GCSE Maths: Order of operations (BIDMAS) (Foundation)
Part of the GCSE Maths number basics chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Order of operations (BIDMAS)
What is 2 + 3 × 4? If you work from left to right you get 5 × 4 = 20, but if you do the multiplication first you get 2 + 12 = 14. A calculation must have only one answer, so mathematicians agreed an order of priority. The 14 is correct. The order is remembered by BIDMAS (some people say BODMAS):
Brackets are done first: 3 × (8 − 5) = 3 × 3 = 9. Brackets are used to change the normal order. If there are brackets inside brackets, work out the innermost ones first.
Indices are powers and roots. A power such as 32 means 3 × 3 = 9 (“3 squared”); 23 means 2 × 2 × 2 = 8 (“2 cubed”). A root undoes a power: √49 = 7 because 72 = 49, and the cube root of 27 is 3 because 33 = 27. Learn the squares up to 152 = 225 and the cubes 1, 8, 27, 64, 125 (see Chapter 2).
Division and multiplication have the same priority, so work from left to right: 12 ÷ 3 × 2 = 4 × 2 = 8 (not 12 ÷ 6 = 2). Addition and subtraction also have the same priority, so work from left to right: 10 − 4 + 3 = 6 + 3 = 9 (not 10 − 7 = 3).
Fraction lines and root signs act like brackets. In 12 + 65 − 2 the top and the bottom are each worked out first, then divided: 18 ÷ 3 = 6. In √(9 + 16), work out 9 + 16 = 25 first, so the answer is √25 = 5. On a scientific calculator you must key in brackets for these: (12 + 6) ÷ (5 − 2).
Write each step on a new line and work out one thing at a time. This stops mistakes and earns method marks in an exam.
Key ideas
- BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.
- Division and multiplication have equal priority, and so do addition and subtraction: work left to right.
- A fraction line and a root sign act like brackets.
- (−3)2 = 9 but −32 = −9: the power only applies to what it touches.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.2 + 3 × 4
- Multiply: 3 × 4. Multiplication and division are done before addition and subtraction.2 + 3 × 4
3 × 4 = 12
= 2 + 12 - Add: 2 + 12. Only addition or subtraction is left, so do it now.2 + 12
2 + 12 = 14
= 14
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 14. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.(6 + 2) × 3 − 42
- Brackets first. Add: 6 + 2. Only addition or subtraction is left, so do it now.(6 + 2) × 3 − 42
6 + 2 = 8
= 8 × 3 − 42 - Indices (powers): work out 42. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.8 × 3 − 42
42 = 4 × 4 = 16
= 8 × 3 − 16 - Multiply: 8 × 3. Multiplication and division are done before addition and subtraction.8 × 3 − 16
8 × 3 = 24
= 24 − 16 - Subtract: 24 − 16. Only addition or subtraction is left, so do it now.24 − 16
24 − 16 = 8
= 8
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 8. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.12 + 65 − 2 + √49 × 2
- Work out the top of the fraction first (the fraction line acts like brackets). Add: 12 + 6. Only addition or subtraction is left, so do it now.12 + 65 − 2 + √49 × 2
12 + 6 = 18
= 185 − 2 + √49 × 2 - Work out the bottom of the fraction first (the fraction line acts like brackets). Subtract: 5 − 2. Only addition or subtraction is left, so do it now.185 − 2 + √49 × 2
5 − 2 = 3
= 183 + √49 × 2 - The fraction line means divide: divide the top by the bottom. A fraction is a division. We do this once the top and the bottom have each been worked out.183 + √49 × 2
18 ÷ 3 = 6
= 6 + √49 × 2 - Indices (roots): work out √49. The square root of a number is the number that multiplies by itself to give it. After brackets, powers and roots come next.6 + √49 × 2
√49 = 7 because 7 × 7 = 49
= 6 + 7 × 2 - Multiply: 7 × 2. Multiplication and division are done before addition and subtraction.6 + 7 × 2
7 × 2 = 14
= 6 + 14 - Add: 6 + 14. Only addition or subtraction is left, so do it now.6 + 14
6 + 14 = 20
= 20
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 20. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Watch out
Do not just work from left to right. 2 + 3 × 4 is 14, not 20. And write −32 carefully: the power is done first, so −32 = −9, but (−3)2 = 9.Exercise 1F Order of operations
