Question

Which ratios have a unit rate of 3? Choose ALL that apply.

A) 2 cups : 3 cup
B) 2 cups : 6 cup
C) 2 cup : 1 cup
D) 1 cup : 4 cup
E) 1 cup : 2 cups
F) 3 cups : 2 cups

Answer 1

None of the given ratios simplify to a unit rate of 3. The simplified forms do not yield a ratio where for every 1 of one quantity, there are 3 of another.

Step-by-step explanation:

To determine which ratios have a unit rate of 3, we need to see if we can simplify the ratio to the form 3:1 or its equivalent. Here are the evaluations:

• A) 2 cups : 3 cups - This simplifies to approximately 0.6667, which is not equal to 3. Hence, it does not have a unit rate of 3.
• B) 2 cups : 6 cups - This simplifies to 1:3, which means for every 1 cup, there are 3 cups. This is the inverse of what we want, so it is not correct.
• C) 2 cups : 1 cup - This simplifies to 2:1, which is not equal to 3. Hence, it is not correct either.
• D) 1 cup : 4 cups - This simplifies to 0.25, which again, is not 3.
• E) 1 cup : 2 cups - This simplifies to 0.5, which is different from 3.
• F) 3 cups : 2 cups - By inverting this ratio, we get 2 cups: 3 cups. To make it a unit rate, we divide both sides by 2, which gives us 1 cup: 1.5 cups, still not a unit rate of 3.

Hence, none of the ratios provided have a unit rate of 3.