A fraction represents a small part of a whole or a collection. A group of two or more fractions with the same denominator is called a like fraction. The entire is divided into a specified number of equal sections in these fractions. For example, \(\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{5}{8}\) and \(\frac{9}{8}\) are like fractions.

This article will learn the definition of like fractions with examples.

Like Fractions Definition

In two or more fractions or a group of fractions, when the denominator is the same, they are said to be like fractions. Or we can say that fractions have the same number at the bottom.

Like fractions examples: \(\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5},\frac{6}{5}\) and \(\frac{8}{5}\)

Here we can see that the denominator of all the fractions is \(5,\) so these fractions are called like fractions.

Like and Unlike Fractions

A fraction is a number representing a part of a single whole object or a group of things. It is determined by two numbers: one on top and the other at the bottom of a fraction bar, known as numerator and denominator. Depending on the similarity of the denominator, we classify two or more fractions into like fractions and unlike fractions.

Like fractions

The fractions with the same denominators are called like fractions.

For example, the below figure shows the representation of like fractions.

This representation can be written as \(\frac{3}{6},\frac{4}{6},\frac{2}{6},\frac{1}{6},\frac{5}{6}\) and \(\frac{6}{6}\) are like fractions.

And, \(\frac{2}{{11}},\frac{{18}}{{11}},\frac{8}{{11}}\) and \(\frac{{31}}{{11}}\) are another set of examples for like fractions.

Unlike fractions

 The fractions with different denominators are called, unlike fractions.

For example, the below figure shows the representation of unlike fractions.

This representation can be written as \(\frac{3}{9},\frac{1}{4},\frac{4}{6}\) and \(\frac{6}{8}\) are unlike fractions.

And \(\frac{4}{{11}},\frac{7}{{15}} = \frac{9}{{17}}\) and \(\frac{{11}}{{28}}\) are another set of examples for unlike fractions.

Important Points on Like Fractions

1. Fractions like \(\frac{{14}}{6},\frac{{25}}{{15}},\frac{{16}}{{12}},\frac{9}{{27}}\) are also like fractions though they have different denominators because when they are written in the simplest form, such as \(\frac{7}{3},\frac{5}{3},\frac{4}{3},\frac{1}{3}\) we get the same denominator here \(3.\)
2. Fraction like \(\frac{3}{5},\frac{3}{7},\frac{3}{{11}},\frac{3}{{17}},\) are not like fractions. Here the numerators are the same, but the denominators are different.
3. Whole numbers like \(11, 35, 72, 23\) are called like fractions because they have the same denominator \(1.\) They are written as \(\frac{{11}}{1},\frac{{35}}{1},\frac{{72}}{1},\frac{{23}}{1}\)

Examples of Like Fractions

Fractions with the same denominators are called fractions.

For example, \(\frac{1}{{11}},\frac{3}{{11}},\frac{7}{{11}},\frac{{13}}{{11}}\) are all like fractions.

Are \(\frac{5}{23}\) and \(\frac{17}{31}\) like fractions? Their denominators are different. Therefore, they are not like fractions. They are called, unlike fractions.

Addition and Subtraction of Like Fractions

Arithmetic operations on like fractions:

Mathematical operations such as addition and subtraction can be done easily with like fractions. As the denominator is the same, we must just add or subtract the numerator accordingly.

Addition

To add two or more like fractions, we may follow the following steps:

Step 1: Obtain the fractions.

Step 2: Add the numerators of all fractions.

Step 3: Maintain the common denominator of all fractions.

Step 4: Write down the fraction as  \(\frac{{{\rm{ Result\, in\, Step\, }}2}}{{{\rm{ Result\, in\, Step\, }}3}}\)

The following examples will illustrate the procedure:

Add the subsequent fractions with the help of a diagram:

Answer: Given fractions are \(\frac{2}{8},\,\frac{3}{8}\) and \(\frac{1}{8}\) respectively. Their addition is given by:

\(\frac{2}{8} + \frac{3}{8} + \frac{1}{8} = \frac{6}{8}\)

Subtraction

To subtract two like fractions, we may follow the following steps:

Step 1: Get the two fractions as well as their respective numerators.

