Year 6: The order of operations
Part of the Year 6 long multiplication, long division and bodmas chapter. Chapter overview · whole chapter on one page
The order of operations
When a calculation has more than one operation, we must follow the order of operations. Otherwise two people could work out the same calculation and get different answers.
- Brackets first.
- Multiplication and division, from left to right.
- Addition and subtraction, from left to right.
A way to remember the order is BIDMAS: Brackets, Indices (powers), Division and Multiplication, Addition and Subtraction. This chapter uses brackets, multiplication and division, and addition and subtraction.
Key ideas
- Brackets come first. Work out the sum inside them.
- Multiplication and division come before addition and subtraction, even if the addition is written first.
- When two operations have the same rank, work from the left: 12 ÷ 3 × 2 = 8, not 2.
- Brackets can change the answer. (2 + 3) × 4 = 20, but 2 + 3 × 4 = 14.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.3 + 4 × 5 = 3 + 20
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.3 + 20 = 23
- Write the answer. 23
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.3 + 4 = 7
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.( 3 + 4 ) × 5 = 7 × 5
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.7 × 5 = 35
- Write the answer. 35
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.20 − 12 ÷ 3 + 2 × 5 = 20 − 4 + 2 × 5
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.20 − 4 + 2 × 5 = 20 − 4 + 10
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.20 − 4 + 10 = 16 + 10
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.16 + 10 = 26
- Write the answer. 26
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.2 + 6 = 8
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.24 ÷ ( 2 + 6 ) × 3 = 24 ÷ 8 × 3
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.24 ÷ 8 × 3 = 3 × 3
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.3 × 3 = 9
- Write the answer. 9
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Watch out
The most common mistake is to work from left to right and ignore the order. In 3 + 4 × 5, the answer is 23, not 35. Another mistake is to forget that division and multiplication are done from left to right: 24 ÷ 8 × 3 is 3 × 3 = 9, not 24 ÷ 24 = 1.Exercise 2E Order of operations
Non-calculatorKey words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.2 + 3 × 4 = 2 + 12
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.2 + 12 = 14
- Write the answer. 14
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.10 − 6 ÷ 2 = 10 − 3
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.10 − 3 = 7
- Write the answer. 7
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.5 × 4 + 6 = 20 + 6
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.20 + 6 = 26
- Write the answer. 26
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.18 ÷ 3 × 2 = 6 × 2
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.6 × 2 = 12
- Write the answer. 12
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.2 + 3 = 5
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.( 2 + 3 ) × 4 = 5 × 4
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.5 × 4 = 20
- Write the answer. 20
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.6 ÷ 2 = 3
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.10 − ( 6 ÷ 2 ) = 10 − 3
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.10 − 3 = 7
- Write the answer. 7
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.4 + 5 = 9
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.3 × ( 4 + 5 ) = 3 × 9
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.3 × 9 = 27
- Write the answer. 27
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.12 − 4 = 8
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.( 12 − 4 ) ÷ 2 = 8 ÷ 2
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.8 ÷ 2 = 4
- Write the answer. 4
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.40 − 6 × 5 + 12 ÷ 4 = 40 − 30 + 12 ÷ 4
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.40 − 30 + 12 ÷ 4 = 40 − 30 + 3
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.40 − 30 + 3 = 10 + 3
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.10 + 3 = 13
- Write the answer. 13
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.20 + 4 = 24
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.( 20 + 4 ) ÷ 6 × 5 = 24 ÷ 6 × 5
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.24 ÷ 6 × 5 = 4 × 5
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.4 × 5 = 20
- Write the answer. 20
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.7 × 8 − 4 × 6 + 2 = 56 − 4 × 6 + 2
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.56 − 4 × 6 + 2 = 56 − 24 + 2
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.56 − 24 + 2 = 32 + 2
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.32 + 2 = 34
- Write the answer. 34
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.3 × 5 + 4 × 2 = 15 + 4 × 2
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.15 + 4 × 2 = 15 + 8
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.15 + 8 = 23
- Write the answer. 23
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.2 × 80 + 95 = 160 + 95
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.160 + 95 = 255
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.500 − ( 2 × 80 + 95 ) = 500 − 255
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.500 − 255 = 245
- Write the answer. 245
Check. The cakes and the drink cost 255p. 500p − 255p = 245p, which is £2.45. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.6 × 12 + 4 × 15 = 72 + 4 × 15
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.72 + 4 × 15 = 72 + 60
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.72 + 60 = 132
- Write the answer. 132
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.2 + 3 = 5
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.( 2 + 3 ) × 4 − 1 = 5 × 4 − 1
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.5 × 4 − 1 = 20 − 1
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.20 − 1 = 19
- Write the answer. 19
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
- Work out inside the brackets. Brackets come first. Inside them, multiply and divide before adding and subtracting.10 − 4 = 6
- Replace the brackets with their answer. The brackets are done, so the calculation is simpler now.( 10 − 4 ) ÷ 2 + 3 = 6 ÷ 2 + 3
- Multiply and divide, from left to right. Multiplication and division come before addition and subtraction.6 ÷ 2 + 3 = 3 + 3
- Add and subtract, from left to right. Work from the left. Addition and subtraction are done last.3 + 3 = 6
- Write the answer. 6
Check. Read the calculation again and follow the same order. ✓
Watch out. Multiplication and division come before addition and subtraction, even when the addition is written first.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Work out the calculation in the order of operations. Sam did the addition first.
- Find Sam's mistake. Sam added 5 and 3 first. Multiplication must come before addition.5 + 3 = 8, then 8 × 2 = 16 (wrong order)
- Work out the multiplication first. Multiply 3 by 2 before you add.3 × 2 = 6
- Add the answer. Now add 5 to the answer from the multiplication.5 + 6 = 11
Check. 5 + 3 × 2 = 5 + 6 = 11. ✓
Watch out. Sam's method is wrong because he did the addition before the multiplication.
Key words. The order of operations is the order in which we work out a calculation. Brackets come first, then multiplication and division (from left to right), then addition and subtraction (from left to right).
Method. Work out each calculation separately, then compare the two answers.
- Work out 2 + 3 × 6. Multiply first: 3 × 6 = 18, then add 2.2 + 18 = 20
- Work out (2 + 3) × 6. The brackets come first: 2 + 3 = 5, then 5 × 6.5 × 6 = 30
- Compare the answers. The brackets changed the order, so the answers are different.20 and 30 are different
Check. 2 + 3 × 6 = 20, and (2 + 3) × 6 = 30. ✓
Watch out. Brackets are a way to change the order. Always look for them first.