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Convert Improper Fractions to Mixed Numbers

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Improper fraction

A fraction in which the numerator is larger than or equal to the denominator, like
5
2
,
17
3
, or
6
6
is called an improper fraction.

Mixed fraction

A mixed number is a combination of a whole number and a fraction.

For example: 2
1
2
.

Convert Improper Fractions to Mixed Numbers

Improper fractions can be written as mixed numbers.

To write an improper fraction as a mixed number,

  • Divide the numerator (top part) by the denominator (bottom part).
  • The quotient is the whole number, and the remainder is the numerator.
 

Let's go through some examples to understand the concept better.

 

Example 1

 
How would you express
17
4
as a mixed number?
 

Solution

 
To write
17
4
as a mixed number,

Divide the numerator by the denominator:

17 ÷ 4 = 4, with a remainder of 1

The quotient, 4, is the whole number.

The remainder, 1, is the numerator. The denominator remains 4.

 
17
4
= 4
1
4
 
 

Example 2

 
How would you express
14
9
as a mixed number?
 

Solution

 
To write
14
9
as a mixed number,

Divide the numerator by the denominator:

14 ÷ 9 = 1, with a remainder of 5

The quotient, 1, is the whole number.

The remainder, 5, is the numerator. The denominator remains 9.

 
14
9
= 1
5
9
 
 

Example 3

 
How would you express
20
5
as a mixed number?
 

Solution

 
To write
20
5
as a mixed number,

Divide the numerator by the denominator:

20 ÷ 5 = 4

The quotient, 4, is the whole number. There is no remainder.

 
20
5
= 4

If there is no remainder, just take the quotient as the whole number.

Summary
  • A fraction in which the numerator is larger than or equal to the denominator, like
    5
    2
    ,
    17
    3
    , or
    6
    6
    is called an improper fraction.
  • A mixed number is a combination of a whole number and a fraction.
  • To write an improper fraction as a mixed number,
    • Divide the numerator (top part) by the denominator (bottom part).
    • The quotient is the whole number, and the remainder is the numerator.
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