Comparing Fractions with Like Numerators – Definition With Examples

What Is a Numerator?

When numbers are written in the form of a fraction, it can be represented as a/b, where a is the numerator and b is the denominator. A numerator is the part of a fraction, which is above the line, and it represents the number of parts out of the whole. On the other hand, a denominator is the total numbers of the parts. 

For example: In the fraction $\frac{3}{5}$, the numerator is 3. 

In the above image, the number of shaded parts out of total parts are 5. So, the numerator is 5 and the denominator is 6. 

Definition

Let us have a look at two fractions, i.e., $\frac{5}{7}$ and $\frac{5}{9}$. We see that the numerators are the same, i.e., 5. Such numerators are said to be like numerators. In other words, when the numerators of two or more fractions are the same and the denominators are different, they are called the same or like numerators. 

Let us look at one more example:

In the above example, the first figure is divided into 3 parts and only 1 is shaded whereas in the second figure, there are 4 equal parts and only 1 is shaded. As a child, you remember you did unit fractions. Unit fractions are the fractions in which the fractions have the numerator 1. 

• Comparing fractions with like numerators

Comparing the fractions with like or same numerators is an easy task. 

Let us compare $\frac{3}{5}$ and $\frac{3}{7}$. 

From the models, we can see that $\frac{3}{5}>\frac{3}{7}$.

In order to compare two or more fractions with the same or like numerators, we just have to compare their denominators. The fraction that has the bigger denominator is smaller.

If we compare $\frac{9}{11}$ and $\frac{9}{17}$, we see that the denominator 17 is larger than the denominator 11. So,  $\frac{9}{11}>\frac{9}{17}$.

• Ordering Fractions with Like Numerators

1. Ascending order 

Ascending is also known as increasing. So when numbers have their values from smallest to largest, we say that it is in ascending order. Ascending order for the fractions with like numerators is quite easy. The larger the denominator, the smaller the fraction. 

For example: Write the numbers in ascending order: $\frac{1}{33},\frac{1}{45},\frac{1}{27},\frac{1}{19}$.

As we know, the larger the denominator, the smaller the fraction. 

45 > 33 > 27 > 19

$\Rightarrow\frac{1}{45}<\frac{1}{33}<\frac{1}{27}<\frac{1}{19}$

2. Descending order

Descending is also known as decreasing. So, when numbers have their values from largest to the smallest, we say that it is in descending order. Descending order is just the opposite of ascending order. The smaller the denominator, the greater the fraction. 

For example: Write the numbers in descending order: $\frac{1}{33},\frac{1}{45},\frac{1}{27},\frac{1}{19}$.

As we know that the larger the denominator, the smaller the fraction. 

19 < 27 < 33 < 45

$\Rightarrow\frac{1}{19}>\frac{1}{27}>\frac{1}{33}>\frac{1}{45}$

• Addition and Subtraction of fractions with like or same numerators

Adding or subtracting the fractions with same or like numerators and unlike denominators is the same as adding or subtracting the fractions with unlike denominators. 

Let us suppose we have to have $\frac{2}{3}$ and $\frac{2}{5}$. To add them, you have to first make the denominators equal. 

LCM (3, 5) = 15

$\frac{2\times5}{3\times5}=\frac{10}{15} $and$\frac{2\times3}{5\times3}=\frac{6}{15}$

$\frac{10}{15}+\frac{6}{15}=\frac{16}{15}$ 

Let’s subtract them. 

$\frac{10}{15}-\frac{6}{15}=\frac{4}{15}$ 

How to Make Like or Same Numerators?

For making the numerators of two or more fractions same or like, we can find out the LCM of the numerators and then multiply the numerators with relevant numbers. It becomes easy to compare if there are the like or same numerators. 

For example: We have to compare $\frac{3}{4}$ and $\frac{9}{11}$.

By finding the LCM, you can find the common numerators. 

LCM (3, 9) = 9

$\frac{3\times3}{4\times3}=\frac{9}{12}$ and $\frac{9}{11}$

For comparing $\frac{9}{12}$ and $\frac{9}{11}$, we just have to look at the denominator. 

Since 12 > 11

 $\frac{9}{12}< \frac{9}{11}\Rightarrow\frac{3}{4}<\frac{9}{11}$

Solved Examples

Example 1: Write the following fractions in descending order. 

$\frac{7}{20},\frac{7}{9},\frac{7}{11},\frac{7}{19}$ and $\frac{7}{25}$

Solution: The smaller the denominator, the greater the fraction when the fractions have like or same numerators.

9 < 11 < 19 < 20  25

$\frac{7}{9}>\frac{7}{11}>\frac{7}{19}>\frac{7}{20}>\frac{7}{25}$ 

Example 2: Find the fractions with the like or same numerators from the following group of fractions.

$\frac{3}{5},\frac{3}{10},\frac{1}{6},\frac{3}{8},\frac{3}{19},\frac{8}{13}$

Solution: 

The fractions with the like or same numerators are:  $\frac{3}{5},\frac{3}{10},\frac{3}{8},\frac{3}{19}$. 

Example 3: Add $\frac{1}{3}+\frac{1}{5}+\frac{1}{9}$. 

Solution: LCM(3, 5 and 9) = 45

$\frac{1\times15}{3\times15}=\frac{15}{45};\frac{1\times9}{5\times9}=\frac{9}{45};\frac{1\times5}{9\times5}=\frac{5}{45}$

$\frac{15}{45}+\frac{9}{45}+\frac{5}{45} = \frac{29}{45}$

Example 4: Write the following fractions in ascending order:

$\frac{135}{178},\frac{135}{199},\frac{135}{101},\frac{135}{119}$ and $\frac{135}{229}$ 

Solution: The greater the denominator, the smaller the fraction when the fractions have like or same numerators.

229 > 199 > 178 > 119 > 101

$\frac{135}{229}<\frac{135}{199}<\frac{135}{178}<\frac{135}{119}<\frac{135}{101}$

Practice Problems

Frequently Asked Questions