# Fraction

A fraction is a number representing a part of a whole. The whole may be a single object or a group of objects.

Consider the fraction 7/12. This fraction is read as ”seven-twelfth” which means that 7 parts out of 12 equal parts in which the whole is divided. In the fraction 7/12, 7 is called the numerator and 12 is called the denominator.

Following are some more fractions:

(i) The fraction 5/7 is read as ”five-seventh” which means that 5 parts out of 7 equal parts in which the whole is divided. In the fraction 5/7, 5 is called the numerator and 7 is called the denominator.

(ii) The fraction 3/10 is read as ”three-tenth” which means that 3 parts out of 10 equal parts in which the whole is divided. In the fraction 3/10, 3 is called the numerator and 10 is called the denominator.

(iii) The fraction 1/5 is read as ”one-fifth” which means that 1 parts out of 5 equal parts in which the whole is divided. In the fraction 1/5, 1 is called the numerator and 5 is called the denominator.

For example:

1. Mrs. Brown has 24 apples. She ate 1/4 of them.

(i) How many apples does she eat?

(ii) How many does she have left?

Solution:

(i) Here the fraction 1/4 means take 1 part from 4 equal parts.

So, arrange 24 apples in four equal groups.

Clearly, each group will contain 24 ÷ 4 = 6 apples.

Thus, 1/4 of 24 is 6.

Hence, Mrs. Brown ate 6 apples.

(ii) Number of left out apples = 24 – 6 = 18.

2. Andrea has a packet of 20 biscuits. She gives 1/2 of them to Andy and 1/4 of them to Sally. The rest she keeps.

(i) How many biscuits does Andy get?

(ii) How many biscuits does Sally get?

(iii) How many biscuits does Andrea keep?

Solution:

(i) Here, 1/2 of 20 means take 1 part from two equal parts.

So, we arrange 20 biscuits in two equal parts.

Clearly, each part will contain 20 ÷ 2 = 10 biscuits.

Therefore, 1/2 of 20 is 10.

Hence, Andy gets 10 biscuits.

(ii) 1/4 of 20 means take 1 part from four equal parts.

So, we arrange 20 biscuits in four equal parts.

Clearly, each part will contain 20 ÷ 4 = 5 biscuits.

Therefore, 1/4 of 20 is 5.

Hence, Sally gets 5 biscuits.

(iii) Clearly, left out biscuits are kept by Andrea.

Therefore, Andrea keeps 20 – 10 – 5 = 5 biscuits.

3. What fraction of a day is 8 hours?

Solution:

We have,

One day = 12 hours.

Therefore, 8 hours = 8/12 of a day.

Hence, 8 hours is 8/12 part of a day.

4. Determine 2/3 of a collection of 9 balls.

Solution:

In order to find 2/3 of a collection of 9 balls, we divide the collection of 9 balls in 3 equal parts and take 2 such parts. Clearly, each row has 9/3 = 3 balls.

When, we take 2 rows out of 3 rows. It represents 2/3 of 9 balls. There are 6 balls in 2 rows.

Hence, 2/3 of 9 balls = 6 balls.

Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions

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