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Convert Mixed Numbers To Improper Fractions and vice versa




 
In these lessons, we will learn how to convert Mixed Numbers to Improper Fractions and Improper Fractions to Mixed Numbers. Mixed Numbers are also called Mixed Fractions.

Related Topics:
More Arithmetic Lessons
Free Math Worksheets for Fractions

Convert Mixed Numbers To Improper Fractions

When converting mixed numbers to improper fractions, we calculate the numerator in the following steps:

Step 1: Multiply the whole number by the denominator

Step 2: Add to the numerator of the fractional part

The denominator is not changed

Example

Write the mixed number as an improper fraction.

Solution:

Convert Improper Fractions To Mixed Numbers

To change an improper fraction to a mixed number we divide the numerator by the denominator.

The quotient (the result of division) is the whole number of the mixed number.

The remainder is the numerator of the fractional part of the mixed number.

Example:

Write the improper fraction as a mixed number.

Solution:

If there were no remainder the improper fraction would simplify to a whole number.
For example




How to convert between Improper Fractions and Mixed Numbers?
Types of fractions
1. A proper fraction is a fraction with a smaller numerator than denominator. Proper fractions are less than 1
2. An improper fraction is a fraction which the numerator is greater or equal to the denominator. Improper fractions are greater than or equal to 1.
3. A mixed number is a number written as the sum of an integer and a proper fraction.

To convert from an improper fraction to a mixed number
a. Divide the numerator by the denominator.
b. Write down the whole number.
c. Place any remainder in the quotient over the denominator.
d. Simplify the fraction if needed.

To convert a mixed number into an improper fraction
a. Multiply the denominator by the whole number.
b. Take that product and add that to the numerator of the fraction.
c. Take that sum and place it over the denominator.
How to convert from a mixed number to an improper fraction and vice versa?


 

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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