How to Compare Fractions

Comparing fractions is a process of comparing two or more fractions. It determines which fraction is larger and which is smaller. To compare fractions, we either need to convert them to equivalent fractions or use cross-multiplication to compare the fractions directly.

There are several ways to compare fractions. It follows certain sets of rules related to the numerators and denominators that make comparison easy. The two common methods for fraction comparison are the decimal method and the same denominator method.

We will learn different methods of fraction comparison in detail.

Decimal Method of Comparing Fractions

In the decimal method of comparing fractions, we convert fractions into their decimal equivalents and then compare the decimal values. The fraction with the larger decimal value is considered the larger fraction.

Example

Which one of the following fractions is bigger?

\frac{3}{6} \quad \text{or} \quad \frac{5}{12}

First, we will convert the fraction into a decimal value by dividing the numbers.

\frac{3}{6} = 0.5

\frac{5}{12} = 0.416\ldots

Now, compare the decimal value.

0.5 is greater than 0.416.

So, the fraction 3/6 is greater than

\frac{5}{12}

It can also be expressed as

\quad \frac{3}{6} > \frac{5}{12}.

Comparing Fractions With Same Denominator

One of the methods of fraction comparison is comparing fractions with same denominator. To compare fractions with like denominators, we just look at the numerators of the fractions. The fraction with the greater numerator is greater.

Example

\text{Consider two fractions } \frac{3}{5} \quad \text{and} \quad \frac{1}{5}.

\text{To find which fraction is greater, we will look at the numerators.}

3 > 1, \quad \text{so} \quad \frac{3}{5} > \frac{1}{5}.

$comparing fractions with same denominator$

Compare Fractions With Unlike Denominators

To compare fractions with unlike denominators, we first need to make the denominators the same. Once the denominators become the same, it becomes easy to compare them.

Let’s look at the example.

Compare

\frac{1}{3} and \frac{3}{5}

Observe the denominators. They are different. So, we will make them the same by finding LCM (the lowest common multiple).

$cross multiplication to compare fractions$

Compare Fractions on a Number Line

A number line helps visualize the fraction. We can easily compare fractions on a number line. On the number line, the fractions increase from left to right. It means that the fraction on the left side of the number line will be smaller than that on the right side.

Example

\frac{2}{4} = 0.5, \quad \frac{3}{4} = 0.75, \quad \frac{4}{4} = 1

Compare Fractions Worksheet

Worksheets are essential tools to learn and understand the comparison of fractions. We provide you with the compare fractions worksheet PDF to fortify your foundation. Download and practice the worksheet to enhance your problem-solving skills.

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Comparing fractions helps us to determine if one fraction is greater than, less than, or equal to another. We used several easy methods of comparing fractions to help students understand it easily.

Comparing Fractions

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