Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Converting Fractions to/from Mixed Numbers

Date: 07/21/97 at 00:01:47
From: Sarai
Subject: Mixed Numbers

How do you change a fraction to a mixed number in simplest form?
For example: 9/5

How do you change a mixed number to an improper fraction? 
For example: 3 1/16

Date: 08/03/97 at 13:57:40
From: Doctor Terrel
Subject: Re: Mixed Numbers

Hi Sarai,

Lucky for us, changing fractions to mixed numbers, and vice versa, is
basically a simple thing to do.  For your examples, here's how:

9/5      Divide 9 by 5.  It's 1 remainder 4.  Answer is 1 4/5.

3 1/16   Multiply 3 by 16; it's 48.  Add the 1 (the numerator); 
         sum is 49.  Put 49 over 16.  Answer is 49/16.

Of course, that's just the "how," not the "why."

In your first example, 9/5 can be thought of as "how many fives 
are in 9?" [one and 4 units left over] So we have "one whole group" 
and 4 parts of a 5-group.  So 1 and 4/5.

We can also think of it as 9 fifths, as if we had several pizzas cut
into 5 equal portions.  Five of those 9 portions would form one 
complete pizza, and the remaining 4 would be, well, 4 fifths.   
Again we have 1 and 4/5.

For your second example, 3 1/16 could be thought of as chocolate 
cakes, each one cut into 16 equally sized pieces, each called "one 
sixteenth". [I hope you aren't getting too hungry with all this 
talk of food. :) ] The 3 whole cakes that we start with would give 
us 48 pieces (3 x 16); then we count the extra piece that came from 
some other cake (I don't know where it was or who cut it) and we get 
49 sixteenths, or 49/16.

I hope this helps you a little bit.  Perhaps you could also check 
with a good textbook to see what it says.  It'll probably have some 

For more information on how to work with fractions, see 

Elementary Fractions & Decimals
http://mathforum.org/library/drmath/sets/elem_fractions.html   ,

Middle School Fractions & Percentages
http://mathforum.org/library/drmath/sets/mid_fractions.html   , or

Compound Fractions - S.O.S. Math
http://www.math.utep.edu/sosmath/algebra/fraction/frac5/frac5.html   .

-Doctor Terrel,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   
Associated Topics:
Elementary Fractions

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.