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- Number skills: order of operations and written methods
Number skills: order of operations and written methods
GCSE Maths starts from the number skills you built in Years 7 to 9. On a non-calculator question these are the skills that carry you, so let's make them rock solid.
Order of operations
Work in this order: Brackets, Indices (powers and roots), Division and Multiplication (left to right), Addition and Subtraction (left to right).
3 + 4 × 5 = 3 + 20 = 23, not 35.
(3 + 4) × 5 = 7 × 5 = 35
3 + 4 × 5 = 3 + 20 = 23, not 35.
(3 + 4) × 5 = 7 × 5 = 35
Written multiplication and division
Column or grid method: 347 × 26 = 347 × 20 + 347 × 6 = 6940 + 2082 = 9022.
Short division: 1652 ÷ 7. 7 into 16 goes 2 remainder 2, 7 into 25 goes 3 remainder 4, 7 into 42 goes 6. Answer 236.
Short division: 1652 ÷ 7. 7 into 16 goes 2 remainder 2, 7 into 25 goes 3 remainder 4, 7 into 42 goes 6. Answer 236.
Decimals
Multiplying: ignore the points, multiply, then put back as many decimal places as the question had in total.
0.4 × 0.3: 4 × 3 = 12, two decimal places in total, so 0.12.
Dividing: multiply both numbers by 10, 100, ... until you divide by a whole number.
4.8 ÷ 0.06 = 480 ÷ 6 = 80
0.4 × 0.3: 4 × 3 = 12, two decimal places in total, so 0.12.
Dividing: multiply both numbers by 10, 100, ... until you divide by a whole number.
4.8 ÷ 0.06 = 480 ÷ 6 = 80
Work out 20 − 12 ÷ 4 + 1
- Division first: 12 ÷ 4 = 3
- Then left to right: 20 − 3 = 17
- 17 + 1 = 18
Answer: 18
Brackets, then powers, then × and ÷, then + and −, working left to right within each level. Count decimal places when multiplying decimals, and make the divisor a whole number when dividing.
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