Question

Select two ratios that are equivalent to 27:9

A. 3:1 and 9:3
B. 6:3 and 9:6
C. 9:3 and 12:3
D. 1:3 and 3:9

Answer 1

Option A

Step-by-step explanation:

In the ratio 27:9 if we cancel 27 and 9 with 9 we get 3:1 and if we cancel 27 and 9 with 3 we get 9:3 which is also equal to 3:1

Answer 2

The correct answer is Option A, which includes 3:1 and 9:3, both of which are equivalent to the ratio 27:9 after simplification.

Step-by-step explanation:

The question revolves around finding two ratios that are equivalent to 27:9. A ratio compares two quantities, which can be simplified similar to fractions. Ratio of 27:9 can be simplified by dividing both numbers by 9, which gives us the ratio 3:1. This simplified ratio is a unit rate because it compares a quantity to one unit.

Now, let's see which options are equivalent to 27:9 by simplifying them:

• Option A: 3:1 is already simplified and equivalent to 3:1, which is our target ratio. 9:3 can be simplified to 3:1, which shows that option A has two ratios equivalent to 27:9.
• Option B: 6:3 simplifies to 2:1 and 9:6 simplifies to 3:2, none of which are equivalent to 3:1.
• Option C: 9:3 simplifies to 3:1, which is equivalent, but 12:3 simplifies to 4:1, which is not equivalent to 27:9.
• Option D: 1:3 and 3:9 are both not equivalent to 3:1 after simplification.

Therefore, the correct answer is Option A, which includes the two equivalent ratios 3:1 and 9:3, representing the same proportion as 27:9.