Means and Extremes in Proportions
Explore the concepts of means and extremes in proportions through various exercises.
Includes
Standards
Topics
Means and Extremes in Proportions
Name:
Date:
Score:
Read each question carefully and follow the instructions to determine the means and extremes of the given proportions, or to solve for the unknown value.
In a proportion, which is an equation stating that two ratios are equal, the 'means' are the two middle terms and the 'extremes' are the two outer terms. For example, in the proportion a/b = c/d, 'b' and 'c' are the means, and 'a' and 'd' are the extremes. A key property of proportions is that the product of the means equals the product of the extremes (b * c = a * d).
For each proportion, identify the means and the extremes.
1. 3/4 = 9/12
Means:
Extremes:
2. 5/x = 10/16
Means:
Extremes:
3. 7/2 = y/6
Means:
Extremes:
Use the property of means and extremes to fill in the blanks and complete the proportions.
4. If 2/5 = 8/x, then 2 * x = 5 * .
5. In the proportion a/b = c/d, the product of the means is , and the product of the extremes is .
6. If 6/y = 18/3, then 6 * 3 = y * .
7. Which of the following is a proportion?
1 + 2 = 3 + 4
1/2 = 3/6
2 * 3 = 6 + 1
5 - 3 = 8 / 4
8. In the proportion 4/10 = 2/5, which numbers are the extremes?
4 and 10
10 and 2
4 and 5
2 and 5
Use the means-extremes property to solve for the unknown variable in each proportion.
9. 6/x = 3/7
10. y/9 = 4/12
11. 15/5 = z/1
Determine if the following statements are true or false.
12. In the proportion 1:2 = 2:4, the means are 1 and 4.
True
False
13. If the product of the means equals the product of the extremes, then the ratios form a proportion.
True
False
Solve the following word problems using your knowledge of proportions, means, and extremes.
14. A recipe calls for 2 cups of flour for every 3 eggs. If you use 9 eggs, how many cups of flour do you need? Set up a proportion and solve.
15. A car travels 150 miles in 3 hours. At this rate, how far will it travel in 5 hours?