Non-calculatorKey words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.2 + 3 × 4
- Multiply: 3 × 4. Multiplication and division are done before addition and subtraction.2 + 3 × 4
3 × 4 = 12
= 2 + 12 - Add: 2 + 12. Only addition or subtraction is left, so do it now.2 + 12
2 + 12 = 14
= 14
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 14. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.20 − 12 ÷ 4
- Divide: 12 ÷ 4. Multiplication and division are done before addition and subtraction.20 − 12 ÷ 4
12 ÷ 4 = 3
= 20 − 3 - Subtract: 20 − 3. Only addition or subtraction is left, so do it now.20 − 3
20 − 3 = 17
= 17
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 17. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.3 × 5 + 2 × 6
- Multiply: 3 × 5. Multiplication and division are done before addition and subtraction.3 × 5 + 2 × 6
3 × 5 = 15
= 15 + 2 × 6 - Multiply: 2 × 6. Multiplication and division are done before addition and subtraction.15 + 2 × 6
2 × 6 = 12
= 15 + 12 - Add: 15 + 12. Only addition or subtraction is left, so do it now.15 + 12
15 + 12 = 27
= 27
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 27. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.18 ÷ 3 + 4 × 2
- Divide: 18 ÷ 3. Multiplication and division are done before addition and subtraction.18 ÷ 3 + 4 × 2
18 ÷ 3 = 6
= 6 + 4 × 2 - Multiply: 4 × 2. Multiplication and division are done before addition and subtraction.6 + 4 × 2
4 × 2 = 8
= 6 + 8 - Add: 6 + 8. Only addition or subtraction is left, so do it now.6 + 8
6 + 8 = 14
= 14
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 14. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.7 + 8 ÷ 2 − 1
- Divide: 8 ÷ 2. Multiplication and division are done before addition and subtraction.7 + 8 ÷ 2 − 1
8 ÷ 2 = 4
= 7 + 4 − 1 - Add: 7 + 4. Addition and subtraction have the same priority, so work from left to right.7 + 4 − 1
7 + 4 = 11
= 11 − 1 - Subtract: 11 − 1. Only addition or subtraction is left, so do it now.11 − 1
11 − 1 = 10
= 10
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 10. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.5 × 4 − 3 × 2
- Multiply: 5 × 4. Multiplication and division are done before addition and subtraction.5 × 4 − 3 × 2
5 × 4 = 20
= 20 − 3 × 2 - Multiply: 3 × 2. Multiplication and division are done before addition and subtraction.20 − 3 × 2
3 × 2 = 6
= 20 − 6 - Subtract: 20 − 6. Only addition or subtraction is left, so do it now.20 − 6
20 − 6 = 14
= 14
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 14. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.(2 + 3) × 4
- Brackets first. Add: 2 + 3. Only addition or subtraction is left, so do it now.(2 + 3) × 4
2 + 3 = 5
= 5 × 4 - Multiply: 5 × 4. This is the only calculation left in this part.5 × 4
5 × 4 = 20
= 20
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 20. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.3 × (8 − 5)
- Brackets first. Subtract: 8 − 5. Only addition or subtraction is left, so do it now.3 × (8 − 5)
8 − 5 = 3
= 3 × 3 - Multiply: 3 × 3. This is the only calculation left in this part.3 × 3
3 × 3 = 9
= 9
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 9. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.(12 + 8) ÷ (7 − 3)
- Brackets first. Add: 12 + 8. Only addition or subtraction is left, so do it now.(12 + 8) ÷ (7 − 3)
12 + 8 = 20
= 20 ÷ (7 − 3) - Brackets first. Subtract: 7 − 3. Only addition or subtraction is left, so do it now.20 ÷ (7 − 3)
7 − 3 = 4
= 20 ÷ 4 - Divide: 20 ÷ 4. This is the only calculation left in this part.20 ÷ 4
20 ÷ 4 = 5
= 5
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 5. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.36 ÷ (2 + 4) × 3
- Brackets first. Add: 2 + 4. Only addition or subtraction is left, so do it now.36 ÷ (2 + 4) × 3
2 + 4 = 6
= 36 ÷ 6 × 3 - Divide: 36 ÷ 6. Multiplication and division have the same priority, so work from left to right.36 ÷ 6 × 3
36 ÷ 6 = 6
= 6 × 3 - Multiply: 6 × 3. This is the only calculation left in this part.6 × 3
6 × 3 = 18
