Which equation correctly shows the multiplication of the means and extremes in the proportion $7.2 / 9.6=21.6 / 28.8$?
A) $7.2 \cdot 21.6=28.8 \cdot 9.6$
B) $7.2 \cdot 28.8=21.6 \cdot 28.8$
C) $9.6 \cdot 21.6=28.8 \cdot 7.2$
D) $7.2 \cdot 9.6=21.6 \cdot 28.8$
Answer (2)
Identify the means and extremes in the proportion.
Multiply the means and multiply the extremes.
Equate the product of the means to the product of the extremes.
The correct equation is 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2 , so the answer is C .
Explanation
Understanding Proportions We are given the proportion 9.6 7.2 = 28.8 21.6 and asked to identify the equation that correctly shows the multiplication of the means and extremes. In a proportion b a = d c , the means are b and c , and the extremes are a and d . The product of the means equals the product of the extremes, i.e., a "." d = b "." c .
Identifying Means and Extremes In the given proportion 9.6 7.2 = 28.8 21.6 , the means are 9.6 and 21.6, and the extremes are 7.2 and 28.8. Therefore, the equation representing the multiplication of the means and extremes is 7.2 ⋅ 28.8 = 9.6 ⋅ 21.6 .
Checking the Options Let's check the given options:
A) 7.2 ⋅ 21.6 = 28.8 ⋅ 9.6 This is incorrect because it multiplies 7.2 and 21.6, which are not both extremes or both means. B) 7.2 ⋅ 28.8 = 21.6 ⋅ 28.8 This is incorrect because it has 28.8 on both sides, and it should be 7.2 ⋅ 28.8 = 9.6 ⋅ 21.6 .
C) 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2 This is correct because it equates the product of the means (9.6 and 21.6) with the product of the extremes (28.8 and 7.2). D) 7.2 ⋅ 9.6 = 21.6 ⋅ 28.8 This is incorrect because it multiplies 7.2 and 9.6, which are not both extremes or both means.
Verifying the Equation The correct equation is 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2 , which is option C. We can verify this by calculating both sides:
7.2 ⋅ 28.8 = 207.36 9.6 ⋅ 21.6 = 207.36
Since both sides are equal, the equation is correct.
Final Answer The equation that correctly shows the multiplication of the means and extremes in the proportion 9.6 7.2 = 28.8 21.6 is 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2 . Therefore, the answer is C .
Examples
Proportions are used in everyday life, such as when scaling recipes. If a recipe calls for 2 cups of flour for 1 cake, you can use proportions to determine how much flour you need for 3 cakes. Another example is calculating distances on a map. If a map has a scale of 1 inch = 10 miles, you can use proportions to find the actual distance between two points on the map.
The correct equation for the multiplication of the means and extremes in the proportion 9.6 7.2 = 28.8 21.6 is 9.6 ⋅ 21.6 = 28.8 ⋅ 7.2 , which corresponds to option C. This follows the property that the product of the means equals the product of the extremes in a proportion.
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