To review these concepts, go to Ratio and Rate Word Problems Study Guide.

**Ratio and Rate Word Problems Practice Questions**

**Practice 1**

**Problems**

- Write this ratio in two other ways: 4 to 5.
- Write this ratio in two other ways: .
- Simplify the ratio: 33 to 44.
- Simplify the ratio: .
- Simplify the continued ratio 20 to 40 to 50.

**Solutions**

- 4:5;
- 1 to 2; 1:2
- 3 to 4. Divide by the greatest common factor, 11.
- . Divide by the greatest common factor, 7.
- 2 to 4 to 5. Divide by the greatest common factor, 10.

**Practice 2**

**Problems**

Find the unit rate for each.

**Solutions**

**Practice 3**

Now that the concepts of ratio and rate have been reviewed, try the following word problems.

**Problems**

- There are 65 boys and 52 girls in the drama club. What is the ratio of boys to girls, in simplest form?
- On a farm that has only two types of animals, there are 34 cows and 12 horses. What is the ratio of horses to the total number of animals on the farm, in simplest form?
- Over a period of 3 hours, 180 leaves fell from a tree. At this rate, how many leaves fell in one hour?
- Georgia drove a total of 252 miles and used 12 gallons of gasoline. What is this rate in miles per gallon?
- Tyler scored 21 goals in 7 soccer games. At this rate, about how many goals did he score each game?
- While climbing down a mountain, Anthony descended 45 feet every hour. At this rate, how many feet will he descend in 6 hours?

**Solutions**

*Read and understand the question*. This question asks for the ratio of boys to girls in simplest form, so the answer will have to be in lowest terms.*Read and understand the question*. This question is looking for the ratio of the number of horses to the total number of animals on a farm. The number of horses and the number of cows is given in the question.*Read and understand the question*. This question is looking for the unit rate, or how many leaves fell in 1 hour, when the number of leaves that fell in 3 hours is given.*Read and understand the question*. This question is looking for the unit rate, or how many miles per gallon Georgia's car got, when the total miles driven and gallons used are given.*Read and understand the question*. This question is looking for the unit rate, or how many goals were scored in each game, when the total goals and number of games are given in the question.*Read and understand the question*. This question is looking for the total number of feet Anthony will descend when the unit rate is given.

*Make a plan*. Find the number of boys first and the number of girls second.

Find the greatest common factor of the two values and divide by this number to simplify.

*Carry out the plan*. The ratio becomes . The greatest common factor of these numbers is 13, so divide each by 13:

This can also be written as 5 boys:4 girls or 5 boys to 4 girls.

*Check your answer*. To check your result, work backward and multiply each value by 13. The values become 65 and 52, respectively, which were the original numbers in the problem. This answer is checking.

*Make a plan*. Compare the number of horses with the total number of animals by adding the number of cows and the number of horses together.

Then, be sure that the answer is in simplest form by dividing by the greatest common factor of both numbers.

*Carry out the plan*. The number of horses is 12, and the total number of animals is 34 + 12 = 46. The ratio can be written as . The greatest common factor of both numbers is 2, so the simplified ratio is .

This can also be written as 6 horses:23 animals or 6 horses to 23 animals.

*Check your answer*. Be sure that you are comparing the correct quantities.

This question asks for the number of horses compared to the total number of animals, which is the number of cows and horses added together. In addition, check to make sure that the value for horses is first, because it was mentioned first in the question. This solution is checking.

*Make a plan*. Divide the number of leaves that fell in 3 hours by 3 to find the unit rate.

*Carry out the plan*:

*Check your answer*. Multiply to check your answer. Sixty leaves per hour for 3 hours is equal to 60 × 3 = 180 leaves. This solution is checking.

*Make a plan*. Divide the number of miles by the number of gallons used to find the unit rate.

*Carry out the plan*:

*Check your answer*. Multiply to check your answer. Twenty-one miles per gallon multiplied by 12 gallons is equal to 21 × 12 = 252 miles. This answer is checking.

*Make a plan*. Divide the number of goals by the total number of games to find the unit rate per game.

*Carry out the plan*:

*Check your answer*. Multiply to check your answer. Three goals per game for 7 games is equal to 3 × 7 = 21 goals. This solution is checking.

*Make a plan*. Multiply the unit rate by the total number of hours he is descending.

*Carry out the plan*: 45 feet per hour multiplied by 6 hours is equal to 45 × 6 = 270 feet.

*Check your answer*. Divide to check your answer.

This solution is checking.

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