Which one of the following statements expresses a true proportion?
A.2:3 = 3:2
B.14:6 = 28:18
C.3:5 = 12:20
D.42:7 = 6:2
I'll be glad to check your answer.
Right.
To determine which one of the following statements expresses a true proportion, we need to check if the ratios on both sides of the equation are equivalent.
Let's evaluate each option:
A. 2:3 = 3:2
The ratio on the left is 2:3, which means that for every 2 units on one side, there are 3 units on the other side. The ratio on the right is 3:2, which means that for every 3 units on one side, there are 2 units on the other side. Since the ratios are not the same, this statement does not express a true proportion.
B. 14:6 = 28:18
The ratio on the left is 14:6, which means that for every 14 units on one side, there are 6 units on the other side. The ratio on the right is 28:18, which means that for every 28 units on one side, there are 18 units on the other side. To determine if the ratios are equivalent, we can simplify both sides of each ratio. Simplifying 14:6 gives us 7:3, and simplifying 28:18 gives us 14:9. Since the simplified ratios are not the same, this statement does not express a true proportion.
C. 3:5 = 12:20
The ratio on the left is 3:5, which means that for every 3 units on one side, there are 5 units on the other side. The ratio on the right is 12:20, which means that for every 12 units on one side, there are 20 units on the other side. To determine if the ratios are equivalent, we can simplify both sides of each ratio. Simplifying 3:5 gives us the same ratio, 3:5, and simplifying 12:20 gives us the same ratio, 3:5. Since the simplified ratios are the same, this statement expresses a true proportion.
D. 42:7 = 6:2
The ratio on the left is 42:7, which means that for every 42 units on one side, there are 7 units on the other side. The ratio on the right is 6:2, which means that for every 6 units on one side, there are 2 units on the other side. To determine if the ratios are equivalent, we can simplify both sides of each ratio. Simplifying 42:7 gives us 6:1, and simplifying 6:2 gives us 3:1. Since the simplified ratios are not the same, this statement does not express a true proportion.
Therefore, the statement that expresses a true proportion is option C. 3:5 = 12:20.