Free Ratio and Proportion Algebra Problems for Math Students

How Can I Review Ratios and Proportions with My Child?

If your child needs some extra ratio and proportion algebra help, you may want her to complete practice problems to stay on track with her algebra studies. In addition to learning ratio and proportion in algebra, she will solve problems with these concepts in later math classes and may benefit from spending a little extra time practicing now.

A ratio tells you how numbers relate to one another. For instance, a car traveling at 25 miles an hour would be represented as a ratio like this: 25/1. A proportion is made up of two ratios that are equal to one another. For instance, we can solve this problem using a proportion: if a car travels 25 miles an hour (25/1), how far will it travel in three hours? For this problem, the proportion is 25/1 = x/3, and you'll find that x = 75.

Problems by Concept

Ratios

1. In a bouquet, there are 12 red flowers and seven pink flowers. What is the ratio of red to pink flowers?

The ratio is 12/7. You can also use a colon when writing ratios - 12:7 - or write it as '12 to 7.'

2. Ian has 13 shirts and three pairs of pants. What is the ratio of shirts to pants?

The ratio is 13/3.

3. In a bag of candy, there are 16 total pieces. Five are green, two are yellow, three are blue and six are red. Write the ratio of each color to the total amount of candy pieces.

This problem is more complex because it requires you to write multiple ratios. For the green pieces of candy, the ratio is 5/16; for yellow pieces, 2/16; for blue pieces, 3/16 and for red pieces, the ratio is 6/16.

Proportions

1. 4/20 = 5/y

Proportions are used to determine an unknown quantity, which in this case is y. Begin by cross multiplying, so that the equation looks like this: (4)(y) = (20)(5). Then, solve for y by multiplying, 20 x 5, and dividing it by four.

A quick way to solve these problems is to skip the step in which you write out the equation. Instead, you would simply cross-multiply, 20 x 5, and then divide by four. Either method will bring you to the conclusion that y = 25.

2. 5/7 = b/10

For this problem, b = 7.1423.

3. 2/60 = 3/t

For this problem, t = 90.

Word Problems

1. Jeanne reads at a pace of 25 pages in 30 minutes. How many pages will she read in 60 minutes?

You'd set up the proportion like this: 25/30 = p/60 and solve for p. The answer is 50 pages.

2. Dave bought four apples for $6. How many apples could Doug buy for $10?

The proportion for this problem is 4/6 = a/10. When you solve for a, you'll find that the answer is 6.67, so Doug can buy 6 apples.