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 

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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