To solve this problem, we'll use the given ratio between ingredient A and ingredient B and apply it to the amount of ingredient A you're using.

Step 1: Understand the ratio

The ratio given is:

• $\frac{1}{2}$ cup of ingredient A for every $1 \frac{1}{5}$ cups of ingredient B.

First, convert the mixed number $1 \frac{1}{5}$ into an improper fraction: $1 \frac{1}{5} = \frac{6}{5} \text{ cups of ingredient B}$

So the ratio can be written as: $\frac{1}{2} \text{ cup of A} : \frac{6}{5} \text{ cups of B}$

Step 2: Set up the proportion

Let $x$ be the amount of ingredient B needed for 2 cups of ingredient A. Set up the proportion based on the given ratio: $\frac{1/2}{6/5} = \frac{2}{x}$

Step 3: Solve the proportion

First, simplify the left side of the equation: $\frac{1/2}{6/5} = \frac{1}{2} \times \frac{5}{6} = \frac{5}{12}$

Now the equation is: $\frac{5}{12} = \frac{2}{x}$

Cross-multiply to solve for $x$: $5x = 12 \times 2$ $5x = 24$ $x = \frac{24}{5} = 4.8$

Step 4: Conclusion

You need 4.8 cups of ingredient B.

Would you like further details on any step? Here are five related questions you might consider:

1. How do you convert a mixed number to an improper fraction?
2. Can you explain cross-multiplication in more detail?
3. How do you determine ratios in recipes?
4. What if the recipe called for a different amount of ingredient A?
5. How would this calculation change if the ratios were reversed?

Tip: Always ensure that units match when setting up proportions, particularly in recipes and measurements.