Improper Fractions and Mixed Numbers

In our last post, we learned about the different properties of addition.  Today, we are going to be learning how to convert improper fractions to mixed numbers.

We discussed fractions before, which consist of a numerator and denominator.  The only difference between a regular fraction and an improper fraction is that an improper fraction has a numerator larger than the denominator.  For example, 7/2 is an improper fraction because the numerator, 7, is larger than 2, the denominator.  Basically, our goal is to convert  our improper fractions to mixed numbers.  Mixed numbers consist of a whole number and a fraction.  An example of a mixed number is 5 1/2 because 5 is a whole number and 1/2 is a fraction; notice that 1/2 is a regular fraction and not an improper fraction.

How to convert from an improper fraction to a mixed number:  Let's start with an example.  Let's use our 7/2 that we used above.  We first ask ourselves: "How many times does our denominator go into our numerator?"  This will be our whole number part of our mixed number.  Next we subtract how ever many times our denominator goes into our numerator by our numerator.  This will give us our new fraction.  It sounds complicated, but let's try it.  So, how many times does 2 go into 7? 3 times.  So, then we subtract 7 - (2 x 3) and we get 1.  1 is our numerator of our new fraction, and we put that over 2 because that's what we originally started with.  So our mixed number is 3 1/2.

More examples: Convert the following improper fractions to mixed numbers.

1.) 17/4 = ?
2.) 9/5 = ?
3.) 19/6 = ?
4.) 15/2 = ?
5.) 24/9 = ?
6.) 13/8 = ?
7.) 11/3 = ?
8.) 16/5 = ?
9.) 12/5 = ?
10.) 28/9 = ?

1.) 4 goes into 17 four times.  4x4 = 16.  17-16 = 1, so our mixed number is 4 1/4.
2.) 5 goes into 9 once. 5x1 = 5.  9-5 = 4, so our mixed number is 1 4/5.
3.) 6 goes into 19 three times.  6x3 = 18.  19-18 = 1, so our mixed number is 3 1/6.
4.) 2 goes into 15 seven times. 2x7 = 14.  15-14 = 1, so our mixed number is 7 1/2.
5.) 9 goes into 24 two times. 9x2 = 18.  24-18 = 6, so our mixed number is 2 6/9, which can be simplified to 2 2/3 because 6/9 = 2/3 since 3 is divisible by 6 and 9.
6.) 8 goes into 13 once. 8x1 = 8.  13-8 = 5, so our mixed number is 1 5/8.
7.) 3 goes into 11 three times. 3x3 = 9.  11-9 = 2, so our mixed number is 3 2/3.
8.) 5 goes into 16 three times. 5x3 = 15.  16-15 = 1, so our mixed number is 3 1/5.
9.) 5 goes into 12 twice.  5x2 = 10.  12-10 = 2, so our mixed number is 2 2/5.
10.) 9 goes into 28 three times.  9x3 = 27.  28-27 = 1, so our mixed number is 3 1/9.

For more help, visit: for practice with converting improper fractions to mixed numbers, 
 YouTube video on further instruction on how to convert improper fractions to mixed numbers

I hope this helps =)