# Comparing Fractions

Fractions are the Numbers which are expressed in form of $\frac{p}{q}$, where ‘p’ and ‘q’ are the whole numbers and q ≠ 0. In this session we are going to learn about comparing Fractions. To compare fractions, we first see that all the fractions are greater than zero. Another thing to be remembered is that while comparing fraction, we first check that if the fraction is a proper fraction or improper fraction. If the fraction is improper it means that it is greater than one and if the fraction is proper fraction it is less than 1. So we conclude that a proper fraction is always smaller than the improper fraction.
e.g, $\frac{3}{5}$ < $\frac{15}{7}$

Now if we come across the fractions, which are both proper or both improper fractions, then another thing which we can check is that are the denominators same or not. In case the denominators of the two fractions are same, we compare the numerators and conclude that the larger numerator represents the larger fraction and the smaller numerator represents the smaller fraction.
e.g, $\frac{7}{8}$ < $\frac{12}{8}$

In case the denominators are different, but the numerators of the two fractions are same, we come to the conclusion that the fraction with smaller denominator represents the larger fraction and the fraction with larger denominator represents the smaller fraction.
e.g, $\frac{3}{13}$ < $\frac{11}{6}$

Now we talk about the comparison of the two fractions, where neither of the situations satisfies. In such cases of comparison of the fractions, we simply cross multiply and the greater result represents the greater fraction. In this way the fractions are compared and arranged in ascending or descending order.

e.g, $\frac{3}{13}$ ? $\frac{11}{6}$

$\frac{3*6}{13*6}$
? $\frac{11*13}{6*13}$

$\frac{18}{78}$
? $\frac{143}{78}$

$\frac{18}{78}$
< $\frac{143}{78}$

## Equivalent Fractions

A fraction is the number which is expressed in form of $\frac{a}{b}$, where ‘a’ and ‘b’ are whole Numbers and ‘b’ ≠ 0. Now we are going to learn about equivalent Fractions. If we have a pair of fractions, which when...Read More

## Comparing Fractions with Different Denominators

Fractions are the Numbers which are expressed in form of $\frac{p}{q}$, where ‘p’ and ‘q’ are the whole Numbers and q ≠ 0. Fractions has two parts: numerator and denominator. In the above given equation 'p' is the numerator and 'q' is the denominator. Comparing fractions is to find the greatest and smallest among the given Set of fractions...Read More

## Comparing Unlike Fractions

Fractions are the Numbers which are expressed in form of $\frac{p}{q}$, where ‘p’ and ‘q’ are the whole Numbers and q ≠ 0. Fractions has two parts: numerator and denominator. In the above given equation 'p' is the numerator and 'q' is the denominator. Comparing Fractions is to find the greatest and smallest among the given Set of fractions. Like fractions are ...Read More

## Comparing Fractions with Same Denominator

Fractions are the Numbers which are expressed in form of $\frac{p}{q}$, where ‘p’ and ‘q’ are the whole Numbers and q ≠ 0. Fractions has two parts: numerator and denominator. In the above given equation 'p' is the numerator and 'q' is the denominator. Comparing Fractions is to find the greatest and smallest among the given Set of fractions. W...Read More

## Further Read

Math Topics
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