Means and Extremes in Proportions
A Grade 8 math worksheet focusing on understanding and applying the concept of means and extremes in proportions to solve problems.
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Means and Extremes in Proportions
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Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.
In a proportion a/b = c/d, the terms 'a' and 'd' are called the extremes, and the terms 'b' and 'c' are called the means. The cross-products of a proportion are equal (ad = bc). This property is often called the Means-Extremes Property or Cross-Multiplication Property.
1. In the proportion 3/4 = 9/12, which numbers are the means?
3 and 12
4 and 9
3 and 9
4 and 12
2. Which of the following statements is true for any proportion a/b = c/d?
a * c = b * d
a * d = b * c
a + d = b + c
a / b = c / d
3. In a proportion, the product of the means is equal to the product of the .
4. If 5/x = 15/21, then the means are and .
5. Use the Means-Extremes Property to determine if the following ratios form a proportion: 6/9 and 10/15. Show your work.
6. Solve for x in the proportion: 4/x = 12/18. Show your work.
7. For the proportion 2/5 = 8/20, the extremes are 5 and 8.
True
False
8. The Means-Extremes Property can only be applied to ratios that are already known to be proportional.
True
False
9. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 8 cups of flour, how many cups of sugar do you need? Use the Means-Extremes Property to set up and solve the proportion.
10. The ratio of boys to girls in a class is 3:5. If there are 18 boys, how many girls are there in the class? Solve using the Means-Extremes Property.
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