Ratios to Know for the ACT, and How to Solve Them

chalkboard featuring examples of how to solve ratios -magoosh

When you want to boost your ACT math score fast, learning common ratios can help you do it. These patterns show up in numerous problems, often providing you with shortcuts to solve questions more quickly and accurately. For that reason alone, they’re one of the most useful ACT math concepts to master! So without further ado, here’s what you need to know about how to solve ratios on the ACT.

How to Solve Ratios on the ACT

There are three crucial types of ACT ratios that you’ll see on the test: triangles, circles, and conversions. Once you understand these ratios, you can fill in the known values the question gives you. Then, because these ratios use a fractional form, you can use cross-multiplication to find the missing value. Take a look!

Triangle Ratios

Each and every time you see a right triangle on the ACT Math section, I want you to take a split second and ask: is there a ratio I can use here? If so, it can save you a ton of time.

When you spot a triangle that uses one? No Pythagorean theorem needed here! Look for Pythagorean triplets instead.

For Right Triangles

  • Look for a 3:4:5 ratio of sides. In other words, the base and height will measure 3 and 4 (or vice-versa), and the hypotenuse will measure 5.
  • Check angle measurements to see if they are 45:45:90. If they are, the corresponding side measures are \( x:x:x√2 \).
  • Check angle measurements to see if they are 30:60:90. If they are, the corresponding side measures are \(x:x√3:2x\)

The ACT can be tricky with these ratios—they may give you a triangle with a base of 6 and a hypotenuse of 10. But if you practice how to solve ratios problems involving triangles, they’ll become second nature to you. Try it out!

Triangle with base 6 hypotenuse 10 and height x

Here, you can use the greatest common factor (2) to see that this reduced ratio is a triple. Use ratio \(3:x:5\), multiply by 2, and you’ll know to label that height 8!

For Similar Triangles
When triangles are similar, their sides and height ratios are the same—and corresponding angles are equal. This is easier seen than read, so take a look at the diagram below!

Then, check out our Magoosh’s expert’s advice for similar triangles!

Circle Ratios

Circles have lots of lovely equivalent ratios. Don’t believe me? Take look at these pairs of values! In a circle:

\(\frac{\text{central angle}}{360} = \frac{\text{arc length}}{\text{circumference}} = \frac{\text{sector area}}{\text{circle area}}\)
 
This comes in handy on test day! For example, take a look at how to solve ratios problems by finding the area of a sector.

Conversion Ratios

Last but definitely not least, conversion ratios pop up all the time on the ACT: for quantities to use in a recipe, for distance calculations, for time questions–all sorts of real-world problems. These are the types of ratios we use in everyday life all the time—but if you’re not careful, they can trip you up!

You’re likely already familiar with the most basic of these, but here are some of the conversions you should know before test day:

  • There are 60 seconds in one minute (60 sec/1 min)
  • There are 60 minutes in one hour (60 min/1 hr)
  • There are 12 inches in one foot (12 inches/1 ft)
  • There are 12 months in one year (12 months/1 yr)
  • There are 3 feet in one yard (3 ft/1 yd)
  • There are 1,000 millimeters in 1 meter (1,000 mm/1m)
  • There are 100 centimeters in 1 meter (100 cm/1m)
  • There are 1,000 meters in a kilometer (1 m/1km)
  • There are 1,000 grams in one kilogram (1,000g/1kg)

You can find a handy tables of equivalent ratios on the ACT website, but don’t waste time memorizing it: for lesser-known conversions, the ACT will put the conversion rates in the question itself.

Takeaways for Learning and Solving ACT Ratios

Still wondering how to solve ratios on the ACT? Practice! Unlike the SAT, the ACT doesn’t include formulas and ratios at the beginning of the math section. Our best advice for memorizing them? Complete tons of ratio practice mathematical problems! It’s one thing to know the ratios—but the ACT isn’t going to ask you to spit out the ratios themselves. Instead, they’re going to ask you to use them in practice. So know your math formulas, yes—but put them to use with ACT math ratio problems, as well! And you’ll have them mastered well before the official exam.

Author

  • Rachel Kapelke-Dale

    Rachel is a Magoosh Content Creator. She writes and updates content on our High School and GRE Blogs to ensure students are equipped with the best information during their test prep journey. As a test-prep instructor for more than five years in there different countries, Rachel has helped students around the world prepare for various standardized tests, including the SAT, ACT, TOEFL, GRE, and GMAT, and she is one of the authors of our Magoosh ACT Prep Book. Rachel has a Bachelor of Arts in Comparative Literature from Brown University, an MA in Cinematography from the Université de Paris VII, and a Ph.D. in Film Studies from University College London. For over a decade, Rachel has honed her craft as a fiction and memoir writer and public speaker. Her novel, THE BALLERINAS, is forthcoming in December 2021 from St. Martin's Press, while her memoir, GRADUATES IN WONDERLAND, co-written with Jessica Pan, was published in 2014 by Penguin Random House. Her work has appeared in over a dozen online and print publications, including Vanity Fair Hollywood. When she isn't strategically stringing words together at Magoosh, you can find Rachel riding horses or with her nose in a book. Join her on Twitter, Instagram, or Facebook!

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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