2nd Grade Basic Concept of Fractions

Concept of fractions will help us to express different fractional parts of a whole.


One Whole:

A whole can be a single object or a collection of objects.

One Whole

Fractions:

Part of a whole are called fractions.

One-half:


When an article or a collection of objects is divided into two equal parts is called as half of the whole. We express one half by the symbol 12.

One-half as 1/2

For example, suppose the cake is cut into two equal parts. Each part is called one half of the cake. We write one-half as 12.


In 34, the numerator is 3 and the denominator is 4.


Examples on One-half:

1. Richa and Naveen divide a cake into 2 equal parts, and eat one part each.

One-half

Each of them gets one-half (12) of the whole cake.


2. Let us take another example. Richard and Thomas want to divide equally 4 balls between them, How many balls would each get?

4 Balls Divide Equally

4 balls can be divided into 2 groups (of 2 balls each).

4 Balls Divide Equally into 2 Groups

Each group is one-half of the whole collection. Richard gets 2 balls and Thomas gets 2 balls.

So, one-half of 4 is 2.


Note: In a fraction, it is important that the 'whole' is divided into 'equal' parts.


Half of a Collection:

A fraction is a part of the whole or part of a collection. 

Half of a Collection

A collection of objects can be divided into two equal parts.

One Half of the Collection
One Half of the Collection


One-Third:

When we divide a whole or a group into three equal parts, each part is called one-third of the whole or a group. We express one third by the symbol 13.

One-third as 1/3

For example, suppose the biscuit is cut into three equal parts. Each part is called one third of the biscuit. We write one-third as 13.

Again,

Look at the figures below and find out how many equal parts are there? We find that in each of the following figures the whole is divided into three equal parts.

Three Equal Parts

Each shaded part is one-third of the whole.

One-Third of the Whole

When an object is divided into three equal parts, each part is called one-third of the object. It is written as 13. It is read as one-third.


1. For example, Sarah, Theresa and Ashley together have to make a three-coloured disc for their science exhibition.

They divide the disc into three equal parts.

Three Equal Parts

Sarah colours one part red, Theresa colours one part green and Ashley colours one part blue.

Red Blue Green: One-Third

They each coloured one-third (13) of the whole disc.


2. Let us take another example.

Nancy, Stephanie and Richard want to divide 12 apples equally among themselves

Divide 12 Apples Equally


12 apples can be divided into 3 groups (of 4 apples each).

Divide 12 Apples Equally into 3 Groups

Each group is one-third of the whole collection.

Nancy, Stephanie and Richard get 4 apples each.

So, one-third of 12 is 4.


One-third of a Collection:

One-Third of a Collection
One-Third of the Collection


One Fourth:

When we divide a whole or a group into four equal parts, each part is called as one fourth of the whole or the group. We express one fourth by the symbol ¼

One-fourth as 1/4

For example, suppose the pizza is cut into four equal parts. Each part is one-fourth or one-quarter of the pizza. We write one-fourth as ¼.


There are four members in Michael's family. Michael divides a pizza into 4 equal parts and each one of them gets equal share. When a whole is divided into 4 equal parts, and each part is called one-quarter.

One-Quarter


      One-quarter is one of four equal parts.

      It is written as 14.

      It is read as one-quarter or one-fourth.

One Whole and One-Fourth
One-fourth of a Circle
One-fourth of 8 Balls

One-fourth of a Circle is shaded pink.

One-fourth of 8 balls is 2 balls.


One-Fourth of a Collection:

One-Fourth of a Collection


Two-thirds:

When we divide a whole or a group into three equal parts, two parts combined together represent two thirds. We express two thirds by the symbol 23.


Three-fourths:

When we divide a whole or a group into four equal parts, three parts combined together represent three fourths. We express three fourths by the symbol 34.     

In 34, the numerator is 3 and the denominator is 4.

Three-fourths of a Circle

Three-fourths of the circle is shaded blue.

Three-fourths of 8 Balls

Three-fourths of 8 balls is 6 balls.

 

Note: The symbol 1213142324, etc. are called fractions.


Fractions (third)


13 tells 1 part out of 3 equal parts.





23 tells 2 parts out of 3 equal parts. 




33 tells 3 parts out of 3 equal parts.

One Third
Two Third
Three Third


Fractions (fourth)


14 tells 1 part out of 4 equal parts.





24 tells 2 parts out of 4 equal parts.





34 tells 3 parts out of 4 equal parts.





44 tells 4 parts out of 4 equal parts.

One Fourth
Two Fourth
Three Fourth
Four Fourth

The basic concept of fractions are explained above along with the pictures.


SUMMARY:

• Fractions are equal parts of a whole.

• Two-halves make a whole

• Three-thirds make a whole.

• Four-fourths make a whole.

• In a fraction, numerator indicates the parts being chose and the denominator indicates the number of equal parts in all.


Worksheet on 2nd Grade Basic Concept of Fractions:

1. Multiple Choice Questions (MCQ) on 2nd Grade Basic Concept of Fractions:

   Tick (the correct option.

(i) 13 is read as

(a) halves;     (b) one-fourth;     (c) one-third


(ii)

Three-fourths of a Flower

shaded part of a flower shows

(a) two-fourths;     (b) one-fourth;     (c) three-fourths


(iii) 13 of 21 =

(a) 6;     (b) 4;     (c) 7


Answer:

1. (i)  (c) one-third

(ii) → (c) three-fourths

(iii) → (c) 7


2. Write the fraction for the following word problems:

(i) In a Math test of 25 marks, Ashley got 19 marks. What fraction of marks did she get?

(ii) In a book of 36 pages, Anthony read 24. What fraction did he read?

(iii) Christopher bought 5 cans of paint and used 3 cans. What fraction of the paint did he use?

(iv) From her homework of 12 sums, Sarah finished doing 8 sums. What fraction of her homework is not finished?

(v) Seven monkeys were sitting on a tree. One of them had a long tail. What fraction of monkeys had a long tail?


Answer:

2. (i) 1925

(ii) 2436

(iii) 35

(iv) 412

(v) 17


FAQ

1. What Is the Meaning of One Half?

When a whole is divided into two equal parts, each part is called one-half and is written as 12.

12 means, '1 part out of 2 equal parts.'

2. What Is the Meaning of One-Third?

When a whole is divided into three equal parts, each part is called one-third and is written as 13.

13 means, '1 part out of 3 equal parts.'

3. What Is the Meaning of One-Fourths?

When a whole is divided into four equal parts, each part is called one-fourths or a quarter, and is written as 14.

As the name suggests, 14 means, '1 part out of 4 equal parts.'

4. What Is the Meaning of three-Fourths?

As one-fourth means 1 part out of 4 equal parts, similarly three-fourths means 3 parts out of 4 equal parts. 

Three-fourths is also called three quarters and is written as 34

Fractional Numbers

Concept of Fractions

Numerator and Denominator 

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