Grade 5 (age 10-11)

grade 5 Mixed Operations

A mixed calculation is an expression that mixes addition, subtraction, multiplication, division and brackets, worked out in an agreed order. Work out 3 + 4 × 2 from left to right and you get 14; do the multiplication first and you get 11. Without an agreed order, the same expression would have two answers. So brackets come first, then multiplication and division, and finally addition and subtraction; operations of the same rank go from left to right. Choose an expression below and move through the steps one at a time to see which part is worked out first.

Why agree on an order?

🤔 What is 3 + 4 × 2?

①Working left to right gives 3 + 4 = 7, then 7 × 2 = 14

②Multiplying first gives 4 × 2 = 8, then 3 + 8 = 11

③Think of 3 loose sweets plus 4 bags of 2 sweets: that is 3 + 8 = 11 sweets, so 11 is right

④The order of operations is an agreement so that everyone gets the same answer from the same expression

The order of operations

💡 Three rules

①Work out what is inside brackets ( ) first

②Then do multiplication (×) and division (÷)

③Do addition (+) and subtraction (−) last

④Multiplication and division share a rank, and so do addition and subtraction; within the same rank, work from left to right

Working step by step

Step0

✅ How to work through one

①First check whether the expression has brackets, and if it does, start inside them

②Underline the multiplications and divisions and work them out from the left

③Then do the remaining additions and subtractions from the left

④24 ÷ (8 − 2) + 5: brackets first, 8 − 2 = 6, then 24 ÷ 6 = 4, and finally 4 + 5 = 9

⑤In 20 − 3 × 4 + 2, after 3 × 4 = 12 you have 20 − 12 + 2, which goes left to right: 20 − 12 = 8, then 8 + 2 = 10. Doing 12 + 2 first would give 6, which is wrong

Summary

Order of operations

Brackets ( ) → × ÷ → + −

Within the same rank, work from left to right

A wrong method

3 + 4 × 2 ≠ 14

Adding first, from the left, gives the wrong answer

The right method

3 + 4 × 2 = 3 + 8 = 11

Work out the multiplication 4 × 2 = 8 first, then add

🎯 At a glance

①Brackets come first

②Multiplication and division come before addition and subtraction

③Within the same rank, go from left to right

④Underlining the part to do first helps you avoid mistakes

⑤Adding brackets can change the order, and so the answer

Examples and Unit Test

Example 1

Work out 3 + 4 × 2.

Multiply before adding: 4 × 2 = 8.

Then add: 3 + 8 = 11.

▸ 11

Choose the first expression in the picture to watch it worked out in the same order.

Example 2

Work out (3 + 4) × 2. Is the answer the same as in Example 1?

Brackets first: 3 + 4 = 7.

Then multiply: 7 × 2 = 14. The brackets make the answer different from the 11 in Example 1.

▸ 14

Brackets change the order of working, so the same numbers and signs can give a different answer depending on where the brackets go.

Unit Test

What is 20 − 12 ÷ 4?

①2

②17

③8

④11

▸ ② 17

Divide first: 12 ÷ 4 = 3.

Then subtract: 20 − 3 = 17.

← Previous

Mixed Number Operations

Congruence & Symmetry

Last updated 2026-10-17