= 18
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 18. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.2 × (3 + 4) × 5
- Brackets first. Add: 3 + 4. Only addition or subtraction is left, so do it now.2 × (3 + 4) × 5
3 + 4 = 7
= 2 × 7 × 5 - Multiply: 2 × 7. Multiplication and division have the same priority, so work from left to right.2 × 7 × 5
2 × 7 = 14
= 14 × 5 - Multiply: 14 × 5. This is the only calculation left in this part.14 × 5
14 × 5 = 70
= 70
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 70. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.32 + 42
- Indices (powers): work out 32. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.32 + 42
32 = 3 × 3 = 9
= 9 + 42 - Indices (powers): work out 42. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.9 + 42
42 = 4 × 4 = 16
= 9 + 16 - Add: 9 + 16. Only addition or subtraction is left, so do it now.9 + 16
9 + 16 = 25
= 25
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 25. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.52 − √49
- Indices (powers): work out 52. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.52 − √49
52 = 5 × 5 = 25
= 25 − √49 - Indices (roots): work out √49. The square root of a number is the number that multiplies by itself to give it. After brackets, powers and roots come next.25 − √49
√49 = 7 because 7 × 7 = 49
= 25 − 7 - Subtract: 25 − 7. Only addition or subtraction is left, so do it now.25 − 7
25 − 7 = 18
= 18
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 18. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.23 × 3
- Indices (powers): work out 23. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.23 × 3
23 = 2 × 2 × 2 = 8
= 8 × 3 - Multiply: 8 × 3. This is the only calculation left in this part.8 × 3
8 × 3 = 24
= 24
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 24. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.√36 + 23
- Indices (roots): work out √36. The square root of a number is the number that multiplies by itself to give it. After brackets, powers and roots come next.√36 + 23
√36 = 6 because 6 × 6 = 36
= 6 + 23 - Indices (powers): work out 23. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.6 + 23
23 = 2 × 2 × 2 = 8
= 6 + 8 - Add: 6 + 8. Only addition or subtraction is left, so do it now.6 + 8
6 + 8 = 14
= 14
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 14. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.3√27 × 22
- Indices (roots): work out 3√27. The cube root of a number is the number that multiplies by itself three times to give it. After brackets, powers and roots come next.3√27 × 22
3√27 = 3 because 3 × 3 × 3 = 27
= 3 × 22 - Indices (powers): work out 22. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.3 × 22
22 = 2 × 2 = 4
= 3 × 4 - Multiply: 3 × 4. This is the only calculation left in this part.3 × 4
3 × 4 = 12
= 12
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 12. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.(3 + 2)2 − 4 × 3
- Brackets first. Add: 3 + 2. Only addition or subtraction is left, so do it now.(3 + 2)2 − 4 × 3
3 + 2 = 5
= 52 − 4 × 3 - Indices (powers): work out 52. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.52 − 4 × 3
52 = 5 × 5 = 25
= 25 − 4 × 3 - Multiply: 4 × 3. Multiplication and division are done before addition and subtraction.25 − 4 × 3
4 × 3 = 12
= 25 − 12 - Subtract: 25 − 12. Only addition or subtraction is left, so do it now.25 − 12
25 − 12 = 13
= 13
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 13. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.150 − 3 × (4 + 2)2
- Brackets first. Add: 4 + 2. Only addition or subtraction is left, so do it now.150 − 3 × (4 + 2)2
4 + 2 = 6
= 150 − 3 × 62 - Indices (powers): work out 62. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.150 − 3 × 62
62 = 6 × 6 = 36
= 150 − 3 × 36 - Multiply: 3 × 36. Multiplication and division are done before addition and subtraction.150 − 3 × 36
3 × 36 = 108
= 150 − 108 - Subtract: 150 − 108. Only addition or subtraction is left, so do it now.150 − 108
150 − 108 = 42
= 42
