To complete the table, let's analyze the relationship between the cups of sugar and flour in each batch.

Given:

• The recipe calls for $\frac{1}{2}$ cup of sugar and 1 cup of flour.

For each row, we’ll find the required flour by determining the multiplier based on the sugar amount.

Solution Steps

1. First Row (already provided):

   • Sugar: $\frac{1}{2}$ cup
   • Flour: 1 cup

   This indicates that $\frac{1}{2}$ cup of sugar corresponds to 1 cup of flour.

2. Second Row (Sugar: $\frac{3}{4}$ cup):

   • Since $\frac{3}{4}$ is 1.5 times $\frac{1}{2}$, we multiply the flour by 1.5.
   • Flour: $1 \times 1.5 = 1.5$ cups, or $1 \frac{1}{2}$ cups.

3. Third Row (Flour: $1 \frac{3}{4}$ cups):

   • Since $1 \frac{3}{4} = 1.75$, we find the corresponding sugar by scaling $\frac{1}{2}$ cup.
   • To find the sugar needed, divide $1.75$ by 1 to get 1.75 times the initial sugar amount.
   • Sugar: $\frac{1}{2} \times 1.75 = \frac{7}{8}$ cup.

4. Fourth Row (Flour: $2 \frac{1}{2}$ cups):

   • $2 \frac{1}{2} = 2.5$, so we find the sugar for 2.5 times the original recipe.
   • Sugar: $\frac{1}{2} \times 2.5 = 1 \frac{1}{4}$ cups.

Completed Table:

Would you like more details or have questions about any step?

Related Questions

1. How do you determine the multiplier for different quantities?
2. What if the recipe requires a different ratio of ingredients?
3. How can we verify the calculations in each step?
4. What if we need an even larger batch—how would we scale it?
5. How do we handle recipes with non-integer multipliers?

Tip: When scaling recipes, always maintain the ratio between ingredients to preserve the intended outcome.