## Introduction: Using Algebra for Hanging Pictures

When traveling in Mexico last year, we bought some odd film stills of a movie called "El Profesor Erotico" (1976). At the time, I thought that it was an old campy Mexican TV show. Further research on the internet showed that it was a B-movie of the Argentinian variety*. We had purchased 4 photographs, got them framed and wanted to hang them on a wall.

In the past, I've done all sorts of division, taping and remeasuring work out how exactly to hang sets of pictures. After thinking about how negative and positive space are a matter of perception, I realized the solution to this would be to **use simple 8th grade algebra.**

This technique will save you tons of hassle of measuring, remeasuring, chicken scratch division and putting blue tape all over the place.

* I have no idea what they are doing with the blow-up doll, but all the film stills are equally puzzling and funny.

## Step 1: Sketch Your Space

Each frame is identical. The plan was to hang them in a row, on the same wall with an equal amount of white space between each picture. On the left side of the wall is a door frame and the right edge is another door. These edges will like be margins on a page with an equal amount of wall space as the center.

Draw a simple diagram of the space. Take your time and refer back to this when you are doing the measurements. I drew mine exceedingly quickly. The doorways are the large rectangles that drift into an imaginary floor and the pictures are the tiny squares.

## Step 2: Make Your Equation

This is a simple x and y equation. In this case **x = the width of the picture frame** and **y = the space between the picture frames. **Also, measure **the total expanse of the wall.**In my case, the total wall space = 126 3/4" which is 126.75 if we express in a decimal (we'll convert back to a fraction when we are done).

Our equations is: **5y + 4x = 126.75**

We have 4 picture frames and 5 negative spaces of equal length.

## Step 3: Measure Your Picture Frames

Measure your frame and this becomes your x value. In this case, the picture frame = 14.5 inches wide.

The equation is: **5y + (4 * 14.5) = 126.75**

## Step 4: Solve for Y

What we want to know is what y =. Remember how torturous algebra was? We're smarter now and have the full use of the web. It's pretty easy. Use your sheet as a scratch pad.

5y + (4 * 14.5) = 126.75

5y + 58 = 126.75

5y = 68.75**y = 13.75**

## Step 5: Convert the Decimal to Fractions

Most rulers are in inches or millimeters and show fractional values. In this case, 13.75 easily converts to 13 3/4.

It's helpful to refer to a decimal to fraction conversion table if you have decimal values you can't convert so easily in your head to fractional measurements.

## Step 6: Now Hang Your Pictures

There are other Instructables on how to hang the pictures themselves such as this one. My Instructable will provides a calculation technique for the horizontal space. I'm a fan of using the blue tape at this point and never marking the wall with a pencil. Mark the blue tape itself. Leave no trace.

## Step 7: Apply the Technique to Other Situations

Here is another hanging situation for an art show I did several years ago.

Each picture is 30" wide. I had 150 inches total wall space, and I wanted to have the middle sections be twice as wide as the wall space on the outside.

Here the equation is **3x + 6y = 150**

You can use the same mickey-mouse algebra to solve this problem. Next time someone says "Math is Hard", remember it's time to liberate your toys.

Enjoy!

## 9 Comments

4 months ago

48. I struggled for an hour hanging four evenly across a 96.75" wall. Then I found this. Then I hung them perfectly with a laser level aid. Then I texted my high school Algebra teacher and told her she was right and I was wrong. Thanks for posting this!

3 years ago

Much easier formula: if you are hanging 3 frames, divide the length of the wall by 4 to get the centre points (from which they'll be hanging).

If you have 4 frames divide by 5, etc.

All have to be same size though

4 years ago

Thank you! Followed your formula and worked a treat.

5 years ago

I am 35 years old. This is the first time in my life I've come across any sort of practical application for algebra I learned in school.

Reply 5 years ago

As a math teacher, I am glad that now there is a tendency to focus on applicable aspects of algebra. Students even seem to be more intested in the subject. I've heard of a contest among students, the task was to count skittles that could fit ito 1 jar.

Here is also a bunch of interactive tests that I use during my classes.

http://yourhomeworkhelp.org/math-tests/2nd-grade-m...

5 years ago

As jmarsh2 mentioned. I have a good teaching tool now for my kids, brains both of them always have a logical excuse to argue with my logic. Got them now on why its important to do the easy math when told to.. thx.

6 years ago

Note:

correction to formula:

X=the number of picture frames

Not the size!!!!

Reply 5 years ago

@Lrcooper54 Scott has it exactly right. X is not the number of pictures - it is the width of the pictures. Did you even read the article? I hope you didn't screw anyone up. Grrrr!

7 years ago

you could develop the formula so that (n+1)y +(n)x = w where w is the width of the wall and n ifs the number of items to be hung.