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 42. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.12 + 65 − 2 + √49 × 2
- Work out the top of the fraction first (the fraction line acts like brackets). Add: 12 + 6. Only addition or subtraction is left, so do it now.12 + 65 − 2 + √49 × 2
12 + 6 = 18
= 185 − 2 + √49 × 2 - Work out the bottom of the fraction first (the fraction line acts like brackets). Subtract: 5 − 2. Only addition or subtraction is left, so do it now.185 − 2 + √49 × 2
5 − 2 = 3
= 183 + √49 × 2 - The fraction line means divide: divide the top by the bottom. A fraction is a division. We do this once the top and the bottom have each been worked out.183 + √49 × 2
18 ÷ 3 = 6
= 6 + √49 × 2 - Indices (roots): work out √49. The square root of a number is the number that multiplies by itself to give it. After brackets, powers and roots come next.6 + √49 × 2
√49 = 7 because 7 × 7 = 49
= 6 + 7 × 2 - Multiply: 7 × 2. Multiplication and division are done before addition and subtraction.6 + 7 × 2
7 × 2 = 14
= 6 + 14 - Add: 6 + 14. Only addition or subtraction is left, so do it now.6 + 14
6 + 14 = 20
= 20
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 20. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Method. Use BIDMAS: multiplication has a higher priority than addition.
- Decide what comes first. In BIDMAS, M (multiplication) comes before A (addition), so 4 × 5 is worked out first, not 3 + 4.4 × 5 = 20
- Do the addition. Now replace 4 × 5 by 20.3 + 20 = 23
Check. If we added first we would get 7 × 5 = 35, which is not the correct priority. The answer is 23. ✓
Watch out. Brackets are the only way to make the addition happen first: (3 + 4) × 5 = 35.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.8 − 3 + 2
- Subtract: 8 − 3. Addition and subtraction have the same priority, so work from left to right.8 − 3 + 2
8 − 3 = 5
= 5 + 2 - Add: 5 + 2. Only addition or subtraction is left, so do it now.5 + 2
5 + 2 = 7
= 7
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 7. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.24 ÷ 4 × 3
- Divide: 24 ÷ 4. Multiplication and division have the same priority, so work from left to right.24 ÷ 4 × 3
24 ÷ 4 = 6
= 6 × 3 - Multiply: 6 × 3. This is the only calculation left in this part.6 × 3
6 × 3 = 18
= 18
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 18. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.20 − 5 − 3
- Subtract: 20 − 5. Addition and subtraction have the same priority, so work from left to right.20 − 5 − 3
20 − 5 = 15
= 15 − 3 - Subtract: 15 − 3. Only addition or subtraction is left, so do it now.15 − 3
15 − 3 = 12
= 12
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 12. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.72
- Indices (powers): work out 72. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.72
72 = 7 × 7 = 49
= 49
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 49. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.43
- Indices (powers): work out 43. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.43
43 = 4 × 4 × 4 = 64
= 64
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 64. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.√81
- Indices (roots): work out √81. The square root of a number is the number that multiplies by itself to give it. After brackets, powers and roots come next.√81
√81 = 9 because 9 × 9 = 81
= 9
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 9. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.3√8
- Indices (roots): work out 3√8. The cube root of a number is the number that multiplies by itself three times to give it. After brackets, powers and roots come next.3√8
3√8 = 2 because 2 × 2 × 2 = 8
= 2
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 2. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.122
- Indices (powers): work out 122. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.122
122 = 12 × 12 = 144
= 144
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 144. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Method. Multiply to find the cost of the tickets and the snacks, then add.
