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GRADE 6 · MATHEMATICS

Order of Operations

When an expression contains more than one operation, the steps must be completed in the correct order. Learn how brackets, multiplication, division, addition and subtraction work together so you can calculate expressions accurately.

Learning time: approximately 25 minutes · Beginner level

What You Will Learn

1. Why Does the Order Matter?

Without agreed rules, the same expression could produce different answers. The order of operations gives everyone a consistent method.

6 + 2 × 3

Multiply first: 2 × 3 = 6. Then add: 6 + 6 = 12.

If you add first, you would get a different result. That is why the order matters.

2. The Correct Order

  1. Brackets: Calculate inside brackets first.
  2. Multiplication and division: Complete these from left to right.
  3. Addition and subtraction: Complete these from left to right.
Important: Multiplication does not always come before division, and addition does not always come before subtraction. Operations at the same level are completed from left to right.

A common memory aid is BIDMAS or PEMDAS. The letters may be arranged differently, but the important rule is that multiplication and division share one level, and addition and subtraction share another.

3. Brackets First

Work out the calculation inside brackets before doing anything outside them.

Worked example: (8 + 4) ÷ 3

  1. Calculate inside brackets: 8 + 4 = 12.
  2. Divide: 12 ÷ 3 = 4.

Answer: 4.

Another example: 5 × (9 − 6) + 2

Brackets: 9 − 6 = 3. Multiplication: 5 × 3 = 15. Addition: 15 + 2 = 17.

4. Multiplication and Division Before Addition and Subtraction

After brackets, complete multiplication and division before addition and subtraction.

Worked example: 18 − 4 × 3

  1. Multiply first: 4 × 3 = 12.
  2. Subtract: 18 − 12 = 6.

Answer: 6.

Another example: 20 ÷ 5 + 7

Divide first: 20 ÷ 5 = 4. Then add: 4 + 7 = 11.

5. Work from Left to Right at the Same Level

When multiplication and division appear together, work from left to right. The same rule applies to addition and subtraction.

Worked example: 24 ÷ 6 × 2

  1. Division and multiplication have equal priority.
  2. Work from left to right: 24 ÷ 6 = 4.
  3. Then multiply: 4 × 2 = 8.

Answer: 8.

Another example: 15 − 4 + 3

Addition and subtraction have equal priority. Work left to right: 15 − 4 = 11, then 11 + 3 = 14.

Common trap: Do not automatically do multiplication before division just because M appears before D in a memory aid. They have equal priority.

6. A Complete Worked Example

30 − (4 + 2) × 3 ÷ 2
  1. Brackets: 4 + 2 = 6. Expression becomes 30 − 6 × 3 ÷ 2.
  2. Multiplication and division from left to right: 6 × 3 = 18.
  3. Then 18 ÷ 2 = 9.
  4. Finally subtract: 30 − 9 = 21.

Answer: 21.

7. Common Mistakes to Avoid

Working strictly from left to right for every operation: Brackets, multiplication and division have priority over addition and subtraction.
Putting multiplication above division: They have equal priority; work from left to right.
Putting addition above subtraction: They have equal priority; work from left to right.
Ignoring brackets: Always complete the calculation inside brackets first.

8. Practice Exercises

Try these before revealing the answers. Show each step.

  1. 7 + 3 × 4
  2. (7 + 3) × 4
  3. 20 − 12 ÷ 3
  4. 24 ÷ 4 × 2
  5. 18 − 5 + 2
  6. 6 + (8 − 2) × 3
  7. 36 ÷ (3 × 4) + 5
  8. 40 − 18 ÷ 3 × 2
Show practice answers and working
  1. 3 × 4 = 12; 7 + 12 = 19.
  2. 7 + 3 = 10; 10 × 4 = 40.
  3. 12 ÷ 3 = 4; 20 − 4 = 16.
  4. 24 ÷ 4 = 6; 6 × 2 = 12.
  5. 18 − 5 = 13; 13 + 2 = 15.
  6. 8 − 2 = 6; 6 × 3 = 18; 6 + 18 = 24.
  7. 3 × 4 = 12; 36 ÷ 12 = 3; 3 + 5 = 8.
  8. 18 ÷ 3 = 6; 6 × 2 = 12; 40 − 12 = 28.

9. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

1. What should you calculate first in 8 + 2 × 5?
2. What is (6 + 4) × 3?
3. What is 24 ÷ 6 × 2?
4. What is 20 − 4 × 3?
5. What is 15 − 4 + 3?

10. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 6 Mathematics

Order of Operations Worksheet

Name: __________________________ Date: _______________

Instructions: Show the order of each step.

  1. 9 + 2 × 6
  2. (9 + 2) × 6
  3. 32 ÷ 4 + 5
  4. 28 − 3 × 6
  5. 36 ÷ 3 × 2
  6. 20 − 7 + 4
  7. 5 + (12 − 4) ÷ 2
  8. 48 − 24 ÷ 4 × 2

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. 9 + 12 = 21.
  2. 11 × 6 = 66.
  3. 8 + 5 = 13.
  4. 28 − 18 = 10.
  5. 12 × 2 = 24.
  6. 20 − 7 = 13; 13 + 4 = 17.
  7. 12 − 4 = 8; 8 ÷ 2 = 4; 5 + 4 = 9.
  8. 24 ÷ 4 = 6; 6 × 2 = 12; 48 − 12 = 36.

11. Lesson Summary

Next learning goal: Apply order of operations to longer expressions and problems with powers when you are ready for the next level.

Educational note: This is a curriculum-neutral Grade 6 lesson. Teachers and parents can adapt examples and practice to their local curriculum.