A number lying between zero and 1 or between zero and -1 is a fraction or decimal **OR** The numbers that have an absolute value less than one as fraction or decimal.

## Fractions

A fraction is just another way of expressing division. The expression 12/17 is exactly the same thing as 12 divided by 17. a/c is a divided by c. Fractions can also be expressed as **Part/Whole.**

### Numerator and Denominator

In fractions x/y, x is known as numerator and y is known as denominator.

### Positive Fractions

A number between zero and 1 is called positive fraction.

### Negative Fractions

A number between zero and -1 is called negative fraction.

### Proper Fractions

If numerator is less than denominator in any fraction, it is called proper fraction.

### Improper Fractions

I numerator is greater than denominator in any fraction, the fraction is called as improper fraction.

### Mixed Fractions

Mixed fraction is a combination of a whole number and a fraction. For example 7 1/2, 7 is whole number and 1/2 is fraction.

### Common Factor

Common factor of two or more numbers is a number that divides these numbers. For example, common factor of 6 and 8 is 2, as 2 divides both values.

**How to find Common Factor**

Break down both the numbers to their prime factors o see what they have in common. Then multiply the shares prime factors to find all common factors. For example, what factors greater than 1 do 135 and 225 have in common?

First we find the prime factors of 135 and 225.

135 = 3 x 3 x 3 x 5 and 225=3 x 3 x 5 x 5. The number share 3 x 3 x 5 in common. Thus, aside from 3 and 5, the remaining common factors can be found by multiplying 3, 3, and 5 in possible combination: 3×3=9, 3×5=15, 3x3x5=45.

### Common Multiple

Common multiple of two or more numbers is a number that is divided by these numbers, for example, common multiple of 3 and 4 is 12 as 3 and 4 both divide 12.

## Decimal

Decimals are real numbers having decimal point. Decimals are another form of fractions. When decimals are added or subtracted, the decimal points must be placed one under the other. For example,

**Addition of Decimals**

3.4 + 0.87 + 6.0, if these are added, these can be written as

3.4

0.87

6.0

To add them add as usual and place the decimal point in the line of decimal points of numbers to be added.

**Multiplication of Decimals**

In this situation the point do not have to be under one another. The product must contain as many numbers after its points as the total of decimal places in two numbers being multiplied. For example product of 0.25 and 0.2, to solve this 0.25 has two numbers after its point and 0.2 has one number after its point, making total of three decimal places. Count three places to the left from the end. 0.05

**Decimal Places in numbers**

**Unit:** Place of number one place on left of decimal point In 123.245, 1 is at unit place.

**Ten:** Placement of number two places on the left of decimal point. In 123.245, 2 is at ten place.

**Hundred:** Placement of number three places on left of decimal point. In 123.245, 3 is at hundred.

**Tenth:** Placement of number one decimal place on right side of decimal point. In 123.245, 2 is at at tenth place.

**Hundredth:** Placement of number two decimal places on right of decimal point. In 123.245, 4 is at hundredth.

**Thousandth:** Placement of number three decimal places on right of decimal point. In 123.245, 5 is at thousandth place.

**Rounding Off Real Numbers**

Nothing more than converting a number of desired lengths (number of digits) is rounding off.

**To round off decimals**

Find place value you want i.e. rounding digit and look at digit just to the right of it.

If resultant digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If resultant digit is greater than or equal to five, add one to the rounding digit and drop all dig its to the right of it.

**To round off whole numbers**

Find the place value you want i.e. rounding digit and look to the digit just to the right of it.

If it is less than 5, do no change the rounding digit but change all digits to the right of rounding digit to “zero”.

If digit is greater than or equal to 5, add one to rounding digit and change all digits to the right of rounding digit to zero.

If the digit to the right of the place is equal to or greater than 5, round the number up by adding 1 to the place, and then eliminate all the digits to the right of the place.