- Write the calculation. Tickets: 3 × £8. Snacks: 2 × £3.50. The total is the sum.3 × 8 + 2 × 3.5
- Do the multiplications first. Multiplication has priority over addition.3 × 8 = 24
2 × 3.5 = 7 - Add. 24 + 7 = 31
Check. Estimate: 3 × 8 + 2 × 4 = 24 + 8 = 32, close to 31. ✓
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.(5 + 7) × 3
- Brackets first. Add: 5 + 7. Only addition or subtraction is left, so do it now.(5 + 7) × 3
5 + 7 = 12
= 12 × 3 - Multiply: 12 × 3. This is the only calculation left in this part.12 × 3
12 × 3 = 36
= 36
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 36. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.5 + 7 × 3
- Multiply: 7 × 3. Multiplication and division are done before addition and subtraction.5 + 7 × 3
7 × 3 = 21
= 5 + 21 - Add: 5 + 21. Only addition or subtraction is left, so do it now.5 + 21
5 + 21 = 26
= 26
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 26. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Method. Check which operation should be done first.
- Find what Sam did. Sam added 6 + 2 = 8 and then multiplied by 5.(6 + 2) × 5 = 40
- Say what was wrong. Multiplication has priority over addition. Sam worked from left to right.The multiplication 2 × 5 should come first.
- Work out the correct answer. 2 × 5 = 10, then 6 + 10 = 16
Check. 6 + 10 = 16, and 16 is not 40. ✓
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.20 − 82 + 4
- Work out the top of the fraction first (the fraction line acts like brackets). Subtract: 20 − 8. Only addition or subtraction is left, so do it now.20 − 82 + 4
20 − 8 = 12
= 122 + 4 - Work out the bottom of the fraction first (the fraction line acts like brackets). Add: 2 + 4. Only addition or subtraction is left, so do it now.122 + 4
2 + 4 = 6
= 126 - The fraction line means divide: divide the top by the bottom. A fraction is a division. We do this once the top and the bottom have each been worked out.126
12 ÷ 6 = 2
= 2
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 2. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.20 − 8 ÷ 2 + 4
- Divide: 8 ÷ 2. Multiplication and division are done before addition and subtraction.20 − 8 ÷ 2 + 4
8 ÷ 2 = 4
= 20 − 4 + 4 - Subtract: 20 − 4. Addition and subtraction have the same priority, so work from left to right.20 − 4 + 4
20 − 4 = 16
= 16 + 4 - Add: 16 + 4. Only addition or subtraction is left, so do it now.16 + 4
16 + 4 = 20
= 20
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 20. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Method. Without brackets 4 + 3 × 2 = 10. Brackets must make the addition happen first.
