Skip to content
SuccessHomeschool
Menu
Log inStart free

Primary 6 · Mathematics · Algebra

Order of operations

Use the conventions for the order of operations, including brackets, to evaluate number sentences and find unknown values.

Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026. How we review

These lessons were written around Australian Curriculum strands and matched to Singapore levels by age (Primary 1 is the first year of primary school). They are not aligned to MOE syllabuses or the PSLE, so check them against the syllabus your child is working towards.

Learning goals

Learners will

  • Understand why we need an agreed order for carrying out operations.
  • Evaluate number sentences using brackets first, then multiplication and division, then addition and subtraction.
  • Use the order of operations to find unknown values and to write number sentences for word problems.

Success looks like

  • I can explain that brackets are done first, then × and ÷ from left to right, then + and − from left to right.
  • I can work out the value of a number sentence with mixed operations, showing each step.
  • I can find a missing number in a number sentence with more than one operation.

The big idea

What is 5 + 3 × 4? If you work from left to right you get 8 × 4 = 32. If you multiply first you get 5 + 12 = 17. Two different answers to the same question would cause chaos, so mathematicians everywhere agree on an order of operations.

The agreed order is:

  • Brackets first.
  • Then multiplication and division, working from left to right.
  • Then addition and subtraction, working from left to right.

So 5 + 3 × 4 = 5 + 12 = 17. If we want the addition done first, we use brackets: (5 + 3) × 4 = 8 × 4 = 32.

Multiplication and division have equal priority, so we do whichever comes first reading from left to right. In 40 ÷ 8 × 2, we divide first: 40 ÷ 8 = 5, then 5 × 2 = 10. The same is true for addition and subtraction: 20 − 5 + 3 = 15 + 3 = 18.

Showing one step per line helps avoid mistakes. Each time, rewrite the whole number sentence with one part worked out, then continue.

The order of operations also helps us write and solve problems. Buying 3 notebooks at $4 each and one pen for $2 can be written as 3 × 4 + 2 = 14. To find an unknown in 3 × ? + 4 = 25, undo the steps in reverse order: first undo the + 4 (25 − 4 = 21), then undo the × 3 (21 ÷ 3 = 7).

Worked examples

Multiplication and division before addition and subtraction

Evaluate 20 − 12 ÷ 4 + 1.

  1. There are no brackets.
  2. Do the division first: 12 ÷ 4 = 3. The sentence becomes 20 − 3 + 1.
  3. Now add and subtract from left to right: 20 − 3 = 17, then 17 + 1 = 18.

Answer: 20 − 12 ÷ 4 + 1 = 18

Brackets first

Evaluate 36 ÷ (2 + 4) × 3.

  1. Brackets first: 2 + 4 = 6. The sentence becomes 36 ÷ 6 × 3.
  2. Division and multiplication have equal priority, so work from left to right.
  3. 36 ÷ 6 = 6, then 6 × 3 = 18.

Answer: 36 ÷ (2 + 4) × 3 = 18

Finding an unknown value

Find the unknown value: (? − 3) × 5 = 40.

  1. The bracket is multiplied by 5 to make 40, so the bracket must equal 40 ÷ 5 = 8.
  2. Now solve ? − 3 = 8. Undo the subtraction: 8 + 3 = 11.
  3. Check: (11 − 3) × 5 = 8 × 5 = 40.

Answer: The unknown value is 11.

Practice check

Have a go, then check your answers. Each answer comes with an explanation.

  1. 1.What is 6 + 4 × 2?
  2. 2.What is (6 + 4) × 2?
  3. 3.What is 18 − 6 ÷ 3?
  4. 4.Which of these is equal to 30?
  5. 5.Evaluate 24 ÷ 4 + 2 × 3.
  6. 6.Evaluate 50 − (12 + 8) × 2.
  7. 7.Find the unknown value: 3 × ? + 4 = 25.
  8. 8.Evaluate 40 ÷ 8 × 2.
Answer guide for parents

  1. What is 6 + 4 × 2?

    14 — Multiply first: 4 × 2 = 8. Then 6 + 8 = 14.

  2. What is (6 + 4) × 2?

    20 — Brackets first: 6 + 4 = 10. Then 10 × 2 = 20.

  3. What is 18 − 6 ÷ 3?

    16 — Divide first: 6 ÷ 3 = 2. Then 18 − 2 = 16.

  4. Which of these is equal to 30?

    (2 + 4) × 5 — (2 + 4) × 5 = 6 × 5 = 30. The others equal 22, 22 and 13.

  5. Evaluate 24 ÷ 4 + 2 × 3.

    12 — Do the division and multiplication first: 24 ÷ 4 = 6 and 2 × 3 = 6. Then 6 + 6 = 12.

  6. Evaluate 50 − (12 + 8) × 2.

    10 — Brackets first: 12 + 8 = 20. Then multiply: 20 × 2 = 40. Finally 50 − 40 = 10.

  7. Find the unknown value: 3 × ? + 4 = 25.

    7 — Undo the + 4: 25 − 4 = 21. Undo the × 3: 21 ÷ 3 = 7. Check: 3 × 7 + 4 = 21 + 4 = 25.

  8. Evaluate 40 ÷ 8 × 2.

    10 — Division and multiplication have equal priority, so work from left to right: 40 ÷ 8 = 5, then 5 × 2 = 10.

Watch out for

  • Always working from left to right, for example 5 + 3 × 4 = 32. Remind the learner that × and ÷ come before + and − unless brackets say otherwise.
  • Thinking multiplication always comes before division (or addition before subtraction) because of the order in a memory aid. In 40 ÷ 8 × 2, divide first because it comes first from the left, giving 10, not 40 ÷ 16.
  • Losing track of numbers when doing several steps at once. Rewrite the whole number sentence after each single step.

Tips for parents

  • Ask the learner to say which operation they will do first, and why, before calculating.
  • Try the same calculation on different calculators or phone apps and discuss any differences. Most scientific calculators follow the order of operations, but some basic ones work left to right.
  • Turn real situations into number sentences, such as the cost of several items plus delivery, and decide together where brackets are needed.

Go further

  • Play “Target 24”: draw four cards and use each number once with +, −, ×, ÷ and brackets to make 24. For example, with 1, 2, 3 and 4 you could write 1 × 2 × 3 × 4 = 24 or (1 + 2 + 3) × 4 = 24. Find as many solutions as you can.
  • Use four 4s and any operations and brackets to make every whole number from 0 to 10. For example, 4 ÷ 4 + 4 ÷ 4 = 2.
  • Write a number sentence with no brackets, then see how many different answers you can make by adding brackets in different places.

About 45 minutes

Make a lesson planAssign to my child

You'll need

  • Paper and pencil
  • A calculator (to explore how calculators handle the order of operations)
  • A pack of playing cards or digit cards (for the enrichment game)

Key words

Operation
A mathematical action such as addition, subtraction, multiplication or division.
Order of operations
The agreed order for working out a calculation with more than one operation.
Brackets
The symbols ( ) that group part of a calculation so it is worked out first.
Evaluate
To work out the value of a number sentence.
Left to right
When operations have equal priority, they are worked out in the order they appear, reading from left to right.
More Primary 6 maths worksheets on Success Tutoring Worksheets →

Still tricky?

For parents

Want an outside view of where your child is at?

Book a free, no-obligation English and maths assessment at a Success Tutoring centre and get a clear starting point.

Book a free assessment

Related algebra lessons

Build up to it (Primary 5)

Next steps (Secondary 1)