Step 2: Subtract the smaller numerator from the larger numerator.

Step 3: Maintain the common denominator.

Step 4: Write down the fraction as  \(\frac{{{\rm{ Result\, in\, Step\, }}2}}{{{\rm{ Result\, in\, Step\, }}3}}\)

The following examples show the same.

Subtract \(\frac{3}{{10}}\) from \(\frac{8}{{10}}\)

Answer: We must find

\(\frac{8}{{10}} – \frac{3}{{10}}\)

\( = \frac{{8 – 3}}{{10}}\)

\( = \frac{5}{{10}}\)

\( = \frac{{5 \div 5}}{{10 \div 5}}\) [Dividing the numerator and denominator by their HCF \(5\)]

\( = \frac{1}{2}\)

Hence, the difference of the given fractions is \(\frac{1}{2}\)

Adding Fractions with Unlike Denominators

To add or subtract unlike fractions, we first convert them into the corresponding equivalent like fractions and then they are added or subtracted. The following steps are used to do the same.

Step 1: Get the fractions as well as their respective denominators.

Step 2: Compute the \({\text{LCM}}\) of the denominators.

Step 3: Convert every fraction into an equivalent fraction getting its denominator equal to the \({\text{LCM}}\) received in step \(2.\)

Step 4: Add or subtract like fractions received in step \(3.\)

The following example will clarify the above procedure.

Add: \(\frac{2}{3}\) and \(\frac{3}{7}\)

Answer: The \({\text{LCM}}\) of the denominators \(3\) and \(7\) is \(21.\)

So, we convert the given fractions into equivalent fractions with denominator \(21.\)

We have, 

\(\frac{2}{3} = \frac{{2 \times 7}}{{3 \times 7}} = \frac{{14}}{{21}}[21 \div 3 = 7]\)

And, \(\frac{3}{7} = \frac{{3 \times 3}}{{7 \times 3}} = \frac{9}{{21}}\) \(\left[{\because \,\,21 \div 7 = 3} \right]\)

Thus, \(\frac{2}{3} + \frac{3}{7} = \frac{{14}}{{21}} + \frac{9}{{21}}\)

\( = \frac{{14 + 9}}{{21}} = \frac{{23}}{{21}}\)

Hence, the sum of the given unlike fractions is \(\frac{{23}}{{21}}.\)

Solve Examples

Q.1. Add the following fractions: \(2\frac{3}{5} + \frac{4}{5} + 1\frac{2}{5}\)
Ans: Given, \(2\frac{3}{5} + \frac{4}{5} + 1\frac{2}{5}\)
\( = \frac{{10 + 3}}{5} + \frac{4}{5} + \frac{{5 + 2}}{5}\)
\( = \frac{{13}}{5} + \frac{4}{5} + \frac{7}{5}\)
\(= \frac{{13 + 4 + 7}}{5}\)
\( = \frac{{24}}{5}\)
Hence, the sum of the fractions is \(\frac{{24}}{5}.\)

Q.2. Compute \(\frac{5}{{12}} – \frac{7}{{12}} + \frac{{11}}{{12}}\)
Ans: We have \(\frac{5}{{12}} – \frac{7}{{12}} + \frac{{11}}{{12}}\)
\( = \frac{{5 – 7 + 11}}{{12}}\)
\( = \frac{{11 – 2}}{{12}}\)
\( = \frac{9}{{12}}\)
\( = \frac{{9 \div 3}}{{12 \div 3}}\) (Dividing the numerator and denominator by their HCF \(3\))
\( = \frac{3}{4}\)
Hence, the obtained fraction is \(\frac{3}{4}.\)

Q.3. Sneha painted \(\frac{1}{5}\) of the wall space in her room. Her sister Neha helped and painted \(\frac{3}{5}\) of the wall space. How much did they paint together?
Ans: Given, Sneha painted \(\frac{1}{5}\) of the wall space in her room, and her sister Neha helped and painted \(\frac{3}{5}\) of the wall space.
We need to find how much they painted together.
Here, we have to add the fraction of the wall space they painted.
That is, \(\frac{1}{5} + \frac{3}{5} = \frac{4}{5}\)
Hence, Sneha and Neha together painted \(\frac{4}{5}\) fraction of the wall space.

