**Fraction review**

A fraction is used to represent a part of the whole. A fraction consists of two parts - a numerator and a denominator.

In the following diagram, the circle is divided into 4 equal parts.

The shaded area is 3 parts out of 4 parts and is represented by the fraction ¾ .

There are different types of fractions such as proper fractions, improper fractions, equivalent fractions, like fractions and also mixed fractions.

**Proper fractions**

When the numerator is less than the denominator it is called a proper fraction. Examples of proper fractions: ½ , ¾

**Improper fractions**

When the numerator is greater than the denominator it is called an improper fraction. Examples of improper fractions: 4/3, 9/7. Improper fractions can be converted into mixed fractions.

**Mixed fractions**

A mixed fraction consists of a whole number and a proper fraction. Examples of mixed numbers: 3 ½ , 4 ⅓

Practice questions

Question: Classify the following fractions as proper, improper or mixed fractions

¾ , ⅚ , 8/5, 4 ½ , 5/9, 11/10, 6 ⅘

( Answer: Proper fractions: ¾ , ⅚ , 5 / 9

Improper fractions: 8 / 5, 11 / 10

Mixed fractions: 4 ½ , 6 ⅘

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**Operations with Fractions**

Fractions can be compared, added, subtracted, multiplied and divided just like whole numbers.

**Finding reciprocals of fractions**

We can obtain the reciprocal of a fraction by turning it upside down i.e. replacing the numerator with the denominator and the denominator with the numerator. In order to find the reciprocal of a mixed fraction, we must first convert it into an improper fraction.

The reciprocal of a proper fraction is an improper fraction and vice versa.

For example:

The reciprocal of 2/7 is 7/2.

The reciprocal of 4 ½ = 2/9

When we multiply a fraction by its reciprocal, the answer is always 1.

**Addition and subtraction of fractions**

In order to add or subtract fractions, we must first convert them into like fractions and then perform the addition or division operation

**Multiplication of fraction**

Before multiplying fractions, we can try to reduce the fractions to their lowest equivalent forms.

**Division of fractions**

In order to divide a fraction by another, use the following steps:

1. Find the reciprocal of the second fraction ( the one you want to divide by)

2. Multiply the first fraction (the one to be divided) by the reciprocal in step 1

For Example:

¾ divided by ½

Step 1: find the reciprocal of ½ = 2/1 = 2

Step 2: Multiply = ¾ * 2 = 3/2 = 1 ½

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