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# Fractions – Definition & Types

The word “fraction” is derived from the** Latin word fractus**, which means the number representing part of the whole or any number of parts. In layman language, a fraction is a number that describes the size of parts of a whole unit. These sizes can be one-half, three-quarters, and a third, etc.

A fraction is normally **written in two parts**, where ** the numerator** is displayed above a line or before a slash whereas,

**is displayed below or before the line.**

*the denominator*The terms numerator and denominator are also used in other fractions such as complex, compound, mixed and complex fractions.

## What are Fractions?

For example, if you have an orange and cut it into 4 equal slices, 1 of those slices is written: 1/4.

### What are Proper Fractions?

A proper fraction is a fraction in which the numerator is less than the denominator. In other words, a proper fraction is less than 1.

*Examples of proper fractions are:*

1/2, 2/3, 2/7, 4/7, 5/11, 15/26, 50/97, etc.

A fraction is said to be an improper fraction when its denominator is smaller than its numerator.

### What are improper fractions?

A fraction is said to be an improper fraction when its denominator is smaller than its numerator. This fraction is generated by the addition of a whole number and one proper fraction. The fractions 11/5, 23/9, 18/5, 3/2, 9/8, etc., are the fractions where the denominators are smaller than the numerators.

*For example:*

(i) 1 + 4/3 = 3/3 + 4/3 = (3 + 4)/3 = 7/3

(ii) 3 + 5/7 = (3 × 7)/7 + 5/7 = (21 + 5)/7 = 26/7

Similarly, fractions such as:13/5, 27/9, 5/3, 17/2, 9/7 are called improper fractions.

### What are Mixed Fractions?

A mixed fraction is a fraction in which a whole number and a proper fraction have been combined. Examples of mixed fractions are 1^{1/}_{3}, 5 ^{2 /}_{3, }6^{1/}_{2,} etc.

#### How to convert improper fraction to mixed fraction?

To convert an improper fraction into a mixed fraction, the numerator is divided by the denominator, and the quotient written as a whole number, and the remainder as the numerator.

*Example 1*

Convert 17/4 as a mixed fraction.

__Solution__

To solve this problem, these are the steps undertaken

- Divide the numerator by the denominator.
- The quotient is 4, and the remainder is 1.
- Combine the whole number 4 with the fraction 1/4
- 4
^{1/}_{4}is the mixed fraction.

* *

*Example 2*

Convert 14/9 to a mixed fraction.

__Solution__

- Begin by dividing the numerator by the denominator
- 14/9 = 1 and 5 as the remainder.
- Take 1 as the whole number and 5 as the numerator,
- Write down the fraction as: 14/9 = 1
^{5/}_{9}

Note: If during division, there is no remainder, then take the quotient as a whole number.

*Example 3*

Convert the fraction 20/5 to a mixed fraction.

__Solution__

- Divide the numerator by the denominator.
- 20/5 =4
- The quotient is 4, and there is no remainder. Therefore, take 4 as the answer.
- 20/5 = 4

#### How to convert mixed fractions as a proper fraction?

A mixed fraction can be expressed as a proper fraction. This I did by multiplying the fraction’s denominator with the whole number, and the product added to the numerator.

For example, to convert a mixed fraction 2 ^{1/}_{3 }to an improper fraction, the following steps are followed:

- Multiply the denominator by the whole number.
- For this case, 2 is the whole number and 3 is the denominator,
- 2 x 3 = 6
- Add the product to the numerator
- 6 + 1 =7
- Now the numerator changes to 7 and the denominator remains 3.
- Write the result an improper fraction as 7/3.

Take another example, suppose we want to convert 5^{2/}_{3 }to an improper fraction.

*These are the steps:*

- First of all, multiply the denominator by the whole number and add this product to the numerator.
- 3 x 5 = 15
- Add the numerator to the product
- 15 + 2 = 17
- Write fraction by taking 17 as the new numerator while 5 remaining as the denominator.
- The result is 17/5