Means and Extremes Worksheet
Explore means and extremes in proportions and their applications in various mathematical contexts.
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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 full credit.
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 Means-Extremes Property (or Cross-Products Property) states that in a proportion, the product of the extremes is equal to the product of the means, i.e., ad = bc.
1. In the proportion 5/8 = 15/24, the means are and the extremes are .
2. If a/x = y/b, then the product of the means is and the product of the extremes is .
3. Use the Means-Extremes Property to determine if the following ratios form a proportion: 6/9 and 10/15. Show your work.
4. Solve for x in the proportion: 4/x = 12/18.
x = 3
x = 6
x = 8
x = 9
5. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to use 5 cups of flour, how much sugar do you need? Use a proportion and the Means-Extremes Property to solve.
6. In the proportion (x+1)/5 = 6/10, the means are (x+1) and 10.
True
False
7. Find the geometric mean of 4 and 9. Explain your steps.
8. Consider the following proportion: 1/2 = 3/6. Draw two fraction bars to visually represent this proportion.