Means and Extremes Worksheet
Grade 10 Math worksheet covering concepts of means and extremes in proportions, including solving for unknown values and applying to real-world scenarios.
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Means and Extremes
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
Understanding Proportions: Means and Extremes
In a proportion a/b = c/d, 'a' and 'd' are called the extremes, and 'b' and 'c' are called the means. The product of the means equals the product of the extremes (ad = bc).
Identify the means and extremes in each proportion.
1. In the proportion 3/4 = 9/12, the means are and , and the extremes are and .
2. For the proportion 5/x = 15/21, the means are and , and the extremes are and .
Solve for the unknown variable in each proportion using the means-extremes property.
3. 6/x = 18/24
4. (y + 1)/5 = 12/20
Choose the best answer for each question.
5. Which of the following statements is true for the proportion a/b = c/d?
ac = bd
ab = cd
ad = bc
a + d = b + c
6. If 4/5 = x/20, what is the value of x?
10
12
16
25
Solve the following word problems.
7. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 8 cups of flour, how much sugar do you need?
8. A car travels 150 miles on 5 gallons of gasoline. How far can it travel on 12 gallons of gasoline?
Determine if each statement is True or False.
9. In the proportion 1/2 = 3/6, the product of the means is 6.
True
False
10. The means-extremes property can only be used with whole numbers.
True
False
Challenge Question:
11. If the ratio of boys to girls in a class is 3:5 and there are 12 boys, how many students are there in total in the class?