Ratios
A ratio is a comparison of one number to another and can be written as:
3:4, 3 to 4, or 3/4A ratio is a fraction. Ratios, like fractions, should always be reduced to lowest terms.
The order of the two numbers is very important in a ratio. We write the ratio in the order that the words are written. It is helpful to read the question first in a ratio or proportion problem to make certain that you are answering the question. In the question, What is the ratio of 15 inches to a yard, look at the number right after “ratio of”. This is the number that goes on the top of the fraction. The number after the word “to,” goes on the bottom.
For example, in the high school equivalency class, there are 2 males for every 5 female students.
This would be written as 2:5, 2 to 5, or 2/5If the question said to compare the number of female students to male students, then the ratio would be written
5:2, 5 to2, or 5/2Example 1:
Sally takes home $800 a month and pays $200 for rent. What is the ratio of her rent to her take-home pay?Step 1: Write a ratio that compares the rent to take-home pay.
200
800Step 2: Reduce the ratio to lowest terms. (If you need a refresher on reducing, refer back to the Intro to Fractions Worksheet.)
200 ÷ 200 = 1
800 ÷ 200 = 4Example 2:
Mike’s softball team won 12 games and lost 8. What is the ratio of the number of games won to the total number played?Step 1: Add the number of games won to the number lost to find the total number of games played. Reading the question carefully is very important because, as you can see, if you had written the ratio before reading the question, you probably would have written 12 to 8.
12+8 = 20Step 2: Write a ratio of the number of games won to the total number played?
12:20 is the correct ratio or
12
20Step 3: Reduce to lowest terms.
12¸÷ 4 = 3
20 ÷ 4 = 5
Be sure to set up the ratio in the same order the question is worded.
Practice
1. Pam sleeps 8 hours every night. What is the ratio of Pam’s time spent sleeping to Pam’s time spent awake?
2. To make lemonade, add 4 cans of water to every can of concentrate. What is the ratio of water to concentrate?
3. A ski resort advertised that it had 23 snow days during January. What is the ratio of snow days to no-snow days?
4. In a local election, Marshall received 582 votes while Hawks received 366 votes. What is the ratio of the number of votes for Hawks to the number of votes for Marshall?
5. Sandra’s living room is 15 feet long and 12 feet wide. What is the ratio of the width to the length?
6. In town Louie gets 16 miles to a gallon of gasoline. In the country he gets 24 miles to a gallon. What is the ratio of his gas mileage in town to his gas mileage in the country?
7. Jack bought a stereo on sale for $450. He saved $150 by buying the stereo on sale. What was the ratio of the sale price to the original price?
8. Dave weighed 280 pounds in March. By the following September he had lost 70 pounds. Find the ratio of his March weight to his September weight.
9. Denise has paid back $1500 of a $5000 car loan. What is the ratio of the amount she has already paid to the amount she still owes?
10. On a test Geraldine got 40 problems right and 16 problems wrong. What is the ratio of the number she got right to the total number of problems?
Resources:
GED Test 5: Mathematics. (2001). Contemporary Books, NTC/Contemporary Publishing Group: Lincolnwood, IL.Howett, Jerry. (1998). GED Program: Mathematics. Cambridge Adult Education: Upper Saddle River, NJ.
Pre-GED: Mathematics. (2000). Steck-Vaughn: Austin, TX.