Converting to Mixed Numbers

For improper fractions, check out: What is an Improper Fraction?

Introduction

It is not uncommon to get answers that are improper fractions while working with fractional values. However, you might rather have it be a mixed number, so you would convert it! Many math problems require answers to be simplified into mixed number format, as it is commonly regarded as simpler than an improper fraction. Some examples of this conversion:

7/2 = 3 1/3
4/3 = 1 1/3
15/12 = 1 3/12

As you can see, mixed numbers are numbers that are a combination of whole numbers and fractions, therefore they are considered to be “mixed”. There is always a whole number first, then immediately following it there is a fractional part.

How is it done?

To convert to mixed number, the first step is to find out how many times the denominator fits into the numerator. If the denominator is 5, and the numerator is 22, (the fraction is 22/5) then how many times does 5 fit in to 22? 5*4=20 with a remainder of 2.

So, the mixed number is 4 and 2/5 because for the left over 2, the denominator is still 5 because we couldn’t get a whole number out of it, and we shouldn’t be changing anything. If the denominator is larger than the numerator, then we don’t need to convert because this would not be a mixed number. As we can see, the 4 comes from how 5 fits into 22 4 whole times.

The outcome of 4 and 2/5 from 22/5 makes sense mathematically because 4 is the same as 20/5. Adding this with the 2/5 makes 20/5 + 2/5 = 22/5, back to the original improper fraction!

More examples of the conversion at work…

If we have the improper fraction 45/6, we can first divide 45 by 6 to see how many whole numbers we can get. This would be 7 with a remainder of 3, as 6 * 7 = 42 and 45 – 42 = 3. We would not change the denominator for the remainder, so it would be 7 and 3/6, which can be further simplified to 1/2.
With the improper fraction of 23/5, dividing 23 by 5 gives us 4 with a remainder of 3 because 5 * 4 = 20 and 23 – 20 = 3. There would be no denominator change for the remainder, so the final mixed number becomes 4 and 3/5.
90/4 is a large mixed number, but it is still convertible! Simply start by dividing 90 by 4, which gives us 22 with a remainder of 2. (22 * 4 = 88, 90 – 88 = 2). We would then have 22 and 2/4, which simplifies to 22 and 1/2.