Example 1 : Suppose you have two chocolates and you want to share with your friend. Then you keep one for yourself and give one to your friend. That means each one of you have taken half of what you have.

Example 2 : Suppose you have six chocolates with you and again you want to share equally with your friend. From the knowledge of
division, you knowthat 6÷2 = 3. Hence each of you take 3 chocolates. Again each one of you have taken half of what you have.

In both these examples, you are dealing with discrete (individually distinct) elements (chocolates) and half of the total is again a set of discrete elements.

Example 3 : Suppose you have a cake and you want to share it with your friend. Then you cut it into two equal parts, give one part to your friend and you take the other part. Each one of you have got half of the total cake. Here half is a part (piece) of the total (cake).

Example 4 : Suppose you and your friend go to a restaurant and order for pizza. Suppose the server brings pizza which is cut into 4 equal pieces. Then each one of you eat two pieces of the pizza. How much of the pizza did each one of you eat? Again it is half of the total pizza.

In Examples 3 and 4, half is a part (piece) of the total (cake/pizza).

Illustrated explanation of Half (1⁄2)

In the figure given below, the part represented by the black portion (green portion) is Half (1⁄2) of the whole figure.

1⁄2 1⁄2

Exercise 1A : Understanding Half (1⁄2)

What is half of 30 ?

What part of 20 is ten ?

What is half of 16 ?

What is 7 half of ?

Half of a number is 9. What is that number?

For Answers see at the bottom of the Page.

Exercise 1B : Understanding Half (1⁄2)

Fill in the Blanks in the Table

Full

Half

Half of half

Ex: 20

10

5

36

----

----

----

14

----

----

----

6

For Answers see at the bottom of the Page.

Understanding Half (1⁄2), Quarter (1⁄4), Three-Fourth (3⁄4) and Relation between them

Look at the questions below.

What is plural of half? How many halves are there in a whole? How do we write a half?

Do you know the Answers?

The plural of half is halves. There are two halves in a whole. We write half as 1⁄2.

Instead of using the slash ("⁄") symbol, we can use the vinculum ("−") ( i.e. horizontal line) symbol to denote half, as shown below. 1 2

Half is also called one by two.

Suppose you and your three friends want to draw pictures.You bought 4 pencils and a chart. You want to share the articles.

How many pencils dooes each one of you get?

I am sure you can answer it as 1.

But, how do you share the chart?

You have to cut it into 4 equal pieces and each one of you gets a piece.

How many of the parts will make the whole chart? What part of the whole chart is each of the pieces with each one of you?

Each one of you received one of the four equal parts of the chart. So what each one of you got is the quarter (1⁄4) of the chart.

What part of the total pencils did each one of you get? Again it is 1⁄4, called quarter or one by four.

How many quarters of the chart did you and one of your friends together take? Two quarters.

What part of the whole chart are they? Half

How many quarters make one half? Two

How many quarters did you and two of your friends togetherreceive? 3 quarters.

Do you know what it is called?

If a whole is divided into four equal parts and three such parts are taken, it is called three-fourths.We write it as 3⁄4.

Illustrated explanation of Half (1⁄2), Quarter (1⁄4), Three-Fourth (3⁄4) and Relation between them

In the figure given below, the part represented by the black portion is Quarter (1⁄4) and the green portion is Three-Fourth (3⁄4) of the whole figure.

As you can see, Three-Fourth (3⁄4) is 3 times Quarter (1⁄4) and by comparing with the previous figure given above, we can say Half (1⁄2) is two times Quarter (1⁄4).

1⁄4 3⁄4

Exercise 2 : Understanding Half, Quarter, Three Fourths.

What is 1⁄4 + 1⁄4 ?

What is 1⁄4 + 1⁄4 + 1⁄4 + 1⁄4 ?

What is 1⁄4 + 1⁄4 + 1⁄4 ?

What is 3⁄4 - 1⁄4 ?

What is 1 - 1⁄4 ?

What is 3⁄4 + 1⁄4 ?

What is 3⁄4 - 1⁄2 ?

What is 1 - 1⁄2 ?

What is 1⁄2 - 1⁄4 ?

You have read 1⁄2 of the book. How much is yet to be read by you ?

A bag contains half kg sweets and quarter kg chocolates.What is the total weight in the bag ?

For Answers see at the bottom of the Page.

Here we have understood the concept of half, quarter, three fourth and relation between them.

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Answers to Exercise 1A : Understanding Half (1⁄2)

15

half

8

14

18

Answers to Exercise 1B : Understanding Half (1⁄2)

Full

Half

Half of half

Ex: 20

10

5

36

18 Ans

9 Ans

28 Ans

14

7 Ans

24 Ans

12 Ans

6

Answers to Exercise 2 : Understanding Half, Quarter, Three Fourths.