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62 Mastering Technical Mathematics
Figure 5-2
Here’s a way to
find a reasonable
common denominator
in a long
sum of fractions.
To begin, find the prime factors of each denominator in order:
4 2 2
3 is already prime
5 is already prime
6 2 3
12 2 2 3
10 2 5
30 2 3 5
15 3 5
Our “ideal common denominator” must contain every prime factor that is in any
denominator. These are 2, 3, and 5. The common denominator is then found by multiplying
all these primes together: 2 2 3 5 60. Notice that the prime number
2 is used twice here. That sort of thing is not unusual when you are finding the prime
factorizations of numbers.
Now convert all the fractions to 60ths:
1/4 15/60
1/3 20/60
2/5 24/60
1/6 10/60