# Comparing Fractions

#### Summary

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Comparing like fractions
Fractions with the same denominator are called like fractions. In like fractions, the fraction with the greater numerator is greater.
e.g. In fractions $\frac{\text{5}}{\text{7}}$ and $\frac{\text{3}}{\text{7}}$. $\frac{\text{5}}{\text{7}}$ > $\frac{\text{3}}{\text{7}}$ as 5 is greater than 3.

Three or more like fractions can be arranged in ascending or descending order by arranging their numerators in ascending or descending order respectively.

Comparing unlike fractions
Fractions with different denominators are called unlike fractions. If two fractions with the same numerator but different denominators are to be compared, then the fraction with the smaller denominator is greater of the two. To compare unlike fractions, we first convert them into like fractions.

e.g. Compare the fractions $\frac{\text{6}}{\text{8}}$ and $\frac{\text{4}}{\text{6}}$.

least common multiple (LCM) of 6 and 8 = 24

$\frac{\text{(6 x 3)}}{\text{(8 x 3)}}$ = $\frac{\text{18}}{\text{24}}$

$\frac{\text{(4 x 4)}}{\text{(6 x 4)}}$ = $\frac{\text{16}}{\text{24}}$

$\frac{\text{18}}{\text{24}}$ > $\frac{\text{16}}{\text{24}}$$\frac{\text{6}}{\text{8}}$ > $\frac{\text{4}}{\text{6}}$

Hence, we can say that $\frac{\text{6}}{\text{8}}$ is greater than $\frac{\text{4}}{\text{6}}$.

### 1 . whose numerator and denominator add up to 10

(c)  Fractions whose numerator and denominator add upto to 10 are
1/9, 2/8, 3/7, 4/6, 5/4, 7/3 etc

### 2 . Write prime numbers between 50 and 70

The prime nos. between 50 and 70 are as follows:
53,59,61,67.

### 3 . If javed was given 5 upon 7 of a basket of oranges

GIVEN TO JAVED=5/7
LEFT=1-(5/7)=2/7

3/4+5/9
=3*9/4*9+5*4/9*4
=27/36+20/36
=27+20/36
=47/36
=1.30555

### 5 . Whose denominator is 4 more than the numerator.

Let the numerator be x then denominator will be (x + 4)
Hence the fraction is [x/(x + 4)]
Put x = 1, the fraction becomes 1/...