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Comparing Fractions

Fractions are compared to know which is greater among them which is smaller among them.

Comparing of like fractions:-

Like fractions are fractions having same denominator. It can be compared easily by comparing numerators. Fraction with larger numerator is greater in value than that of smaller numerator having same denominator.

Example:

Which is greater : $\frac{3}{4}$ or $\frac{2}{4}$

Here 3 is greater than 2. And both have same denominator 4

So, $\frac{3}{4}$ > $\frac{2}{4}$

i.e. $\frac{3}{4}$ is greater than $\frac{2}{4}$

Comparing of unlike fractions:-

In this case fractions have different denominators,so can't be compared directly. It can be compared only on converting them into equivalent fraction or corresponding decimals.

There are twp ways to compare unlike fractions --

1. Using decimals

2. Using common denominator.

Decimal method of comparing:-

Fractions are converted into decimals and decimals can be easily compared.

Example:

1) Which is larger : $\frac{3}{5}$ or $\frac{1}{2}$

$\frac{3}{5} = 0.6$

$\frac{1}{2} = 0.5$

As 0.6 > 0.5

So, $\frac{3}{5}$ > $\frac{1}{2}$

i.e. $\frac{3}{5}$ is larger than $\frac{1}{2}$

Common denominator method of comparing:-

In this method, before addition and subtraction of such fraction,we must first change them to equivalent fraction so that they have common denominator.

In this method LCM of both denominator is evaluated and rewrite the fraction as equivalent fraction with the LCM as denominator.

Example:

1) Which is larger : $\frac{3}{5}$ or $\frac{3}{4}$

LCM of 5 and 4
5 = 5
4 = 2 X 2
LCM = 5 X 2 X 2 = 20
$\frac{3}{5} = \frac{3 X4}{5 X 4} = \frac{12}{20}$
$\frac{3}{4} = \frac{3 X 5}{4 X 5} = \frac{15}{20}$
As 15 is grater than 12
So, $\frac{3}{4} > \frac{3}{5}$
i.e. $\frac{3}{4}$ is greater than $\frac{3}{5}$

Some Useful short-cuts used in special cases:-
1. Whenever two fractions have same numerator then fraction with smaller denominator is greater than that of larger denominators.
Example:
1). Which is greater $\frac{3}{5} or \frac{3}{4}$
Here numerator is same 3 and denominators are 4 and 5. As 4 < 5 .
So, $\frac{3}{4} > \frac{3}{5}$.

2.We can cross multiply numerators with denominator of other fraction to compare two fractions. Greater value after multiplication is corresponding to greater fraction.

Example:
1). Which is greater $\frac{3}{5}$ or $\frac{4}{7}$
$\frac{3}{5}$ , $ \frac{4}{7}$
3 X 7 , 4 X 7
As 21 > 20.
So, $\frac{3}{5}$ > $\frac{4}{7}$