# Proper, Improper and Mixed Fractions

There are three types of fractions:

PROPER FRACTION

## Examples:

2/3 , 3/4 , 1/4 , 5/8

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IMPROPER FRACTION

## Examples:

128/5 , 29/15 , 35/12

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MIXED FRACTION

## Examples:

4 1/3 , 5 82/210 , 6 9/20

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Steps to convert improper fraction into mixed number

## Proper Fraction

A fraction in which numerator is less than denominator is called proper fraction, means a fraction that is less than 1.

## Explanation:

Since 12 > 7 , Hence 12/7 is not a proper fraction.

## Explanation:

Since 3 < 8 , Hence 3/8 is a proper fraction.

## Explanation:

Since 1 < 4 , Hence 1/4 is a proper fraction.

## Explanation:

Since 14 < 15 , Hence 14/15 is a proper fraction.

## Explanation:

Since 4 < 5 , Hence 4/5 is a proper fraction.

## Improper Fraction

A fraction in which numerator is greator than or equal to denominator is called proper fraction, means a fraction that is greator than or equal to 1.

## Explanation:

Since 4 > 3 , Hence 4/3 is a improper fraction.

## Explanation:

Since 11 > 4 , Hence 11/4 is a improper fraction.

## Explanation:

Since numerator and denominator of the fraction are equal , Hence 7/7 is a improper fraction.

## Mixed Fraction

A mixed number is a fraction that includes both whole number and a proper fraction.

## Explanation:

Divide the numerator by the denominator.

 1 3 4 3 1

The whole number is the quotient which is 1.
The numerator of the mixed number is the remainder which is 1.
The denominator remains to be 3.
Therefore, 4/3 in mixed number form is 1 1/3

## Explanation:

Divide the numerator by the denominator.

 2 4 9 8 1

The whole number is the quotient which is 2.
The numerator of the mixed number is the remainder which is 1.
The denominator remains to be 4.
Therefore, 9/4 in mixed number form is 2 1/4

## Explanation:

Divide the numerator by the denominator.

 16 5 82 80 2

The whole number is the quotient which is 16.
The numerator of the mixed number is the remainder which is 2.
The denominator remains to be 5.
Therefore, 82/5 in mixed number form is 16 2/5

### Improper Fraction into Mixed Number

•   Divide the numerator by the denominator.

For Example : Convert 5/4 to mixed Number

 1 4 5 4 1
•   Use the quotient as the whole number.

in our example quotient is 1.

•   Use the remainder as the numerator of the proper fraction.

in our example remainder is 1.

•   The denominator will stay the same.

in our example denominator is 4.

Hence the required mixed number is 1 1/4

### Mixed Number into Improper Fraction

Multiply the whole number by the denominator.

For Example : Convert 2 1/4 to improper fraction

In our example whole number is 2 and denominator is 4

hence 2 x 4 = 8

Add the product to the numerator of the proper fraction. The sum is the numerator of the improper fraction.

Here numerator is 1
adding numerator and product we get,
numerator= 8 + 1= 9

The denominator will stay the same.

denominator = 4

Hence the improper fraction is 9/4

## Explanation:

Divide the numerator by the denominator.

 2 5 11 10 1

The whole number is the quotient which is 2.
The numerator of the mixed number is the remainder which is 1.
The denominator remains to be 5.
Therefore, 11/5 in mixed number form is 2 1/5

## Explanation:

Multiply the whole number by the denominator.
3 x 4 = 12
Add the product to the numerator of the proper fraction.
12 + 3 = 15
The numerator of the improper fraction is 15.
The denominator remains to be 4.
Therefore, improper fraction form for 3 3/4 is 15/4

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