The four operations
The order of operations
Work out brackets first, then powers (indices), then multiplication and division, then addition and subtraction.
Multiplication and division have equal rank, so work left to right between them; the same for addition and subtraction.
- 7 + 3 × 4
- multiplication first: 3 × 4 = 12
- 7 + 12 = 19 (not 10 × 4 = 40)
Negative numbers
- Adding a negative is subtracting: 5 + (−3) = 2.
- Subtracting a negative is adding: −7 − (−3) = −7 + 3 = −4.
- Multiplying or dividing: same signs give a positive, different signs give a negative. (−6) × (−4) = 24, (−20) ÷ 5 = −4.
Long multiplication and using a fact you know
Split the second number into tens and ones, multiply by each, then add.
- 347 × 26
- 347 × 6 = 2082
- 347 × 20 = 6940 (the 2 is worth 20)
- 2082 + 6940 = 9022
If you know 23 × 47 = 1081, then 2.3 × 4.7 = 10.81: each number was divided by 10, so the answer is divided by 100.
Counting combinations: with 4 starters and 6 mains there are 4 × 6 = 24 different meals, because each starter goes with each main.
Check the order of operations
Type 7 + 3 × 4 into the calculator exactly as written, then (7 + 3) × 4. Then try 20 − 8 ÷ 4 and (20 − 8) ÷ 4. Before each one, say what you expect. A scientific calculator follows the order of operations; where you need something else, you add brackets.
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