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### Finding Fractions on a Ruler

```
Date: 08/16/99 at 01:17:09
From: Brian Strope
Subject: Defining Fractions of an Inch

Dear Dr. Math,

My question is simple. I want to know how to read all the measurements
within 1 inch. We know that every line on a ruler or tape measure
(whichever) has a fractional meaning. I want to learn how these
fractions are arranged.

I hope you understand what I mean by all fractions in an inch.
Example: where is 7/8 of an inch compared to 5/16 of an inch on a tape
measure? I know where the basic measurements are, such as 1/4, 1/2,
and 3/4 of an inch. It's just the other measurements that I don't get.

Thank you.
F. Brian Strope
```

```
Date: 08/16/99 at 11:17:58
From: Doctor Peterson
Subject: Re: Defining Fractions of an Inch

Hi, Brian.

There's a lot of information hidden in a ruler, and it can take some
practice to find it all.

We have a very complete explanation of reading a ruler here in our
archives:

http://mathforum.org/library/drmath/view/58333.html

I'll give you a simpler, quick answer that may meet your needs. Here's
a ruler showing 16ths, with the meaning of each mark indicated:

0                                                               1
|                              1/2                              |
|                               |                               |
|              1/4              |              3/4              |
|               |               |               |               |
|      1/8      |      3/8      |      5/8      |      7/8      |
|       |       |       |       |       |       |       |       |
|  1/16 |  3/16 |  5/16 |  7/16 |  9/16 | 11/16 | 13/16 | 15/16 |
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

Some rulers only go to eighths, and it might be easier to start with
that:

0                                                               1
|                              1/2                              |
|                               |                               |
|              1/4              |              3/4              |
|               |               |               |               |
|      1/8      |      3/8      |      5/8      |      7/8      |
|       |       |       |       |       |       |       |       |
+-------+-------+-------+-------+-------+-------+-------+-------+
0      1/8     2/8     3/8     4/8     5/8     6/8     7/8      1

As the marks go down in size, the denominator of the fraction doubles.
The biggest mark between two inches is the half; between that and
either inch mark the next largest mark is the quarter inch; and so on.
To find eighths, just go down the scale finding 1/2, then 1/4, then
1/8. All the marks that are that size or bigger are eighths: 1/8, 2/8
(which is the same as 1/4), 3/8, 4/8 (which is the same as 1/2), 5/8,
and so on. If you want, you can just count all the marks that are the
same size, counting by odd numbers: 1/8, 3/8, 5/8, 7/8.

Try doing the same thing on the 16ths ruler above; the only hard part
will be to ignore the smaller 16ths marks while you're looking for
8ths. To find 5/8, for example, find which size marks are 8ths, then
count 1, 3, 5/8 until you find it.

Now you should be able to work out 32nds yourself:

0                                                               1
|                              1/2                              | /2
|                               |                               |
|              1/4              |              3/4              | /4
|               |               |               |               |
|      1/8      |      3/8      |      5/8      |      7/8      | /8
|       |       |       |       |       |       |       |       |
|  1/16 |  3/16 |  5/16 |  7/16 |  9/16 | 11/16 | 13/16 | 15/16 | /16
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
| 1 | 3 | 5 | 7 | 9 | 11| 13| 15| 17| 19| 21| 23| 25| 27| 29| 31| /32
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

If you need any more help, feel free to write back.

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

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