Comparing and Ordering Fractions

# Comparing and Ordering Fractions

## 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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