Lesson: Order of Operations (Grade 5)

Math has rules about what to do first, so everyone gets the same answer.

The puzzle

What is 3 + 4 × 2?

• If you add first: 3 + 4 = 7, then 7 × 2 = 14. ❌
• If you multiply first: 4 × 2 = 8, then 3 + 8 = 11. ✔

The right answer is 11, because multiplying comes before adding.

Walk down the stairs

Always start at the top step and walk down.

1. Brackets ( ) first
2. Powers like 3² (that's 3 × 3)
3. Times and divide
4. Plus and minus

Memory trick: Please Excuse My Dear Aunt Sally (PEMDAS).

The tricky part

On step 3, times and divide are friends. Neither goes first. You just go left to right, like reading.

Step 4 is the same: plus and minus go left to right.

• 12 ÷ 3 × 2 → 12 ÷ 3 = 4, then 4 × 2 = 8
• 10 − 4 + 3 → 10 − 4 = 6, then 6 + 3 = 9

A full example

2 + 3 × (8 − 5)²

Write a new line after every step:

2 + 3 × (8 − 5)²     brackets: 8 − 5 = 3
2 + 3 × 3²           power: 3² = 9
2 + 3 × 9            times: 3 × 9 = 27
2 + 27               plus
29

Answer: 29

Your turn

• 6 + 2 × 5 = ? (16)
• (6 + 2) × 5 = ? (40)
• 20 − 2³ = ? (12, because 2³ = 2 × 2 × 2 = 8)
• 18 ÷ 6 × 3 = ? (9)

Practice

Try Order of Operations with Exponents. For an easier start, use the Grade 4 version, which has no powers.