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### 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
drawings.

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

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