Proper, Improper and Mixed Fractions

There are three types of fractions:


Types of Fraction


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.

Example 1:
 No

Explanation:

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

Example 2:
 Yes

Explanation:

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

Example 3:
 Yes

Explanation:

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

Example 4:
 Yes

Explanation:

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

Example 5:
 Yes

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.

Example 1:
 Yes

Explanation:

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

Example 2:
 Yes

Explanation:

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

Example 3:
 Yes

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.

Example 1:
 Yes

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`

Example 2
 Yes

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`

Example 3:
 Yes

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`


  Steps for Converting

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`



Proper, Improper & Mixed Fraction Examples

Example 1:
 `2 1/5`

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`

Example 2:
 `15/4`

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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