# Similar and dissimilar fractions | Like and unlike fractions

Similar fractions are fractions with the same denominators and dissimilar fractions are fractions with different denominators. 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.

## 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 $c \neq d$.

Related Topics: How to Write a Mixed Number as an Improper Fraction

Simple fractions and Compound fractions

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 and dissimilar fractions | Like and unlike fractions

Basic concepts of surds

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:

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

## How to add similar and dissimilar fractions?

Adding of similar and dissimilar fractions: We will understand the addition of similar and dissimilar fractions with an example. Note that $\dfrac{1}{2}, \dfrac{3}{2}$ are similar fractions and they are dissimilar with $\dfrac{1}{3}$. Let us find the sum

$\dfrac{1}{2}+ \dfrac{3}{2}+\dfrac{1}{3}$

= $\dfrac{3}{6}+ \dfrac{9}{6}+\dfrac{2}{6}$ (here we make the fractions with common denominator 6).

= $\dfrac{3+9+2}{6}$

= $\dfrac{14}{6}$

= $\dfrac{7 \times \cancel{2}}{3 \times \cancel{2}}$

= $\dfrac{7}{3}$.

## 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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