A fraction is a number stated as a quotient with a numerator divided by a denominator into mathematical terms. A simple fraction is made up of two parts: an integer numerator and a non-zero integer denominator. Equivalent fractions are those with different numerators and denominators but their fractional values are the same. 5/10 and 7/14, for example, are similar fractions because they are both equal to 1 / 2 when simplified. Each fraction represents a part of a whole. If two or more fractions are equal to the same fraction when simplified, they are said to be equivalent.

## Improper Fractions

There are three types of fractions,

- Proper fraction,
- Improper fraction, and
- Mixed fraction.

__Proper Fraction__- When the value in the numerator is smaller than the value in the denominator it is a proper fraction. For example ⅗, ⅚, ⅞, are all proper fractions.

__Improper Fraction__

If the numerator is equal to greater than the denominator it is called the** improper fraction**. For example 8/5, 7/7, 9/4 are all improper fractions.

__Mixed Fraction__

When a whole number and a fraction are together then it is a mixed fraction. For example, 2 ¾,5 ⅓,4 ⅖ are mixed fractions.

**How to Find Equivalent Fractions?**

**There are two ways in which you can find the Equivalent Fractions**

- Multiplication Method
- Division Method

**1. Multiplication Method**

**Step 1: **Multiply both the numerator and denominator of a fraction by the same whole number.

**Step 2:** If you multiply the top and bottom of the fraction by the same number, you will not change the value of the fraction.

## Example on Equivalent Fractions

Find fractions equivalent to ⅖ by multiplying the numerator and denominator by the same whole number

**Solution:**

Multiplying the numerator and denominator by 3

** =**

Multiplying the numerator and denominator by 4

** =**

Multiplying the numerator and denominator by 5

** =**

Multiplying the numerator and denominator by 6

** =**

Therefore these are all equivalent fractions:

2/5, 6/15, 8/20, 10/25 ,12/30

In the lowest terms, all of these fractions equal 2/5.

**2. Division Method**

**Step 1:** Divide the numerator and denominator of any fraction by the same number to find the equivalent fraction.

**Example: **Find an equivalent fraction of 60/90.

**Solution:**

2 is a common factor of 60 and 90.

Thus, 60/90=

60÷2

90÷2

= 30/45

Again, 3 is a common factor of 30 and 45.

Thus,30/45=

30÷3

45÷3

= 10/15

Here, 5 is a common factor of 10 and 15.

Thus, 10/15=

10÷5

15÷5

= 2/3

Therefore, a few equivalent fractions of 60/190 are 30/45, 10/15, 2/3,

## Understanding Improper Fractions with Examples

### Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps:

- The whole number part is multiplied by the denominator.
- Add that to the numerator
- Add the result to the denominator.

**Example:** Convert 4 to an improper fraction.

**Solution:** In multiplying the whole number by the denominator, you get:

4 × 5 = 20

Add that to the numerator:

20 + 3 = 23

Then write that result above the denominator:

**∴ Fraction 4** ** = 23/5**

### Converting Improper Fractions to Mixed Fractions

In order to convert an improper fraction to a mixed fraction, follow these steps:

- Divide the numerator by the denominator.
- Write down the whole number answer
- Then write down any remainder above the denominator.

**Example:** Convert to a mixed fraction.

**Solution:**

Divide 13 by 5 the remainder will be 3 and the quotient will be 2

First, write down the quotient 2 and then write down the remainder (3) above the denominator (5).

**∴ Fraction** ** = 2**

If you want to learn more about equivalent fractions and improper fractions visit Cuemath.

## Also Read

How to Hack Instagram Account- Ultimate Guide

Can You See Who Viewed Your TikTok – Guide