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1 0
4. +
5 2
2 3 4
5. + +
3 4 5

11 13
6. +
15 25
17 3
7. −
51 50
5 4
8. −
3 13

11 2
9. −
5 25
11 11
10. −
7 17

3 1
11. −
2 12
6 11
12. −
7 17
11 2
13. −
20 25

3.9 Comparison of Fractions

When two fractions have the same denominator, it is clear that the larger fraction is the one with the
larger numerator. This suggests a simple way to compare any set of fractions: replace each fraction by
an equivalent fraction having the LCD. Then the largest fraction is the one with the largest numerator,
the second-largest is the one with the second-largest numerator, etc.
2 3
Example 113. Which is larger, or ?
3 4
Solution. The LCD is 12,
2 8 3 9
= , and = .
3 12 4 12
9
The larger of the two fractions with denominator 12 is the one with the larger numerator, 12 .It follows
2
that 3 is larger than .
4 3
Numbers arranged in increasing order are written from left to right, separated by the < symbol.
(This is the left-to-right ordering on the number line.) We can also arrange numbers in decreasing
order, from left to right, separated by the > (“greater than”) symbol.
3 2 7
Example 114. Arrange the fractions , ,and in increasing order.
4 3 9

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