# The One Math Concept I Use All The Time… Ratios and Proportions

I spent 15 years of my life learning a ton of things in math, but there’s only one thing I learned that I still use all the time as a designer. That’s using ratios and proportions (which I guess is kind of like really basic algebra). If you’re going into the design industry,** I can’t stress how much understanding them is going to save you headaches**.

Now I’ll admit, Math was one of my better subjects, but I by no means would consider myself good at it. I use a calculator for most everything. I promise, I’m going to make learning proportions super easy so that you don’t have to really think about what’s going on.

## What are Ratios and Proportions

The basic idea of * ratios* is to describe parts of the whole or a relationship between things. A

*is the process of extracting a ratio into a new form that is mathematically equal to the same original ratio but just looks a little different.*

**proportion**We’ll start simple…

Case A) If you have 1 red squares and 2 blue squares your ratio is 1:2.

Case B) If you have 3 red squares and 6 blue squares your ratio would still be 1:2.

Even though case A & B have different total quantities, their ratio is the same, and so** they are directly proportional**.

## How to Set Ratios and Proportions Up To Solve for an Unknown

If you ever run into case where you know the original ratio of something and but are having trouble finding proportional information, you can always do some basic algebra to solve for the unknown.

Let’s say I’m given a roof slope of 6:12 (rise/run) by an architect. That means for every vertical 6″ I must also increment 12″ horizontally.

I know that from the roof edge to my ridge (the topmost portion of my roof) is 33.6″ but I don’t know the height. For this, I can use ratios and proportions to solve for the unknown.

We start by turning 6:12 into a fraction. 6/12. They’re basically the same thing, the ” **:** ” (colon) is simply a shorthand of letting someone know it’s a ratio to be used proportionally.

We then need to set what our ratio is equal to. For this we have to keep like items in alignment. The 12″ run of the ratio is relational to the 33.6 length we already know. We’ll put those two on the same side of the division line because of that. In the same idea, 6″ is the rise of our ratio and will be directly proportional to the X rise we intend to find. We’ll keep both of those on the top of our fractions.

## Solving Proportions

If you set up your proportions the way I describe above, you can solve for x pretty easily. I’ve developed the mnemonic device called **MAD** to help you remember.

**M **ultiply

**A **cross

then

**D **ivide

What you’re doing when you multiply across and then divide is reworking the equation to solve for x. Just so you know, I’ve rewritten what it looks like below. Don’t be alarmed though, you can just follow the above MAD rule and don’t have to worry about knowing the algebra.

## Where Using Proportions is Helpful

I shared a few examples above, but I use proportions in a bunch of ways:

- In programs that don’t allow you to scale to a reference and you need to scale with a percentage or factor
- When a drawing is at a particular scale and you only have a measuring tape
- When you like the way something looks but want to make it larger or smaller to an exact size
- When I want to convert between similar units like miles and yards

**What type of things do you use ratios and proportions for? Leave a comment below!**

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Very effective and informative article.Thanks for sharing such an important tutorial.

Really helpful website

I feel very grateful that I read this. It is very helpful and very informative and I really learned a lot from it.

Thank you for this website. The practice questions are helpful.

Taking this test on Saturday. Last 4.0 exam to complete for the trio, then on to 5.0. This site is my go-to place when organizing what materials I’ll be studying

Hi , very good article.

thanks for sharing, keep up the good work

Good advice. Best of luck to all!

This is my favorite site for practicing for my tests! Great advise and super helpful.

Nice post to read. A complete guide that can help all of us.

Nice one… very helpful! Thanks!!!

Nice post

Great post!

In the NCARB ARE 5.0 handbook they reference Fundamentals of Building Construction: Materials and Methods in both of their example questions for cost estimating. Unfortunately there isn’t a specific chapter on cost estimating, it’s woven throughout the content.

What is the best reference for cost estimating for PDD.

Thanks! Great advice

Deciduous trees should only be used for shade (especially in temperate climates). Deciduous trees lose their leaves in the fall and will have little protection against wind in the winter when it is most needed. Likewise, the leafless trees allow solar heat gain in the winter when it is desired, and shade in the summer.

Coniferous trees are only to be used to block wind and views. Since they don’t lose their needles, they work great for these two items year-round.

Hello. My name is Shahid. This comment is for anyone who would like to reply. On the Siteplanning test. To block the wind, can you use a Deciduous tree or must you use a Coniferous tree?

Hi Tony,

I need to take 5.0 PPD & PDD. Do you plan on posting notes such as “Caroline’s Notes” that you had posted for the various 4.0 exams for either of those sections? I found those notes to be some of the best resources in studying for the 4.0 sections. If so any idea when? Thanks

Hi Tony,

Any updates on the SS exam ? If there’s an expected release date ? Thanks

Paige,

We are releasing practice exams for the SS exam later this fall.

Best,

Tony

Will you have SS questions on here at some point?

Great post, very helpful with the lists of suggested materials, I just passed CDs in July and am taking PPP in November so I definitely needed the list.