{"id":16357,"date":"2021-06-24T14:44:09","date_gmt":"2021-06-24T21:44:09","guid":{"rendered":"https:\/\/magoosh.com\/act\/?p=16357"},"modified":"2021-06-24T14:44:09","modified_gmt":"2021-06-24T21:44:09","slug":"how-to-solve-ratios","status":"publish","type":"post","link":"https:\/\/magoosh.com\/act\/how-to-solve-ratios\/","title":{"rendered":"Ratios to Know for the ACT, and How to Solve Them"},"content":{"rendered":"

\"chalkboard<\/p>\n

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<\/a>! So without further ado, here’s what you need to know about how to solve ratios on the ACT. <\/p>\n

How to Solve Ratios on the ACT<\/h2>\n

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!<\/p>\n

Triangle Ratios<\/h3>\n

Each and every time you see a right triangle<\/strong> 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<\/strong> of time.<\/p>\n

When you spot a triangle that uses one? No Pythagorean theorem needed here! Look for Pythagorean triplets<\/strong> instead.<\/p>\n

For Right Triangles<\/strong><\/p>\n

    \n
  • Look for a 3:4:5 ratio of sides.<\/strong> In other words, the base and height will measure 3 and 4 (or vice-versa), and the hypotenuse will measure 5.<\/li>\n
  • Check angle measurements to see if they are 45:45:90.<\/strong> If they are, the corresponding side measures are \\( x:x:x\u221a2 \\).<\/li>\n
  • Check angle measurements to see if they are 30:60:90.<\/strong> If they are, the corresponding side measures are \\(x:x\u221a3:2x\\)<\/li>\n<\/ul>\n

    The ACT can be tricky with these ratios\u2014they 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!<\/p>\n

    \"Triangle<\/p>\n

    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!<\/p>\n

    For Similar Triangles<\/strong>
    \nWhen triangles are similar, their sides and height ratios are the same\u2014and corresponding angles are equal. This is easier seen than read, so take a look at the diagram below!<\/p>\n

    Then, check out our Magoosh’s expert’s advice for similar triangles!<\/p>\n