Tip #21 to Get a Top ACT Math Score

A ratio simply expresses a relationship between two numbers, such as to bake granola bars, use 7 cups of oats to 2 cups of maple syrup. This can be written as 7 : 2 or or even 7 to 2. The ACT likes to see if you can play with the ratios. For example, since the ratio of oats to syrup is 7 : 2, we could also say that the ratio of oats to the oats/syrup combo is 7: 9, since 7 + 2 = 9. Also, remember that the numbers in a ratio may be reduced versions of the actual numbers. For example, if we bake a double batch, we will use not 7: 2, but 14 : 4.

Two ratios that are equal, such as are called a proportion. On the ACT, if one of the four numbers in that proportion is unknown, use cross-multiplying to solve for it. For example, if and you want to find the value of x, just cross-multiply: (5)(40) = (12)(x). Then use algebra to solve for x (divide both sides by 12 to get x = 16.66). Anytime the ACT shows you a proportion, cross-multiply. It's totally predictable. I love things we can absolutely predict on the ACT! So when you come to a proportion on the ACT, get excited, stand up from your desk, and say, "I love the ACT!" People might look at you, but with our mantra, you will always get the question right!

Let's look at this question:

Solution: If one side of the triangle is 19 and the perimeter is 89, then the other two sides add up to 89 – 19 = 70. One of these must be the largest side, and we know that these two sides must have a ratio of 3 : 7. Rewrite the ratio as part : total instead of part : part, and set up the proportion:

Then cross-multiply to get 10x = 490. Divide both sides by 10 and x = 49.

Correct answer: E

Example Problems

Easy

1. On the line segment below, the ratio of lengths MN to MO is 2:3. What is the ratio of MN to NO ?



1. 1:2
2. 2:1
3. 1:3
4. 3:1
5. Cannot be determined from the given information
2. At a glassworks, 60 pounds of composite is required to produce 15 pounds of glass. How many pounds of composite are required to produce 3 pounds of this glass?
   6. 12
   7. 18
   8. 24
   10. 36
   11. 45

Medium

3. On the blueprint for Shantel's house, inch represents an actual length of 1 foot. What is the area, in square inches, of Shantel's living room, which is a rectangle 2 inches by 2 inches on the blueprint?
   1. 33
   2. 34
   3. 68
   4. 136
   5. 272

Hard

4. The ratio of x to y is 2 to 5, and the ratio of z to y is 3 to 4. What is the ratio of x to z ?
   6. 2 to 3
   7. 5 to 9
   8. 7 to 8
   10. 8 to 15
   11. 9 to 2