Introduction to Fractions:

A fraction is used to represent a part of the whole. A fraction consists of two parts - a numerator and a denominator. Example: 5/7. The number at the top is called the numerator and the number at the bottom is called the denominator.

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


The shaded area is 1 part out of 4 parts and is represented by the fraction ¼ . In this case, the numerator is 1 and the denominator is 4.

Practice examples

Question: Identify the numerator and the denominator in the following fractions
3 / 5, 6 / 7, 12/ 14, 6/ 9, 1/ 100

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

Operations with Fractions

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

What is the reciprocal of a fraction?

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.

For example: the reciprocal of 2/7 is 7/2.

Practice examples

Question: Write down the reciprocals of the following fractions
3 / 5, 6 / 7, 12/ 14, 6/ 9, 1/ 100

( Answer:
    5 / 3, 7 / 6, 14 / 12, 9 / 6, 100 /1

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

To find the reciprocal of a mixed fraction, we must first convert it into an improper fraction.
When we multiply a fraction by its reciprocal, the answer is always 1. For example: 3/7 * 7/3 = 1.

Reciprocal are useful when we need to divide fractions.

Practice questions

Question: Find the reciprocal of the mixed fraction 3 ⅘.

( Answer: 
Step 1: First convert the mixed fraction into an improper fraction
            3 ⅘ = 19/ 5
    Step 2: Now find the reciprocal of the improper fraction
            Reciprocal is 5/19

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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