# Similar and dissimilar fractions | Like and unlike fractions

We will learn about similar fractions and dissimilar fractions on this page. They are also known as like and unlike fractions.

## What are Similar Fractions

Definition of similar fractions: Two or more fractions are called similar (or like) fractions if they have the same denominator (the bottom number of a fraction).

Similar fractions are sometimes known as like fractions.

Note: From the definition, it is clear that two similar fractions will be of the forms $\dfrac{a}{c}$ and $\dfrac{b}{c}$, where $c \neq 0$.

Examples of similar fractions:

(i) $\dfrac{1}{2}$, $\dfrac{3}{2}$, $\dfrac{4}{2}$, $\dfrac{7}{2}$ are examples of like fractions as they all have the same denominator 2.

(ii) All of $\dfrac{1}{12}$, $\dfrac{3}{12}$, $\dfrac{5}{12}$ have the same denominator 12. So by the definition of similar fractions, they are similar or like fractions.

(iii) Non-examples of similar fractions: As both $\dfrac{1}{2}$ and $\dfrac{1}{3}$ have different denominators 2 and 3, they are not similar fractions.

Also Read: Basic concepts of surds

## What are Dissimilar Fractions

Definition of dissimilar fractions: Two or more fractions are called dissimilar or unlike fractions if they have different denominators.

Dissimilar fractions are sometimes known as unlike fractions.

Note: From the definition, we know that the general forms of two dissimilar fractions are $\dfrac{a}{c}$ and $\dfrac{b}{d}$ where $c \neq d$.

Examples of dissimilar fractions:

(i) $\dfrac{1}{2}$, $\dfrac{3}{5}$, $\dfrac{4}{7}$, $\dfrac{7}{6}$ are examples of dissimilar or unlike fractions as they all have different denominators.

(ii) $\dfrac{1}{12}$, $\dfrac{3}{10}$, $\dfrac{5}{17}.$

(iii) Non-examples of dissimilar fractions: Note that both $\dfrac{1}{5}$ and $\dfrac{2}{5}$ have the same denominator 5. So they are not dissimilar/unlike fractions.

Conclusion: Two fractions are either similar or dissimilar. In other words, if two fractions are not similar then they must be dissimilar; and vice-versa.

Also Read: Similar surds and dissimilar surds

## How to add similar fractions?

How to add two like fractions? Suppose that we are given two fractions. The below steps have to be followed to add them.

Step 1: First check whether the given fractions are similar or not (that is, they have the common denominator or not). If they are similar fractions, then go to step 2.

Step 2: Add the numerators of the given fractions.

Step 3: Then the sum of the given two similar fractions will be

$=\dfrac{\text{sum of numerators}}{\text{common denominator}}.$

Mathematically, if the two similar fractions are $\dfrac{a}{c}$ and $\dfrac{b}{c}$, then their sum will be

$\dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}.$

## How to add dissimilar fractions?

How to add two unlike fractions? As we know that two dissimilar fractions are of the forms $\dfrac{a}{c}$ and $\dfrac{b}{d}$ where $c \neq d$, applying algebra we get their sum as follows:

$\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}.$

## FAQs

Q1: What are like fractions?

Answer: Fractions with the same denominator are called like fractions. For example, 4/5 and 7/5 are like fractions.

Q2: What are unlike fractions?

Answer: Fractions with different denominators are called unlike fractions. For example, 3/5 and 5/9 are unlike fractions.

Q3: How to convert unlike fractions into like fractions?

Answer: Yes, unlike fractions can be converted into like fractions. Let us consider two unlike fractions 3/5 and 5/9. Note that 3/5 = (3×9)/(5×9) = 27/45 and 5/9 = (5×5)/(9×5) = 25/ 45. Observe that 27/45 and 25/45 are like fractions as they have the same denominator 45.

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