- Work out the calculation without brackets. Multiplication first.4 + 3 × 2 = 4 + 6 = 10, which is not 14
- Try brackets round 4 + 3. Then the addition is done first.(4 + 3) × 2 = 7 × 2 = 14 ✓
- Write the answer. (4 + 3) × 2 = 14
Check. Brackets round 3 × 2 would not change anything: 4 + (3 × 2) = 10. ✓
Exercise 1G Using a calculator with BIDMAS
Calculator allowedKey words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.12.5 + 3.4 × 2.5
- Multiply: 3.4 × 2.5. Multiplication and division are done before addition and subtraction.12.5 + 3.4 × 2.5
3.4 × 2.5 = 8.5
= 12.5 + 8.5 - Add: 12.5 + 8.5. Only addition or subtraction is left, so do it now.12.5 + 8.5
12.5 + 8.5 = 21
= 21
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 21. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.(12.5 + 3.4) × 2.5
- Brackets first. Add: 12.5 + 3.4. Only addition or subtraction is left, so do it now.(12.5 + 3.4) × 2.5
12.5 + 3.4 = 15.9
= 15.9 × 2.5 - Multiply: 15.9 × 2.5. This is the only calculation left in this part.15.9 × 2.5
15.9 × 2.5 = 39.75
= 39.75
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 39.75. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.18.6 − (4.2)2
- Indices (powers): work out (4.2)2. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.18.6 − (4.2)2
(4.2)2 = 4.2 × 4.2 = 17.64
= 18.6 − 17.64 - Subtract: 18.6 − 17.64. Only addition or subtraction is left, so do it now.18.6 − 17.64
18.6 − 17.64 = 0.96
= 0.96
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 0.96. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.(3.5)2 + 2.4 × 1.5
- Indices (powers): work out (3.5)2. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.(3.5)2 + 2.4 × 1.5
(3.5)2 = 3.5 × 3.5 = 12.25
= 12.25 + 2.4 × 1.5 - Multiply: 2.4 × 1.5. Multiplication and division are done before addition and subtraction.12.25 + 2.4 × 1.5
2.4 × 1.5 = 3.6
= 12.25 + 3.6 - Add: 12.25 + 3.6. Only addition or subtraction is left, so do it now.12.25 + 3.6
12.25 + 3.6 = 15.85
= 15.85
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 15.85. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.√(6.4 + 2.6)
- Work out what is under the root sign first (it acts like a bracket). Add: 6.4 + 2.6. Only addition or subtraction is left, so do it now.√(6.4 + 2.6)
6.4 + 2.6 = 9
= √9 - Indices (roots): work out √9. The square root of a number is the number that multiplies by itself to give it. After brackets, powers and roots come next.√9
√9 = 3 because 3 × 3 = 9
= 3
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 3. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.23 × 1.25 − (0.5)2
- Indices (powers): work out 23. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.23 × 1.25 − (0.5)2
23 = 2 × 2 × 2 = 8
= 8 × 1.25 − (0.5)2 - Indices (powers): work out (0.5)2. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.8 × 1.25 − (0.5)2
(0.5)2 = 0.5 × 0.5 = 0.25
= 8 × 1.25 − 0.25 - Multiply: 8 × 1.25. Multiplication and division are done before addition and subtraction.8 × 1.25 − 0.25
8 × 1.25 = 10
= 10 − 0.25 - Subtract: 10 − 0.25. Only addition or subtraction is left, so do it now.10 − 0.25
10 − 0.25 = 9.75
= 9.75
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 9.75. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.7.2 + 4.83.5 − 1.5
- Work out the top of the fraction first (the fraction line acts like brackets). Add: 7.2 + 4.8. Only addition or subtraction is left, so do it now.7.2 + 4.83.5 − 1.5
7.2 + 4.8 = 12
= 123.5 − 1.5 - Work out the bottom of the fraction first (the fraction line acts like brackets). Subtract: 3.5 − 1.5. Only addition or subtraction is left, so do it now.123.5 − 1.5
3.5 − 1.5 = 2
= 122 - The fraction line means divide: divide the top by the bottom. A fraction is a division. We do this once the top and the bottom have each been worked out.122
12 ÷ 2 = 6
= 6
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 6. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.15.6 − 3.60.8 × 1.5
- Work out the top of the fraction first (the fraction line acts like brackets). Subtract: 15.6 − 3.6. Only addition or subtraction is left, so do it now.15.6 − 3.60.8 × 1.5
15.6 − 3.6 = 12
= 120.8 × 1.5 - Work out the bottom of the fraction first (the fraction line acts like brackets). Multiply: 0.8 × 1.5. This is the only calculation left in this part.120.8 × 1.5
0.8 × 1.5 = 1.2
= 121.2 - The fraction line means divide: divide the top by the bottom. A fraction is a division. We do this once the top and the bottom have each been worked out.121.2
12 ÷ 1.2 = 10
= 10
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 10. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.32 + 425
- Work out the top of the fraction first (the fraction line acts like brackets). Indices (powers): work out 32. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.32 + 425
32 = 3 × 3 = 9
= 9 + 425 - Work out the top of the fraction first (the fraction line acts like brackets). Indices (powers): work out 42. A power tells us how many times to multiply a number by itself. After brackets, powers and roots come next.9 + 425
42 = 4 × 4 = 16
= 9 + 165 - Work out the top of the fraction first (the fraction line acts like brackets). Add: 9 + 16. Only addition or subtraction is left, so do it now.9 + 165
9 + 16 = 25
= 255 - The fraction line means divide: divide the top by the bottom. A fraction is a division. We do this once the top and the bottom have each been worked out.255
25 ÷ 5 = 5
= 5
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 5. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Method. The cost is the fixed charge plus the cost of the miles. Multiply before adding.
