Means and Extremes Worksheet

Means and Extremes

Read each question carefully and answer to the best of your ability. Remember that in a proportion, the product of the means equals the product of the extremes.

A proportion is a statement that two ratios are equal. For example, 2/3 = 4/6 is a proportion. In a proportion a/b = c/d, 'a' and 'd' are called the EXTREMES, and 'b' and 'c' are called the MEANS. An important property of proportions is that the product of the means equals the product of the extremes.

1. In the proportion 5/10 = 1/2, the means are   and  , and the extremes are   and  .

2. For the proportion 3:4 = 9:12, the extremes are   and  , and the means are   and  .

3. Identify the means and extremes in the proportion 7/14 = 1/2. Means:  , Extremes:  .

4. Which of the following statements is true about the proportion 4/8 = 1/2?

5. If the product of the means is 30, and one extreme is 5, what is the other extreme?

6. Explain in your own words the relationship between the means and extremes of a proportion.

7. In the proportion a/b = c/d, 'a' and 'c' are always the means.

8. If the product of the means does not equal the product of the extremes, then the ratios do not form a proportion.

9. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 6 cups of flour, how much sugar do you need? Use means and extremes to solve.

Consider a balance scale to understand proportions. When the scale is balanced, the ratios on both sides are proportional.