Page 70 - Start Up Mathematics_5

Example 7: Arrange the following like fractions in descending order.

,
,
,
,
18 19 12 16 13 Quick Tip
21 21 21 21 21
When denominators are same, we
Solution: 19 > 18 > 16 > 13 > 12 compare the numerators.
So, 19 > 18 > 16 > 13 > 12 . Larger numerator → Larger fraction
21 21 21 21 21
Ordering of Unlike Fractions with Equal Numerator
9 9 9 9 9
Unlike fractions with equal numerator are of the type , , , , .
4 6 2 8 5
To arrange them in ascending or descending order, we compare their denominators. The
fraction with the smallest denominator is the largest.

Example 8: Arrange the following fractions in ascending order.

,
,
12 12 12 12 12 12 Quick Tip
,
,
,
8 4 6 2 9 5
Solution: Arranging the denominators in When numerators are same, we
descending order, we get compare the denominators.
9 > 8 > 6 > 5 > 4 > 2 Larger denominator → Smaller
fraction
So, 12 < 12 < 12 < 12 < 12 < 12 .
9 8 6 5 4 2
Example 9: Arrange the following fractions in descending order.

,
,
,
,
,
23 23 23 23 23 23
19 4 16 15 9 11
Solution: Arranging the denominators in ascending order, we get
4 < 9 < 11 < 15 < 16 < 19
So, 23 > 23 > 23 > 23 > 23 > 23 .
4 9 11 15 16 19

Ordering of Unlike Fractions with Unequal Denominator
To arrange unlike fractions with unequal denominators, we first change them to like fractions.
Then we compare their numerators and arrange the fractions in ascending or descending
order.

6 2 4
Example 10: Arrange , , , 7 and 11 in ascending order.
5 3 9 12 20
Solution: LCM of 5, 3, 9, 12, 20 = 3 × 3 × 5 × 2 × 2 = 180 3 3 , 5 , 9 , 12 , 20

6 = 6 × 36 = 216 ( 180 ÷ 5 = 36, we 3 1 , 5 , 3 , 4 , 20
5 5 × 36 180 multiply the numerator and 5 1 , 5 , 1 , 4 , 20

2 = 2 × 60 = 120 the denominator by 36) 2 1 , 1 , 1 , 4 , 4
3 3 × 60 180 2 1 , 1 , 1 , 2 , 2

4 = 4 × 20 = 80 1 , 1 , 1 , 1 , 1
9 9 × 20 180

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