1.1 Doing calculations in the right order
Consider now the calculation . If you simply work from left to right in this case, adding 3 and 2 gives 5, then multiplying by 4 gives 20, but this is the incorrect answer.
There is a rule, applied by mathematicians and scientists everywhere, which states that:
multiplication and division should be carried out before addition and subtraction.
Applying this rule to the calculation , the multiplication of 2 and 4 should be done first, giving 8, then the 3 is added to give the correct final answer of 11. Most modern calculators ‘know’ this rule (which is known as a rule of precedence, where precedence means ‘priority’), so entering into your calculator in exactly the order in which it is written should give the correct answer of 11. Check this on your calculator now.
Question 1.2
Do the following calculations without using your calculator. Use your calculator to check the answers.
- a.
The multiplication should be done before the addition, so
- b.
The multiplication should be done before the addition, so
(Note that the answers to (a) and (b) are the same. This is because addition and multiplication are individually commutative, i.e. is the same as and 12 + 2 is the same as 2 + 12. Remember though that the multiplication must be done before the addition.)
- c.
The division should be done before the addition, so
- d.
The division and multiplication should be done before the subtraction, so