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### Improper Fractions

```
Date: 04/15/99 at 20:32:29
From: Priyana Kumar
Subject: Fractions (Mixed number.....)

Dear Dr. Math,

I really need help on how to make an improper fraction into a mixed
number.
```

```
Date: 04/16/99 at 16:44:05
From: Doctor Peterson
Subject: Re: Fractions (Mixed number.....)

Hi, Priyana. Dr. Math to the rescue!

Let's look at an improper fraction this way: I'll give you 53 blocks
of wood, and tell you that each piece is 1/6 of a board. How many
boards did I use to make them?

+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
| 1 | | 7 | | 13| | 19| | 25| | 31| | 37| | 43| | 49|
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
| 2 | | 8 | | 14| | 20| | 26| | 32| | 38| | 44| | 50|
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
| 3 | | 9 | | 15| | 21| | 27| | 33| | 39| | 45| | 51|
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
| 4 | | 10| | 16| | 22| | 28| | 34| | 40| | 46| | 52|
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
| 5 | | 11| | 17| | 23| | 29| | 35| | 41| | 47| | 53|
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
| 6 | | 12| | 18| | 24| | 30| | 36| | 42| | 48|
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+

I can divide 53 by 6 to find out how many boards I can make by putting
the blocks back together in groups of 6:

___8_
6 ) 53
48
--
5

This says I can make 8 whole boards, using 8x6 = 48 of the pieces, and
I'll have 5 blocks left. Since each block is 1/6 of a board, that
means I've made 8 5/6 boards:

+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
|   | |   | |   | |   | |   | |   | |   | |   | |   |
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
|   | |   | |   | |   | |   | |   | |   | |   | |   |
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
|   | |   | |   | |   | |   | |   | |   | |   | |   |
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
|   | |   | |   | |   | |   | |   | |   | |   | |   |
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
|   | |   | |   | |   | |   | |   | |   | |   | |   |
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
|   | |   | |   | |   | |   | |   | |   | |   |
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
\_____________________________________________/ \___/
8 boards = 48/6                   5/6

The rule for changing an improper fraction into a mixed number is to
divide the numerator by the denominator; the whole-number quotient is
the whole number part of the answer, and the remainder is the
numerator of the fraction part:

+------------------------+
|                        |
|               5 <--+   |
| ___8_----> 8 ---   |   |
6 ) 53          6 <--|---+
48               |
--               |
5 --------------+

Another way to say it is that we find the largest multiple of 6 that
is less than 53 (that's what dividing means), and change that part
into a whole number:

53   48+5   48    5       5
-- = ---- = -- + --- = 8 ---
6     6     6    6       6

I hope that helps you make sense of mixed numbers. Here are some other
explanations in our archives if you need more help:

Fractions, Improper Fractions, Mixed Numbers
http://mathforum.org/library/drmath/view/58069.html

Converting Fractions to/from Mixed Numbers
http://mathforum.org/library/drmath/view/58875.html

Improper Fractions and Mixed Numbers
http://mathforum.org/library/drmath/view/58936.html

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Fractions
Middle School Fractions

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