Discover Mathematics P6: Term 1, Unit 3, Lessons 3–5
GoalUse the order of operations, including brackets and exponents, to work out numerical expressions.
New words
exponent · a small number that tells how many times to multiply the basebase · the number that is multiplied by itselfbrackets · ( ) mean: work this part out first
Explanation
An exponent shows repeated multiplication of the same number. In 2³ the base is 2 and the exponent is 3, so 2³ = 2 × 2 × 2 = 8. Likewise 5² = 5 × 5 = 25 and 10² = 100. Note that 3² means 3 × 3 = 9, not 3 × 2 = 6. When an expression has several operations, we follow a fixed order. First brackets. Second exponents. Third multiplication and division, from left to right. Last addition and subtraction, from left to right. So 4 + 3 × 2² = 4 + 3 × 4 = 4 + 12 = 16, but (4 + 3) × 2² = 7 × 4 = 28.
Same digits, different answers. Take the numbers 2, 3 and 4 and the signs + and ×. Make as many different expressions as you can, with and without brackets, such as 2 + 3 × 4 and (2 + 3) × 4. Work them out in the right order and compare. How many different answers did you find?
Practice
1
Work out 5² and 10³.
5² = 25 and 10³ = 10 × 10 × 10 = 1,000.
2
Work out 2³ + 4.
2³ = 8, so 8 + 4 = 12.
3
Work out (6 + 2) × 3 and 6 + 2 × 3. Why are the answers different?
