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How to Convert from Improper Fractions to Mixed Fractions (Mathematics Lesson)

Converting from Improper to Mixed Fractions

Improper fractions can be converted to mixed fractions.



  • An improper fraction (or top-heavy fraction) is a fraction where the top number is greater than (or equal to) the bottom number.

  • A mixed fraction has a whole number and a fraction.

How to Convert from Improper to Mixed Fractions

An Example Question

Convert the improper fraction below to a mixed fraction.
Step 1
Divide the top number (called the numerator) of the fraction by the bottom number (called the denominator).

Express it as a quotient and a remainder.
5 ÷ 2 = 2 r 1
Don't forget: If a number does not divide exactly into another, you get a quotient (2 in our example) and a remainder (1) that is left over.

r means remainder. See the Note.

Step 2
2 r 1 (the answer from Step 1) is used to write the mixed fraction.

Write the quotient (2) as the whole number part of the mixed fraction.



Step 3
2 r 1 (the answer from Step 1) is used to write the mixed fraction.

Write the remainder (1) as the numerator of the fraction part of the mixed fraction.



Step 4
The last part of the mixed fraction to find is the denominator of the fraction.
2 1/?
The denominator of the original improper fraction (2) becomes the denominator of the fraction part of the mixed fraction.



Step 5
Simplify the fraction if possible. (The fraction in our example is already as simple as possible.)

2 1/2 (two and a half) is 5/2 (five-halves) written as a mixed fraction.

A Real Example of How to Convert from Improper to Mixed Fractions

The slider below shows another example of converting improper fractions to mixed fractions:
Interactive Test
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Here's a second test on converting improper fractions to mixed fractions.
Here's a third test on converting improper fractions to mixed fractions.
Note

What Is a Remainder?

A remainder is the amount left over after a division.

A number can often be divided exactly by another number. For example, 4 ÷ 2 = 2. This means 4 objects can be divided into 2 equal groups of 2:



However, try 5 ÷ 2. There are 2 equal groups of 2, but 1 is left over:



5 ÷ 2 = 2 with a remainder 1

5 ÷ 2 = 2 r 1.

2 is the quotient.

1 is the remainder.

How to Find the Quotient and Remainder with a Calculator

This Note explains how to find Step 1 in our example.

Question: Find 5 ÷ 2, expressing the answer as a quotient and a remainder.

Using the on-screen calculator:
  • Type 5 ÷ 2.


  • Click the = button. The answer is 2.5.

The number to the left of the decimal point (2 in our example) is the quotient.

The quotient is 2.

To find the remainder, start with 2.5 still showing in the calculator.
  • Subtract the quotient.
    Type - 2.


  • Click the = button. The answer is 0.5.


  • Multiply by the number you first divided by (2 in this example, as we are finding 5 ÷ 2).
    Type × 2.


  • Click the = button. The answer is 1. This is the remainder.

The remainder is 1.

5 ÷ 2 = 2 r 1.