Means and Extremes in Proportions
This worksheet focuses on understanding and applying the concepts of means and extremes in proportions for Grade 9 mathematics.
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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. Remember that in a proportion a/b = c/d, 'a' and 'd' are the extremes, and 'b' and 'c' are the means. The product of the means equals the product of the extremes.
1. In the proportion 3/4 = 9/12, the means are and , and the extremes are and . (Use numbers from the proportion)
2. For the proportion 5/x = 15/21, the means are and , and the extremes are and . (Use numbers or variables from the proportion)
3. The product of the means is always equal to the product of the extremes in a true proportion.
True
False
4. If the product of the means does not equal the product of the extremes, then the ratios do not form a proportion.
True
False
5. Solve for x: 6/9 = x/12
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8
9
10
6. Find the value of y: 4/y = 16/20
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8
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 in 3 hours. At this rate, how far will it travel in 7 hours?
9. Consider the balance scale below. If the ratio of weights on the left to the right is 3:5, and the left side has a total weight of 12 kg, what is the weight on the right side?
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