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Convert Mixed Numbers to Improper Fractions

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Mixed Numbers

A mixed number is a combination of a whole number and a fraction, for example: 2
1
2
.

Improper Fractions

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.

Convert Mixed Numbers to Improper Fractions

A mixed number can be expressed as a fraction.

Improper

  • Multiply the whole number by the denominator.
  • Then add the result to the numerator.
  • This result becomes new numerator.
  • The denominator remains the same.
 

Let's illustrate through examples.

 

Example 1

 
Write 2
1
2
as an improper fraction.
 

Solution

 
To write 2
1
2
as an improper fraction,

Multiply the whole number by the denominator.

The whole number is 2.

The denominator is 2.

2 x 2 = 4

Add the result to the numerator:

The numerator is 1.

4 + 1 = 5

The numerator is 5. The denominator remains 2.

2
1
2
=
5
2
 
 

Example 2

 
Write 5
2
3
as an improper fraction.
 

Solution

 
To write 5
2
3
as an improper fraction,

Multiply the whole number by the denominator.

The whole number is 5.

The denominator is 3.

5 x 3 = 15

Add the result to the numerator:

The numerator is 2.

15 + 2 = 17

The numerator is 17. The denominator remains 3.

5
2
3
=
17
3
Summary
  • A mixed number is a combination of a whole number and a 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.
  • A mixed number can be expressed as a fraction.
    • Multiply the whole number by the denominator.
    • Then add the result to the numerator.
    • This result becomes new numerator.
    • The denominator remains the same.

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