The question

Question: work out 24 ÷ 4 × 3.

24 ÷ 4 × 3

1 Times and divide

Times and divide: we go from left to right.

same kind: left → right

24 divided by 4 is 6.

= 6 × 3

6 times 3 is 18.

= 18

So the answer is 18.

Answer
= 18

▶ Watch it solved

Calculate -2^2 + 3 × 4 Harder

The question

Question: work out −2² + 3 × 4.

−22 + 3 × 4

1 Powers

Powers come before plus and times.

In −2², the power is only on the 2.

The minus stays in front.

Order: ( ) → x² √ → × ÷ → + −

Careful!

It is not (−2)².

Without brackets, the minus stays outside.

Careful: not −22 = 4 ✗

2² means 2 times 2.

22 = 2 × 2 = 4

That is 4.

= −4 + 3 × 4

2 Times and divide

Times comes before plus.

3 times 4 is 12.

= −4 + 12

3 Plus and minus

Start at −4.

Go up 12.

We land on 8.

= 8

So the answer is 8.

Let's look back.

First: powers.

Then: times and divide.

Last: plus and minus.

Answer
= 8

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. 5 + 4 × 2
    Answer
    = 13
  2. 10 - 6 ÷ 2
    Answer
    = 7
  3. (5 + 3) × 2
    Answer
    = 16
  4. 20 ÷ (2 + 3)
    Answer
    = 4
  5. 7 × 2 - 5
    Answer
    = 9
  6. 18 - 3 × 4
    Answer
    = 6
  7. 2 × (9 - 4)
    Answer
    = 10
  8. 12 - 3 × 4
    Answer
    = 0
  9. 4 + 12 ÷ 4 - 1
    Answer
    = 6
  10. 6 × 3 ÷ 9
    Answer
    = 2

Medium

  1. 24 ÷ 4 × 3
    Answer
    = 18
  2. 2 + 3^2 × 2
    Answer
    = 20
  3. (8 - 2)^2 ÷ 4
    Answer
    = 9
  4. 5 × (2 + 6) ÷ 4
    Answer
    = 10
  5. 3 + 2 × (7 - 4)^2
    Answer
    = 21
  6. 40 - (3 + 2)^2
    Answer
    = 15
  7. 2^3 - 4 × 3
    Answer
    = −4
  8. 18 ÷ (5 - 2) × 2
    Answer
    = 12
  9. 6 ÷ (1 + 3)
    Answer
    = 32
  10. 16 - 8 ÷ 2 + 1
    Answer
    = 13

Harder

  1. -2^2 + 3 × 4
    Answer
    = 8
  2. (12 - 4) ÷ (5 - 1) × 3
    Answer
    = 6
  3. 4 + 3 × (8 - 2^2) ÷ 6
    Answer
    = 6
  4. 20 ÷ (1 + 3) - 2^2 × 2
    Answer
    = −3