## 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!

## 10 Comments

22 days ago

Hanging artwork on a wall to "fill up space" evenly over a broad expanse--in your example-- is not the proper way to hang artwork. Your example is what an engineer would do. This is NOT what a designer would do. Huge difference.

Find the center point of the wall between the two doorways. Using your eye, determine what the most attractive distance would be (usually no more than 3" but this is subjective and dependent upon the size of the artwork. Larger pieces can be spaced ~ 3", smaller pieces can be ~ 2"). When the proper distance between the artwork is determined, cut a piece of painter's tape to that length and use it as spacing for all artwork to the left and right of the middle piece. Even numbered artwork pieces are not recommended, but if so, just use that spacing distance, divided in half, of the center point.

1 year 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!

5 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

6 years ago

Thank you! Followed your formula and worked a treat.

7 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 6 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...

6 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.

7 years ago

Note:

correction to formula:

X=the number of picture frames

Not the size!!!!

Reply 7 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!

9 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.