Question: You need 1 1/4 cups of sugar to make 20 cookies. To make 14 cookies, you will need ____ cups of sugar.
1. **State the problem:**
You need $1 \frac{1}{4}$ cups of sugar to make 20 cookies. How many cups of sugar are needed to make 14 cookies?
2. **Convert mixed number to improper fraction:**
$1 \frac{1}{4} = \frac{5}{4}$ cups.
3. **Set up the proportion:**
Let $x$ be the cups of sugar needed for 14 cookies.
$$\frac{5}{4} \text{ cups} : 20 \text{ cookies} = x \text{ cups} : 14 \text{ cookies}$$
4. **Write the proportion equation:**
$$\frac{5}{4} / 20 = x / 14$$
5. **Rewrite division as multiplication:**
$$\frac{5}{4} \times \frac{1}{20} = \frac{x}{14}$$
6. **Simplify left side:**
$$\frac{5}{4} \times \frac{1}{20} = \frac{5}{80} = \frac{1}{16}$$
7. **Now solve for $x$:**
$$\frac{1}{16} = \frac{x}{14}$$
8. **Cross multiply:**
$$1 \times 14 = 16 \times x$$
$$14 = 16x$$
9. **Divide both sides by 16:**
$$x = \frac{14}{16}$$
10. **Simplify fraction:**
$$x = \frac{\cancel{14}}{\cancel{16}} = \frac{7}{8}$$
11. **Final answer:**
You need $\frac{7}{8}$ cups of sugar to make 14 cookies.