FRACTIONS MADE EASY - FRACTIONS, NUMERATOR, DENOMINATOR, UNLIKE FRACTIONS, LINKS

Go to
Fractions Made Easy through Fun Games.
For details, see near
the bottom of this page.

Please study
Fractions,
if you have not already done so.

There we studied about half, quarter, three fourth with examples and exercises.

Here, we will see fractions in general.

Understanding the concept of Fractions

Look at the following Table :

Solved Examples 1, 2, 3 and Exercises 1A, 1B are based on the following table.

Illustrated presentation of the data :

sweets             chocolates         fruits              cookies       ice creams

What part of the total eatables are sweets ?
Write the answer in words also.

Solution :

Sweets = 5; Total Eatables = 30.

So sweets form 5⁄30 of the total eatables.
In words, sweets = five by thirty.

You can see from the illusration given above,
there are 5 black blocks (representing sweets)
out of total 30 blocks.

I hope this illustration makes you to understand
the fraction 5⁄30 (five by thirty) clearly.

Exercise 1A : Concept of Fractions Made Easy

1. What part of the total eatables are chocolates ? Write the answer in words also.
2. What part of the total eatables are fruits ? Write the answer in words also.
3. What part of the total eatables are cookies ? Write the answer in words also.
4. What part of the total eatables are ice creams ? Write the answer in words also.

Solved Example 2 : Fractions Made Easy

What part of the total are the chocolates and cookies ?

Solution:

chocolates = 6; cookies = 7; Total = 30

Part of chocolates and cookies = Part of chocolates + Part of cookies

= 6⁄30 + 7⁄30 = (6 + 7)⁄30 = 13⁄30
In words, chocolates plus cookies = thirteen by thirty.

You can see from the illusration given above,
there are 6 green blocks (representing chocolates)
plus 7 red blocks (representing cookies) (= 13 blocks)
out of total 30 blocks.

I hope this illustration makes you to understand
the fraction 13⁄30 (thirteen by thirty) clearly.

Solved Example 3 : Fractions Made Easy

Leaving Fruits, what part of the total eatables are the other eatables?

Solution:
Total = 30; Fruits = 8;

Part of Total = 30⁄30; Part of Fruits = 8⁄30;

Part of other eatables = 30⁄30 - 8⁄30 = (30 - 8)⁄30 = 22⁄30
In words, other eatables (leaving fruits) = twenty two by thirty.

You can see from the illusration given above,
there are 22 blocks after leaving
8 blue blocks(representing fruits)
out of total 30 blocks.

I hope this illustration makes you to understand
the fraction 22⁄30 (twenty two by thirty) clearly.

Exercise 1B : Concept of Fractions Made Easy

Write you answers in words also.

1. What part of the total are the fruits and ice creams?
2. What part of the total are the sweets and chocolates?
3. What part of the total are the cookies and fruits?
4. What part of the total are the ice creams and sweets?
5. Leaving cookies, what part of the total eatables are the other eatables?
6. Leaving ice creams, what part of the total eatables are the other eatables?
7. Leaving sweets and chocolates, what part of the total eatables are the other eatables?
8. Leaving cookies and fruits, what part of the total eatables are the other eatables?

Fractions made easy

1⁄2, 1⁄4, 3⁄4, 4⁄30, 7⁄30, ........ indicate the part of a whole, don't they? These are called fractions.

Ex : Can you say what 6⁄7 means?
6⁄7 means we have taken 6 parts of 7 equal parts.
We read it as 6 over 7 or 6 by 7.

Solved Example 4 : Fractions Made Easy

If you take 2 items out of 3 items, how do you write it? and how do you read it?

Solution:
We write it as 2⁄3.
We read it as 2 over 3 or 2 by 3.

Exercise 2A : Fractions made easy

1. Taking 5 things out of 7 is written as ...........
2. 4 out of 10 is written as ...........
3. A whole is divided into 8 parts and if 4 parts are taken, the fraction is written as ...........
4. Suppose you have 6 chocolates. You gave 2 chocolates to your friend. What part of the chocolates did you give to your friend?

Exercise 2B : Fractions made easy

Suppose you were reading a book containing 40 pages.
On the first day, you read 10 pages,
on the second day 12 pages,
on the third day 16 pages.

1. What fraction of the book did you read on the first day?
2. What fraction of the book did you read on the second day?
3. What fraction of the book did you read on the third day?
4. What fraction of the book did you read in three days?
5. What fraction of the book is yet to be read by you?

Numerator and Denominator of a Fraction

The numbers of the form a⁄b, where a and b(≠0) are whole numbers are called fractions. Here a is called the Numerator and b is called the Denominator of the fraction a⁄b.

For Example, In 4⁄5, 4 is called the Numerator and 5 is called the Denominator.

Exercise 3 : Numerator and Denominator of a Fraction

Fill in the Blanks in the Table

Like and Unlike fractions

Fractions having the same number as denominator are called like fractions.

Examples of like fractions :
(i) 4⁄11, 7⁄11, 12⁄11, 29⁄11
(ii) 1⁄8, 7⁄8, 12⁄8, 21⁄8

Fractions having different denominators are called unlike fractions.

Examples of unlike fractions :
(i) 4⁄3, 1⁄2, 12⁄11, 2⁄7

The idea of Like and Unlike fractions is used in the following topics of Fractions.

Equivalent Fractions

Comparing Fractions

Adding Fractions

Subtracting Fractions

Simplifying Fractions

Fraction word Problems

Proper, Improper and Mixed Fractions

The definitions of these and conversion from improper fractions to mixed fractions and mixed fractions to improper fractions is covered in

Help With Fractions.

The multiplying and dividing of fractions
are covered respectively in

Multiplying Fractions

and

Dividing Fractions

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Answers to Exercise 1A : Concept of Fractions

1. 6⁄30, six by thirty
2. 8⁄30, eight by thirty
3. 7⁄30, seven by thirty
4. 4⁄30, four by thirty

Answers to Exercise 1B : Concept of Fractions

1. 12⁄30, twelve by thirty
2. 11⁄30, eleven by thirty
3. 15⁄30, fifteen by thirty
4. 9⁄30, nine by thirty
5. 23⁄30, twenty three by thirty
6. 26⁄30, twenty six by thirty
7. 19⁄30, nineteen by thirty
8. 15⁄30, fifteen by thirty

Answers to Answers to Exercise 2A : Fractions made easy

1. 5⁄7, five by seven
2. 4⁄10, four by ten
3. 4⁄8, four by eight
4. 2⁄6, two by six

Answers to Exercise 2B : Fractions made easy

1. 10⁄40, ten by forty
2. 12⁄40, twelve by forty
3. 16⁄40, sixteen by forty
4. 38⁄40, thirty eight by forty
5. 2⁄40, two by forty

Answers to Exercise 3 : Numerator and Denominator of a Fraction