1.1 Doing calculations in the right order

Consider now the calculation three plus two multiplication four . 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 three plus two multiplication four , 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 three plus two multiplication four 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. three multiplication four plus two
  • The multiplication should be done before the addition, so

    equation sequence part 1 three multiplication four plus two equals part 2 12 plus two equals part 3 14

    • b. two plus four multiplication three
  • The multiplication should be done before the addition, so

    equation sequence part 1 two plus four multiplication three equals part 2 two plus 12 equals part 3 14

    (Note that the answers to (a) and (b) are the same. This is because addition and multiplication are individually commutative, i.e. three multiplication four is the same as four multiplication three and 12 + 2 is the same as 2 + 12. Remember though that the multiplication must be done before the addition.)

    • c. 35 division five plus two
  • The division should be done before the addition, so

    equation sequence part 1 35 division five plus two equals part 2 seven plus two equals part 3 nine

    • d. four multiplication two minus 21 division seven
  • The division and multiplication should be done before the subtraction, so

    equation sequence part 1 four multiplication two minus 21 division seven equals part 2 eight minus three equals part 3 five

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1 Doing calculations, with or without a calculator
Next : 1.2 What about powers? 
1.2 What about powers?