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

Ratios & 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 proportion 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.

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.

Roof Slope ProtionI 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.

roof proportion

 

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.ratios and proportions

 

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

solving proportions

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.

solving proportions

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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24 Comments

  1. classboat01 October 17, 2018 at 7:37 am #

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  2. mikemoreno September 5, 2018 at 3:48 am #

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  3. jogesh12345 August 14, 2018 at 1:55 am #

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

  4. FLMIMA August 11, 2018 at 9:20 pm #

    Really helpful website

  5. Rumi July 15, 2018 at 7:16 am #

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

  6. RJennings April 28, 2018 at 6:12 pm #

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

  7. Scott March 22, 2018 at 1:50 pm #

    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

  8. shozab January 30, 2018 at 2:22 pm #

    Hi , very good article.

    thanks for sharing, keep up the good work

  9. dyba January 27, 2018 at 1:08 am #

    Good advice. Best of luck to all!

  10. KendraShirley January 16, 2018 at 4:04 pm #

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

  11. reximagetrim January 16, 2018 at 10:37 am #

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

  12. tylerstockholm December 17, 2017 at 9:37 pm #

    Nice one… very helpful! Thanks!!!

  13. Aartiwalvekar November 21, 2017 at 8:56 am #

    Nice post

  14. Aartiwalvekar October 9, 2017 at 9:45 pm #

    Great post!

  15. Tony August 30, 2017 at 7:07 am #

    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.

  16. Spencer August 30, 2017 at 1:15 am #

    What is the best reference for cost estimating for PDD.

  17. Amy July 26, 2017 at 3:24 pm #

    Thanks! Great advice

  18. Tony June 29, 2017 at 7:23 am #

    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.

  19. Shahid Logan June 28, 2017 at 4:50 pm #

    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?

  20. Mike January 4, 2017 at 11:04 am #

    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

  21. Stephen October 17, 2016 at 9:30 pm #

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

  22. DesignerHacks October 4, 2016 at 12:11 pm #

    Paige,

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

    Best,
    Tony

  23. Paige October 4, 2016 at 11:34 am #

    Will you have SS questions on here at some point?

  24. Daniel September 9, 2016 at 8:47 am #

    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.

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