# Fractions – Introduction

Suppose you have borrowed Rs. 20 from your friend in the last month. Now he has asked you to return his money. But you are paying him only Rs. 10 and the rest amount you want to return next month. It means you are paying the total amount not in one lot but in a fraction that means “in parts”.

So we can say that any when any unit of a thing is divided into equal parts and some parts are considered, then it is called a fraction. For example 1/2, 3/4, 2/5, 3/7 ,etc.

3/4 is read as three fourth.

## TERMINOLOGIES

Denominator= The lower value indicates the number of parts into which the whole thing or quantity is being equally divided and it is known as Denominator.

Numerator= The upper value indicates the number of parts taken into consideration (or for use) out of total parts known as Numerator.

So in the fractions 2/3, 5/7, 1/4, etc. 2, 5, 1 are Numerators and 3, 7, 4 are Denominators.

The numerators and denominators are also called the ‘terms’ of a fraction.

## TYPES OF FRACTIONS

1. Proper Fraction= A fraction whose numerator is less than its denominator, but not equal to zero is called a Proper Fraction. For example 1/2, 3/4, 2/7, 11/20, etc.
2. Improper Fraction= A fraction whose numerator is equal to or greater than its denominator is called an Improper Fraction. For example 7/2, 8/5, 21/11, 63/15, etc.
3. Mixed Fraction= A number which consists of two parts (i) a natural number (ii) a proper fraction, is called a Mixed Fraction.
4. Like Fraction = The fractions whose denominators are the same are called Like Fractions, For example, 3/11, 4/11, 5/11, 9/11, etc.
5. Equivalent Fraction = The fractions whose values are the same i.e., the ratio is the same is called Equivalent Fractions. For example 2/3 = 4/6 = 6/9 = 8/12 = 10/15 = 12/18. It implies that: (i) if we multiply the numerator and the denominator by the same non-zero number, the value of the fraction remains unchanged. (ii) if we divide the numerator and the denominator by the same non-zero number, the value of the fractions remains unchanged.

## REDUCTION OF FRACTION TO SIMPLEST FORM:

1. HCF Method: Divide the numerator and denominator both by their HCF. e.g., to reduce 21/35 to its lowest term just divide 21 and 35 by their HCF. So, $\frac { 21 }{ 35 } \div \frac { 7 }{ 7 } =\frac { 3 }{ 5 }$
2. Prime Factorisation Method: Just cancel out the common prime factors of both the numerator and denominator. For example, to reduce 42 and 140 we cancel out the common prime factors as $\frac { 42 }{ 140 } =\frac { 2\times 3\times 7 }{ 2\times 2\times 5\times 7 } =\frac { 3 }{ 10 }$

The short tricks related to the Comparison of Fractions will be discussed in the next part.