NUMBERS

BASIC MATHS

1. what is Natural Number.??

            ANS: It is also called counting numbers. It starts from 1.

                       Eg.1,2,3,4,5,......etc..

    

      2.  what is Whole Number...??

               

               ANS: It is the number which starts from 0.

                          Eg.0,1,2,3,4,5,......etc..

                   

       3.   what is Prime number and composite number..??

                ANS: A Prime Number can be divided evenly only by 1 or itself.

                      And it must be a whole number greater than 1.
           

When a number can be divided up evenly it is a Composite Number







When a number can not be divided up evenly it is a Prime Number
Example:
6 can be divided evenly by 2, or by 3:
6 = 2 × 3
Like this:
	or
divided into 2 groups		divided into 3 groups


But 7 cannot be divided up evenly:

TYPES OF FRACTIONS

Proper Fractions

		A Proper Fraction has a top number less than its bottom number
3/8
(Three-Eighths)

Examples

3/8

1/4

14/15

4/5

See how the top number is smaller than the bottom number in each example? That makes it a Proper Fraction.

Three Types of Fractions

There are three types of fraction:

Fractions

A Fraction (such as 3/8) has two numbers:

Numerator

Denominator

The top number is the Numerator, it is the number of parts you have.
The bottom number is the Denominator, it is the number of parts the whole is divided into.

Example: 3/4 means:

• We have 3 parts
• Each part is a quarter (1/4) of a whole

So we can define the three types of fractions like this:

Proper Fractions:	The numerator is less than the denominator
	Examples: 1/3, 3/4, 2/7
Improper Fractions:	The numerator is greater than (or equal to) the denominator
	Examples: 4/3, 11/4, 7/7
Mixed Fractions:	A whole number and proper fraction together
	Examples: 1 1/3, 2 1/4, 16 2/5

Proper Fractions

So, a proper fraction is just a fraction where the numerator (the top number) is less than the denominator (the bottom number). Here are some examples of proper fractions:

1/2	1/4	3/8
(One-Half)	(One-Quarter)	(Three-Eighths)

Improper Fractions

7 4 (seven-fourths or seven-quarters)

An Improper Fraction has a top number larger than (or equal to) the bottom number.
It is "top-heavy"

More Examples

3		7		16		15		99
2		3		15		15		5

See how the top number is bigger than (or equal to) the bottom number?
That makes it an Improper Fraction, (but there is nothing wrong about Improper Fractions).

Improper Fraction

So an improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator): it is top-heavy.

4/4

Can be Equal

What about when the numerator is equal to the denominator? For example 4/4 ?

Well it is the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction.

Improper Fractions or Mixed Fractions

We can use either an improper fraction or a mixed fraction to show the same amount. For example 1 3/4 = 7/4, shown here:

1 3/4		7/4
	=

Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps: 

	Divide the numerator by the denominator. Write down the whole number answer Then write down any remainder above the denominator.

Example: Convert 11/4 to a mixed fraction.

Divide:

11 ÷ 4 = 2 with a remainder of 3

Write down the 2 and then write down the remainder (3) above the denominator (4), like this:

2	3
	4

Converting Mixed Fractions to Improper Fractions

To convert a mixed fraction to an improper fraction, follow these steps: 

	Multiply the whole number part by the fraction's denominator. Add that to the numerator Then write the result on top of the denominator.

Example: Convert 3 2/5 to an improper fraction.

Multiply the whole number by the denominator:

3 × 5 = 15

Add the numerator to that:

15 + 2 = 17

Then write that down above the denominator, like this:

17

5

Mixed Fractions

(Also called "Mixed Numbers")

1  3 4 (one and three-quarters)

A Mixed Fraction is a whole number and a proper fraction combined. 

such as 1 3/4 .

Examples

2 3/8

7 1/4

1 14/15

21 4/5

See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number).

Equivalent Fractions

Equivalent Fractions have the same value, even though they may look different.

These fractions are really the same:

1 2

=

2 4

=

4 8

Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value.

The rule to remember is:

"Change the bottom using multiply or divide,
And the same to the top must be applied"

So, here is why those fractions are really the same:

	× 2		× 2
1	=	2	=	4
2		4		8
	× 2		× 2

And visually it looks like this:

1/2		2/4		4/8
	=		=

SIMPLIFYING FRACTIONS

To simplify a fraction, divide the top and bottom by the highest number that
can divide into both numbers exactly.

Method 1

Divide both the top and bottom of the fraction by the Greatest Common Factor (you have to work it out first!).

Example: Simplify the fraction 812 :

The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4.

Divide both top and bottom by 4:

	÷ 4
8	=	2
12		3
	÷ 4

That is as far as we can go. The fraction simplifies to 23