Improper Fractions to Mixed Numbers

Converting an improper fraction to a mixed number is a very useful skill to learn that helps students to understand fractions and how to express them in different ways. It also teached them about fractions of a whole, and more advanced things like the greatest common factor (GCF) when simplifying fractions.

In this article, we'll explain how to convert any improper fraction into a mixed number with links to a lot of different examples to help you fully understand the concept.

Looking for improper fraction worksheets? Click here to see all of our free improper fraction worksheets.

Enter your improper fraction in the A and B boxes, and click "Calculate" to convert it to a mixed number.

The first step is to make sure we understand all of the terms in the problem we are trying to solve. We'll use the example of 64:

  • Numerator - this is the number above the fraction line. For 64, the numerator is 6.
  • Denominator - this is the number below the fraction line. For 64, the denominator is 4.
  • Improper fraction - an improper fraction is when the numerator is greater than the denominator.
  • Mixed number - A mixed number is a way to express the improper fraction by converting it to a whole number (an integer) and a smaller proper fraction.

Find the Whole Number of Improper Fraction 64

To convert this to a mixed number, we need to find out what the whole number of our new fraction should be. To do that we divide the numerator by the denominator and round the answer down so that we have a whole number with no decimal places:

6 ÷ 4 = 1.5

As you can see, 1.5 is not a whole number, and so we have to round this down to 1.

Get the New Numerator

We have the whole number, so we now need to calculate the new proper fraction, starting with the new numerator.

In this step, we take the whole number we just calculated, 1, and multiply it by the denominator, which is 4. The result of that calculation is then subtracted from the original number, 6:

6 - (1 × 4) = 2

Complete the Mixed Fraction

The good news is that the denominator in a mixed number is the same as the original improper fraction. All we need to do is take the new numerator and put it above the original denominator, with the whole number before it:

1 2 4

Simplifying 24 to Lowest Terms

You might have noticed that the new fraction part of the mixed number, 24, can be simplified down to lower terms.

To do this, we need to calculate something called the greatest common factor (GCF) of those two numbers. Sometimes this is called the greatest common divisor (GCD). This is the smallest number that both 2 and 4 can be divided by.

The GCF of 2 and 4 is 2. We can now divide both by the GCF to find the simplified fraction:

2 ÷ 2 = 1

4 ÷ 2 = 2

This gives us a final answer with a simplified proper fraction of 12:

1 1 2

Practice Improper Fractions Worksheets

Like most math problems, converting improper fractions like 6/4 to a mixed number is something that will get much easier for you the more you practice the problems and the more you practice, the more you understand.

Whether you are a student, a parent, or a teacher, you can create your own improper fraction worksheets using our improper fraction worksheet generator. This completely free tool will let you create completely randomized, differentiated, improper fraction problems to help you with your learning and understanding of fractions.

Practice Improper Fractions to Mixed Numbers Using Examples

If you want to continue learning about how to convert an improper fraction to a mixed number, take a look at the quick calculations and random calculations in the sidebar to the right of this blog post.

We have listed some of the most common fractions in the quick calculation section, and a selection of completely random fractions as well, to help you work through a number of problems.

Each article will show you, step-by-step, how to change an improper fraction to a mixed number, simplifying the fraction to its lowest terms where necessary, and will help students to really learn and understand this process.

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