Q.4. Shubam was given \(\frac{3}{5}\) of a basket of oranges. What portion of oranges has been left in the basket?
Ans: Shubam was given \(\frac{3}{5}\) of a basket of oranges.
We need to find the fraction of oranges was left in the basket.
So, \(1 – \frac{3}{5} = \frac{1}{1} – \frac{3}{5}\)
\( = \frac{{1 \times 5}}{{1 \times 5}} – \frac{3}{5} = \frac{5}{5} – \frac{3}{5}\)
\( = \frac{{5 – 3}}{5} = \frac{2}{5}\)
Hence, the fraction of oranges left in the basket was \(\frac{2}{5}.\)

Q.5. Kshama had \(\frac{5}{6}\) of a cake. She gave \(\frac{2}{6}\) out of that to her elder brother. How much cake is left with her? 
Ans: A diagram can explain the situation. Note that here, the given fractions are like fractions.

We find that \(\frac{5}{6} – \frac{2}{6} = \frac{{5 – 2}}{6}\)
\( = \frac{3}{6}\) or \(\frac{1}{2}\)
Hence, the cake left with Kshama is \(\frac{1}{2}\)

Summary

In this article, we learnt about like fractions definition, like and unlike fractions, examples of like fractions, the addition and subtraction of like fractions, adding fractions with unlike denominators, solved examples on like fractions and FAQs on like fractions. The learning outcome is that it is easy to perform arithmetic operations such as addition and subtraction on like fractions.

Study The Types of Fractions

FAQs

Q.1. What is like and unlike fraction?
Ans: Like fractions: Fractions with the very same denominators are called fractions.
For example, \(\frac{3}{{11}} , \frac{5}{{11}} , \frac{7}{{11}}\) and \(\frac{8}{{11}}\) are like fractions.
Unlike fractions: Fractions with different denominators are called, unlike fractions.
For example,\(\frac{4}{{11}} , \frac{7}{{15}},\frac{9}{{17}}\) and \(\frac{{11}}{{28}}\) are unlike fractions.

Q.2. How do you convert unlike fractions to like fractions?
Ans: To convert unlike fractions to like fractions, use the following steps.
Step 1: Get the denominators of the fraction and find their \({\text{LCM}}\).
Step 2: Convert each fraction to its equivalent fraction with the denominator equal to the \({\text{LCM}}\) obtained in step \(1.\)

Q.3. What are the \(7\) types of fractions?
Ans: 1. Like fractions: Fractions that have the same denominator are called like fractions.
2. Unlike fractions: Fractions that do not have the same denominator are called, unlike fractions.
3. Unit fractions: Fractions in which the numerator is \(1\) are called unit fractions.
4. Equivalent fractions: Fractions that have the same value or represent the same part of a whole are called equivalent fractions.
5. Proper fractions: Fraction in which the numerator is less than the denominator is called proper fractions.
6. Improper fractions: Fraction in which the numerator is greater than or equal to the denominator is called an improper fraction.
7. Mixed fractions: Fraction that combines a whole number and a proper fraction is called mixed fraction or mixed number.

Q.4. How to add like fractions?
Ans: To add two or more like fractions, we may follow the following steps:
Step 1: Get the fractions.
Step 2: Add the numerators of all fractions.
Step 3: Maintain the common denominator of all fractions.
Step 4: Write down the fraction as  \(\frac{{{\rm{ Result\, in\, Step\, }}2}}{{{\rm{ Result\, in\, Step\, }}3}}\)

Q.5. Which set is an example of like fractions?
Ans: A fraction is represented by a portion of a single whole object or a group of things. It is defined by two numbers: one on top and the other at the bottom of a fraction bar referred to as the numerator and denominator. Depending on the similarity of the denominator, we classify two or more fractions into like fractions and unlike fractions.
Like fractions: The fractions with identical denominators are called like fractions.
For example, \(\frac{3}{{11}} , \frac{5}{{11}} , \frac{7}{{11}}\) and \(\frac{8}{{11}}\) are like fractions.