By Geoff Buckwell (auth.)
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Additional info for Mastering Mathematics
In its 2 This cancelling is often written ~ (dividing by 12). 3 If you cannot see the full cancellation in one step, you could proceed in several steps. Hence 24 36 (+2) 24 12 M6 (+3) ß2 = ;>6 18 = l-89 = (+2) (ü) (+2) (+2) 2 ? 3 = 3" (+3) Common denominator There are many occasions when you want to change two or more fractions into fractions which have the same denominator. This will be referred to as the common denominator of the fractions. The technique is particularly useful when you are adding or comparing fractions.
If the numerator and denominator of i are multiplied by 3, we get: 3 4 - 3x3 4x3 9 12 If we multiply by 5 we get: 3 3x5 4 4 x 5 15 20 Continuing this, the complete set of equivalent fractions is obtained: 3 4 6 8 9 12 12 16 15 20 18 24 i is the simplest form of all of these fractions. 28 MASTERING MATHEMATICS Reversing this process is called cancelling. Start with the fraction ~. Divide the numerator and denominator by 12: So 24 + 12 36 + 12 24 36 2 3 l Hence ~ = Since ~ cannot be reduced any further, then we say that ~ lowest terms.
Look at the fractions involved (leaving out the units). savings . magazme -2:1 } 1 =4 This means she has 1 2 1 4 3 4 -+-=- ! left (the remainder). Now l of the remainder = ~ of 1 3 1 4 ~ 1 12 =-x-=- 3191105 Hence the amount spent = - + - = - + - = - = 4 12 12 12 12 6 At the end of all of this then, ~ has been spent, and so ~ has not been spent. 80. WORKING WITH FRACTIONS AND DECIMALS 37 Exercise 2(a) ~ 1 Reduce the following fractions to their lowest terms: (i) (v) 2 6 16 45 75 (ii) 16 24 18 (iii) 48 60 240 ( ...