## Introduction: How to Read a Ruler (and Other Simple Tricks).

The cool thing about knowing how to label the fractions inside of an inch is that you can use it as a calculator to reduce fractions! Follow along and I'll show you how. This instructable may be a little hard to follow if you don't read it through all the way to the end before trying it out.

## Step 1: Start Your Inches!

Gather supplies. See *Picture 1*. You need:

Paper

Pencil or Pen

That's it!

A few definitions that might help you understand this instructable a little better:**Numerato**r: The number above the line in a common fraction**Denominator**: The number below the line in a common fraction

The easiest way I have found to explain an inch is to draw it out, starting with a mark representing zero and a mark representing 1. These DO NOT HAVE TO BE ACCURATE!!! I find it is a lot easier if you make your "inch" BIG to give you more room to write in the fractions. SO:

On the paper, Draw a rectangle as shown in* Picture 2 and 3*. This is going to be our "ruler". Remember to make it big! On the ruler, make a mark, also as shown in *Pictures 2, 3, and 4*. This will be out 1 inch mark.

## Step 2: Cut & Double- Halves

Now that you have your inch started, we can "Cut and Double". Inside of the inch mark you have drawn, put another mark in the middle, cutting the inch in half as shown in *Picture 1*. Most people understand that this is a half an inch, or 1/2, as shown in *Picture 2 and 3. *

To explain this further, lets talk about the "Cut and Double" for a minute. When we marked the 1/2 inch on our ruler, we CUT the inch in half, and DOUBLED the denominator of the previous fraction. See* Picture 2*. For example, we cut the inch in half and made a mark. Then we took the previous fraction- ONE INCH which converted to a fraction with a numerator and denominator is 1/1- and DOUBLED the denominator. 2 x 1 = 2, so our new fraction will be 1/2. See *Pictures 3 and 4*. Confused? Maybe a little... Lets do it one more time in the next step and see if we start to catch on.

## Step 3: Cut & Double- Quarters

If you understood the last step, the rest is simple. Just repeat it as many times as you want!

CUT again! For each section of your inch, cut it in half as shown in *Picture 1*. Notice there are TWO marks now instead of one, because we have TWO sections- one on each side of the 1/2 inch mark.

DOUBLE again! The denominator of the last fraction is 2, so 2 x 2 = 4 as shown in *Picture 2*. That means our new fraction is going to be 1/4 as shown in *Picture 3*.

Here's where it gets a little different. There are TWO unlabeled marks on the ruler. We are going to count them off in quarters- the first mark being 1/4, the second mark would be 2/4, but it's already labeled as 1/2, and the 3rd mark will be labeled as 3/4. Count by 1/4'ths- 1/4, 2/4, 3/4, 4/4. See *Picture 4*.

## Step 4: Cut & Double- Eighths

CUT again! For each section of your inch, cut it in half as shown in Picture 1. Notice there are FOUR marks now instead of 2, because we have FOUR sections- one on each side of the 1/4 inch marks.

DOUBLE again! The denominator of the last fraction is 4, so 2 x 4 = 8 as shown in Picture 2. That means our new fraction is going to be 1/8 as shown in Picture 3.

Fill in the missing fractions by counting each mark as an eighth- 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, and 8/8. You will ONLY LABEL THE FRACTIONS WITH AN ODD NUMERATOR! See* Picture 4*.

## Step 5: Cut & Double- Sixteenths

CUT again! For each section of your inch, cut it in half as shown in *Picture 1*. Notice there are EIGHT marks now instead of 4, because we have EIGHT sections- one on each side of the 1/8 inch marks.

DOUBLE again! The denominator of the last fraction is 8, so 2 x 8 = 16 as shown in *Picture 2*. That means our new fraction is going to be 1/16 as shown in* Picture 3*.

Fill in the missing fractions by counting each mark as an eighth- 1/16, 2/16, 3/16, 4/16, 5/16, 6/16, 7/16, 8/16, 9/16, 10/16, 11/16, 12/16, 13/16, 14/16, 15/16, and 16/16. You will ONLY LABEL THE FRACTIONS WITH AN ODD NUMERATOR! See* Picture 4*.

## Step 6: Tips, Tricks, and Continuing On.

You've Drawn your Inch! Here's what your completed Inch should look like- see *Pictures 1 and 4*. Now lets show you a couple of patterns and give you some tips and tricks!**Trick 1**

Take a minute and look at the fractions. Do you see any patterns? There are two that stand out that can come in handy to check your work to make sure you drew your inch correctly...

1. Look at picture one again. What do you notice about ALL of the numerators?! THEY ARE ALL ODD. If you have an even number as a numerator, it needs to be reduced or you haven't got it in the right spot!

2. Look at the last fraction in each set as shown in* Picture 2*. Notice that in each fraction, the numerator is ONE LESS than the denominator!**Trick 2**

You can use your completed inch as a calculator for reducing fractions. If you were to write ALL of the fractions down every time you did a set, your Inch would look like* Picture 3*. Each mark on the ruler that ends up with multiple fractions can be reduced to the top most fraction in the set!**Trick 3**

Continuing on! You can continue the Cut and Double forever! Each time just split the last section in half and double the denominator of the last fraction. After 16ths, you would have 32nds, 64ths, 128ths, 256ths, 512ths, 1024ths, 2048ths, and on and on and on... But it does get a little hard to draw. :)

I'm sure there are a lot more cool things you can do with a ruler, and I'd love to hear about them! In the meantime, the best way to get good at this is to practice practice practice! After doing this about 20 times, my students can just about do it in their sleep- and their ability to read a ruler shows in their metals projects.

Once you have your Inch down, you can try some of my other projects. Making a Perfect Paper Cube is great practice at reading and using a ruler! See it here: https://www.instructables.com/id/Perfect-Paper-Cube-Laying-out-a-project-using-pa/

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## 9 Comments

Excellent! I am thrilled that I found this page. For the first time in my life I finally understand. I have always had a mental math block and this has made it EASY. Thank you for making me feel less than dense. YAYS!!!!

This is excellent. I'm so glad I found your video. You have totally lifted the fog I enter whenever I see measurements. You made my DAY!!

Fantastic!

Here's my little piece of the world...

http://www.craft-a-project.com/Ruler-Measurements.html

Wow! How cool is this. Every everybody should know this little trick. This has taught me how to read a ruler and I do not think I will forget it. Thank you soooo much for sharing this.

Thanks! Glad it could help. I've wondered who views this instructable- There are hardly any comments yet it has over 100k views. Would love to hear how (if?) others are using this in some way?

A nice instructable! Some times one needs to discuss the obvious. I am a physicist, I live in a metric world and during my education I had to use the log rule a lot. The way I see it the metric system is more "flat" since 0.7 has no qualitative difference than 0.8 and it is easier to think of the increase, on the other hand when you jump from 1/4 to 3/8 you have to re-adjust your mind in dividing the pie in 8 instead of 4 pieces. Not to mention that if you ask me where the 13/16 is on the ruler I'll have to think a little.

This is a great way to explain and use fractional measurements in any project, or to learn and practice fractions for any other purpose. Kudos for your teaching method! (I agree, metric is a LOT easier, but sometimes you just have to work with what you've got.) Next, maybe somebody can show how to use those 3-sided architectural scale rulers ...

..Still don't get the reason why one should choose to hurt himself so much...

Why not simply jump to the metric ???

I agree... The metric system is just so much easier. Unfortunately, my students still need to know BOTH systems. Guess which one they struggle with more? I will say this though, my students understand their fractions a lot better after learning their inch.