- Write the calculation. Fixed charge + (cost per mile × number of miles).3.20 + 1.45 × 12
- Multiply first. Multiplication has priority over addition.1.45 × 12 = 17.4
- Add. Write the answer in pounds and pence.3.20 + 17.40 = £20.60
Check. Estimate: 3 + 1.5 × 12 = 3 + 18 = 21, close to 20.60. ✓
Method. The total is the weekly cost for 52 weeks plus the joining fee. Multiply before adding.
- Write the calculation. Weekly cost × number of weeks, then add the joining fee.9.5 × 52 + 30
- Multiply first. 9.5 × 52 = 494
- Add the joining fee. 494 + 30 = £524
Check. Estimate: 10 × 50 + 30 = 530, close to 524. ✓
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.15 + 0.08 × 300
- Multiply: 0.08 × 300. Multiplication and division are done before addition and subtraction.15 + 0.08 × 300
0.08 × 300 = 24
= 15 + 24 - Add: 15 + 24. Only addition or subtraction is left, so do it now.15 + 24
15 + 24 = 39
= 39
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 39. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Key words. BIDMAS is the order of priority in a calculation: Brackets, Indices (powers and roots), Division and Multiplication (same priority, left to right), Addition and Subtraction (same priority, left to right).
Method. Follow BIDMAS: brackets first, then indices (powers and roots), then division and multiplication, then addition and subtraction. Work from left to right within each level.
- Write the calculation and remember the order. Calculations are not simply done from left to right. The agreed order is BIDMAS: Brackets, Indices (powers and roots), Division and Multiplication, Addition and Subtraction.5 + 0.12 × 300
- Multiply: 0.12 × 300. Multiplication and division are done before addition and subtraction.5 + 0.12 × 300
0.12 × 300 = 36
= 5 + 36 - Add: 5 + 36. Only addition or subtraction is left, so do it now.5 + 36
5 + 36 = 41
= 41
Check. A scientific calculator follows the same order (BIDMAS), so typing in the whole calculation gives 41. ✓
Watch out. Do not work from left to right just because it looks easier. In 2 + 3 × 4 the multiplication comes first, so the answer is 14, not 20.
Method. Compare the two costs by subtracting.
- Say which is smaller. Plan A costs £39 and Plan B costs £41.39 < 41
- Find the difference. Take the smaller from the larger.41 − 39 = 2
- Write the answer. Plan A is cheaper by £2.
Check. 39 + 2 = 41. ✓
Method. Think about which parts of the calculation the fraction line covers.
- Work out what her calculator did. The calculator follows BIDMAS, so it divided 6 by 5 first.12 + 6 ÷ 5 − 2 = 12 + 1.2 − 2 = 11.2
- Say what she needs. The fraction line means (top) ÷ (bottom). The top and the bottom each need brackets.(12 + 6) ÷ (5 − 2)
- Work it out. Brackets first, then divide.18 ÷ 3 = 6
Check. 6 × 3 = 18. ✓