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Numbers, units and arithmetic
Numbers, units and arithmetic

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Activity 52

Evaluate each of the following.

  • (a) one divided by two minus one divided by three

  • (b) one divided by three plus one divided by five

Answer

  • (a) one divided by two equals three divided by six and one divided by three equals two divided by six . So equation sequence part 1 one divided by two minus one divided by three equals part 2 three divided by six minus two divided by six equals part 3 one divided by six

  • (b) equation sequence part 1 one divided by three plus one divided by five equals part 2 five divided by 15 plus three divided by 15 equals part 3 eight divided by 15 .

Activity 53

Evaluate each of the following, giving each answer in its simplest form.

  • (a) 10 division one divided by two

  • (b) two divided by five division five divided by seven

Answer

  • (a) equation sequence part 1 10 division one divided by two equals part 2 10 multiplication two equals part 3 20 (reciprocal of one divided by two is two divided by one ).

  • (b) equation sequence part 1 two divided by five division five divided by seven equals part 2 two divided by five multiplication seven divided by five equals part 3 14 divided by 25 (reciprocal of five divided by seven is seven divided by five ).

Activity 54

Explain how to multiply fractions, to somebody who does not know how to do it.

Answer

There are several ways of explaining this. For example:

‘To multiply two fractions, multiply the top two numbers together (the numerators) and multiply the bottom two numbers together (the denominators). To give the answer in its simplest form, check whether top and bottom numbers have a factor in common and, if so, divide through by it.’

Or

‘To multiply two fractions by cancelling, find a number that goes into (divides) a number on the top and a number on the bottom i.e. cancel. Repeat this until there are no numbers left which will cancel with each other. Then multiply together the top two numbers (the numerators) and the bottom two numbers (the denominators). This fraction should be in its simplest form.’