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

\[\dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}.\]

**Also Read: How to add surds?**

## 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.