1. What is a fraction?

If a whole object or a group is divided into equal parts then each part is called a fraction of that whole object or group.

2. Each fraction has two parts: Numerator and Denominator.

Example:

3 = Numerator

4 = Denominator

The whole object is divided into 4 parts. 3 of those 4 parts are represented as ^{3}⁄_{4}. represent the selected 3 parts.

A fractions denominator can never be zero.

If the numerator of a fraction is zero (0) then the value of the fraction is zero.

3. What is the use of fractions?

Fractions are used to denote part between two numbers or two fractions.

Example: 0 < ^{3}⁄_{4} < 1. To denote a value between 0 and 1 fractions are used.

4. There are infinite number of fractions in between two numbers or two different fractions.

1. If two or more different fractions represent same values (amount or quantity), those fractions are called equivalent fractions.

2. Equivalent fractions can be generated by multiplying/dividing both numerator and denominator by a whole number.

Example: ^{2}⁄_{3}, ^{4}⁄_{6}, ^{6}⁄_{9} : Both ^{4}⁄_{6} and ^{6}⁄_{9} are equivalent fractions of ^{2}⁄_{3}.

By multiplying both the numerator and denominator by 2 we get ^{4}⁄_{6}.

By multiplying both the numerator and denominator by 3 we get ^{6}⁄_{9}.

In the above picture ^{2}⁄_{3} and ^{4}⁄_{6} covers the same amount (area). So ^{2}⁄_{3} and ^{4}⁄_{6} are equivalent fractions.

1. If the highest common factor (HCF/GCF/GCD) of the numerator and the denominator of a fraction is 1 then the fraction is in the lowest term. It can't be reduced further.

2. If hcf(or gcf/gcd) of numerator and denominator of a fraction greater than 1 then the fraction can be reduced. To reduce the fraction divide the numerator and the denominator by the hcf (gcf/gcd).

3. The reduced fraction and the original fractions are equivalent fractions.

Example: Reduce the ^{6}⁄_{18} to its lowest term.

Find HCF (GCF/GCD) of 6 and 18 by prime factorisation method. HCF (GCF/GCD) of 6 and 18 is 6.

Divide the numerator and denominator of the fraction ^{6}⁄_{18} by the HCF, 6.

^{6}⁄_{18} *divide by* ^{6}⁄_{6} = ^{1}⁄_{3}

Answer = ^{1}⁄_{3}