Fractions Class 3 Notes Maths

Imagine you have a delicious apple. Now, if you eat just half of it, that's like a special way of talking about it called a "fraction." And if you eat only a quarter of the apple, that's another kind of fraction. So, fractions help us describe and share things when we're talking about parts of a whole, like your tasty apple!

Fractions are a way of naming and talking about equal parts of something, like a piece of cake or a group of toys.

Understanding Fractions:

Now we know that 1 /4 is a fraction where 1 is the numerator and 4 is the denominator and the whole ¹/₄ is called a fraction.

A fraction consists of two parts:-

1. Numerator: The part which is written above the horizontal line is called as numerator.
2. Denominator: The part which is written below the sleeping line horizontal line is called as denominator.

Thus, a number is written above and a below the horizontal line and then the arrangement is called as fraction.
Let's explore further,

Halves

Two Equal Parts
(a) Anuja buys a chocolate bar. She divides it into two equal parts so that she can give one part each to her two children.

• Two equal parts are called halves.
• Each one of the equal parts is called one-half.
• One-half means 1 part out of 2 equal parts. It is written as 1 / 2.

(b) Look at the figures given alongside.
 Each shape is divided into 2 equal parts.
One part is shaded in each shape. Each shaded part represents 1 / 2.

Thirds

Three Equal Parts
(a) Rajat and Seema went to a restaurant to eat pizza with their mother.
The mother ordered one pizza. She told them to share it equally. They divided it into 3 equal parts. Three equal parts are called thirds.
Each one of the equal parts is one-third of the whole. It is written as 1 / 3.
(b) In the picture given alongside, each shape is divided into 3 equal parts. One part out of the 3 parts is shaded. Each shaded part of the shape is one-third of the whole.

Fourths

Four Equal Parts
(a) Rajat’s mother cut the pizza into four equal parts for Rajat and his three friends.
When we divide a whole into 4 equal parts we say that we divide it in fourths. Each part is one-fourth or one-quarter of the whole. This is also written as 1 / 4.
(b) Each shape, given alongside, is divided into 4 equal parts.     
One out of the 4 equal parts is shaded. Each shaded part of the shape is one-fourth of the whole.
Each equal part is called one-fourth.
One-fourth is also called as one-quarter.
One-fourth means 1 part out of 4 equal parts.

More than Four equal Part

Just as you say one-half, one-third, one-fourth and write them as 1 / 2, 1 / 3 and 1 / 4 respectively, similarly, you can name other equal parts as under:
(a) When a whole is divided into five equal parts, each part is called one-fifth. 
It is written as 1 / 5.
(b) When a whole is divided into six equal parts, each part is called one-sixth. 
It is written as 1 / 6.
(c) When a whole is divided into seven equal parts, each part is called one-seventh. It is written as (1 / 7).
In a similar way, you have one-eighth (1 / 8), one-ninth (1 / 9), one-tenth (1 / 10), one-eleventh (1 / 11) and so on.

Numerals such as 1 / 2, 1 / 3, 1 / 4, 1 / 5, etc, ... are called fractions. 
Numbers named by the fractions are called fractional numbers.

More than one out of many Equal Parts

(a) In a birthday party, Aastha’s mother cut a cake into three equal parts and wanted to give one piece to Aastha. But she insisted on taking two pieces. So, Aastha got 2 out of 3 equal parts. You can express it as two-thirds or 2 / 3.
(b) Bunty had a sandwich which he divided into four equal pieces as shown alongside. He ate 3 pieces out of the 4 pieces. We say, he ate three-fourths or 3 / 4 of the sandwich.
(c) The following pictures show other fractions. These will help you to understand clearly the meaning of given fractions.

Fraction of a Group or a Collection

Fractions can also be used to name parts of a group or a collection.
Study the following examples.

1. 2 out of 3 balloons are green. Two-thirds of the balloons are green. The fraction for green balloons is 2 / 3.
   Here,
   
2. One out of five apples are red.
   One-fifth of the apples are red. The fraction of red apples is 1 / 5.
   
3. 3 out of 4 animals are rabbits.
   Three-fourths of the animals are rabbits. The fraction of rabbits is 3 / 4.
   

Numerator and Denominator

In the fraction 5 / 7, 5 is called the numerator and 7 is called the denominator.

A Fraction Represents a Division Numeral

Look at the following pictures.
The division numeral, 1 ÷ 5 indicates that out of 5 equal parts, 1 part is shaded.
The division numeral, 3 ÷  4 indicates that 3 oranges out of 4 oranges are taken.
The fractions 1 / 5 and 3 / 4 also express these facts respectively.
Therefore, 1 ÷ 5 = 1 / 5 and 3 ÷ 4 = 3 / 4.

Using Division to find Fractional Part of a Whole

1. Lakshya had 8 strawberries. He ate one-half of them. How many did he eat?
   To find the number of strawberries Lakshya ate, divide the strawberries, into 2 equal parts and count the number in one of these parts.
   We have, 1 / 2 or 8 = 4
   So, Lakshya ate 4 strawberries.
2. Ritu had 9 balls. She gave 1 / 3 of them to her friend. How many balls did she give away?
   To find the number of balls Ritu gave to her friend, divide the balls into 3 equal groups and count the number in one of these groups.
   We have: 1 / 3 of 9 = 3.
   So, Ritu gave 3 balls to her friend.
   If Ritu gave two-thirds of balls to her brother, then you need to count the balls in two groups. Two groups contain 6 balls,
   ∴ 2 / 3 of 9 = 6.Similarly, to find 1 / 2 of 6 pencils, you divide the 6 pencils into 2 groups and count the number of pencils in 1 group, which is 3 pencils.
   ∴ 1 / 2 of 6 = 3.
   To find 2 / 3 of 6 pencils, you count the number of pencils in 2 groups out of 3 groups. This is four pencils.
   ∴ 2 / 3 of 6 = 4.
   You can also find 2 / 3 of 9 as shown below. 
   2 / 3 of 9 = 2 × (9 ÷ 3) =  2 × 3 = 6
   You can also write 2 / 3 of 9 as under: 
   2 / 3 of  9 = (2 × 9) ÷ 3 = 18 ÷ 3 = 6

Problems Based on Real Life Situations

Example 1: Ria had 14 crayons in a packet. She gave one-half to her friend. How many crayons did she give to her friend?

One-half of

Thus, Ria gave 7 crayons to her friend.

Fraction on the Number Line

As numbers are represented on a number line, fractions can also be shown on a number line.

• Each fraction number line starts at 0 and ends in 1.
• The denominator of the fraction decides into how many equal parts we divide the whole number line from 0 to 1.
• The numerator of the fraction decides how many of these equal parts we take.

For example:
To represent 1 / 2, we divide the number line into two equal parts and take one part out of those.
To represent 2 / 3, we divide the number line into three equal parts and take two parts out of those.
To represent 3 / 4, we divide the number line into four equal parts and take three parts out of those.
Now, look at the number line and write the fractions represented by the points A and B.
A represents 2 / 5 and B represents 4 / 5 on the number line.