A recipe calls for 4 carrots for every 2 cups of water. Which expression can be used to find the number of carrots needed for 1 cup of water?

StartFraction 4 carrots Over 2 cups of water EndFraction
StartFraction 4 cups of water Over 2 carrots EndFraction
StartFraction 2 carrots Over 4 cups of water EndFraction
StartFraction 2 cups of water Over 4 carrots EndFraction

1 answer

To find the number of carrots needed for 1 cup of water based on the given ratio of 4 carrots for every 2 cups of water, we can set up the proportion.

The ratio of carrots to water can be expressed as:

\[ \frac{4 \text{ carrots}}{2 \text{ cups of water}} \]

To find the number of carrots needed for 1 cup of water, we need to simplify the ratio.

First, we can rewrite the proportion so that we have the carrots per cup of water:

\[ \frac{4 \text{ carrots}}{2 \text{ cups of water}} = \frac{4 \text{ carrots}}{2} \times \frac{1 \text{ cup of water}}{1 \text{ cup of water}} = \frac{4 \text{ carrots}}{2 \text{ cups of water}} \times \frac{1 \text{ cup of water}}{1} \]

This simplifies to:

\[ \frac{4 \text{ carrots}}{2 \text{ cups of water}} = \frac{2 \text{ carrots}}{1 \text{ cup of water}} \]

Thus, to find the expression for the number of carrots needed for 1 cup of water, we can express it as:

\[ \frac{2 \text{ carrots}}{4 \text{ cups of water}} \]

In this format, that would be the third option given which is:

\[ \frac{2 \text{ carrots}}{4 \text{ cups of water}} \]

Therefore, the correct expression is:

\[ \frac{2 \text{ carrots}}{4 \text{ cups of water}} \]