Page 114 - Start Up Mathematics_4

Comparing Unlike Fractions

There are two ways of comparing unlike fractions.

• By cross-multiplication
• By changing into like fractions

4 3
Example 12: Compare and .
13 15
Solution: Comparison by cross-multiplication

4 3 4 × 15 = 60 13 × 3 = 39
13 15
Since 60 > 39, 4 > 3 .
13 15
Comparison by changing into like fractions

4 = 4 × 15 = 60
13 13 × 15 195
3 3 × 13 39
= =
15 15 × 13 195
60 39 4 3
Since > , > .
195 195 13 15

Comparing Mixed Fractions

• To compare mixed fractions, compare the whole numbers in them. The mixed fraction
1
1
with the bigger whole number is bigger. For, example, 9 is bigger than 7 .
2 3
• If the whole number in both the mixed fractions is the same, compare the fractional
parts. The mixed fraction with the bigger fractional part is bigger. For example, 7 4 is

bigger than 7 3 as 4 > 3 (See example 12). 13
15 13 15
• To compare a mixed fraction with any fraction, convert the mixed fraction to improper
1 11 7
fraction and then compare. For example, 2 = is bigger than .
5 5 5
1 15
Example 13: Compare 4 and .
2 2

1 (4 × 2) + 1 9
Solution: 4 = =
2 2 2

9 15 1 15
Since < , 4 < .
2 2 2 2
Ordering of Fractions

To arrange fractions in ascending or descending order, first convert them into like fractions.
Now that you have learnt to compare like fractions, you can arrange them in ascending or
descending order.

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