Comparing Fractions
Comparison of Like Fractions
To compare like fractions, numerators of the fractions
are compared. The fraction having greater numerator is the greater fraction.
Example: Compare 3/5 and 1/5 .
Solution: 3/5 and 1/5 are like fractions, that is, both have
the same denominator.
So, compare the numerators. On comparison, we find that 3 > 1.
Hence, 3/5
> 1/5.
Comparison of Unlike Fractions
Two cases arise while
comparing unlike fractions.
Case 1: Fractions with the same numerator.
Example: Arrange 7/12, 7/23, 7/17, 7/11 in descending
order.
Solution: In this case, the
fraction with the larger denominator is smaller.
Hence, in the above fractions, 7/23 is the smallest.
Next, 7/17, then 7/12 and 7/11 is the largest.
Therefore, 7/11 > 7/12 > 7/17 > 7/23.
Case 2:
Fractions with different numerators.
Convert these type of
unlike fractions into like fractions by making the denominator same.
Example: Compare 1/4 and 3/8.
Solution: Convert 1/4 to a like fraction as given
below.
1/4 = (1 ×
2)/(4 × 2) = 2/8 [Multiplying
numerator and denominator by the same number]
Now, the
given fractions 2/8 and 3/8 are like fractions.
On comparing
the numerators, we get 3 > 2.
Therefore,
3/8 > 2/8 or 3/8 > 1/4.
Comparison of Mixed Fractions
To compare mixed fractions, we first convert the fractions into improper fractions and then compare as unlike fractions.
Ordering Fractions
Arranging
Fractions in Ascending and Descending Order
Writing fractions from the smallest to the largest is called ascending order of fractions and writing fractions from the largest to the smallest is called descending order of fractions.
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