Page 83 - ArithBook5thEd ~ BCC

Example 90. Find lower terms for the fraction 28 .
70
Solution. Since 7 is a common factor of the numerator and denominator, it can be cancelled, yielding

✚❃
✚ 28 4 = 4 (cancelling 7).
✚❃
✚ 70 10 10
Still lower terms are possible, since 4 and 10 have the common factor 2:

✚ 4 ✚❃ 2 = 2 (cancelling 2).
✚❃
✚ 10 5 5

If the only common factor of the numerator and denominator is 1, then no further reduction is
possible, and the fraction is said to be in lowest terms.For example, 2 and 5 have no common factor
5
2
other than 1, so the fraction , and also the improper , are in lowest terms.
5 2
Example 91. Reduce the fraction 24 to lowest terms.
36
Solution. A common factor of the numerator and denominator is 4, so we can reduce the terms as
follows: 6
✚❃
24 ✚ 24 6
= = (cancelling 4);
36 ✚❃ 9 9
✚ 36
6 and 9 have the common factor 3, so we can further reduce

2
6 ✁ 6 ✁✕ 2
= = (cancelling 3).
9 3 3
✁ 9 ✁✕

It is clear that 2 is in lowest terms, since 2 and 3 have no common factor other than1.
3
Note that this reduction to lowest terms could have been accomplished in one step, had we realized,
at the outset, that both 24 and 36 are divisible by 12:

✚❃
24 ✚ 24 2 2
= = (cancelling 12).
36 ✚❃ 3 3
✚ 36

Example 92. Reduce the fraction 13 to lowest terms.
39
Solution. A common factor of the numerator and denominator is 13, so that
13 1 · 13 1
= = .
39 3 · 13 3

Example 93. Reduce the fraction 15 to lowest terms.
3
Solution. 15 = 5 =5.
3
1

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