**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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