There are 16 tablespoons in 1 cup and 3 teaspoons in 1 tablespoon. A recipe calls for [tex]\frac{1}{2}[/tex] cup of sugar, but Ali only has a teaspoon to measure her ingredients.

1. How many tablespoons are in [tex]\frac{1}{2}[/tex] cup?
[tex]\frac{1}{2}[/tex] cup = [tex]\square[/tex] tablespoons

2. How many teaspoons are in 8 tablespoons?
8 tablespoons = [tex]\square[/tex] teaspoons

3. How many teaspoons are in [tex]\frac{1}{2}[/tex] cup?
[tex]\frac{1}{2}[/tex] cup = [tex]\square[/tex] teaspoons

Let's break down the problem step by step.

### Part 1: How many tablespoons are in [tex]$\frac{1}{2}$[/tex] cup?

1. We know from the problem that there are 16 tablespoons in 1 cup.
2. Since we need to find out the number of tablespoons in [tex]$\frac{1}{2}$[/tex] cup, we multiply the number of tablespoons in one cup by [tex]$\frac{1}{2}$[/tex]:

[tex]\[
\frac{1}{2} \text{ cup} \times 16 \text{ tablespoons per cup} = 8 \text{ tablespoons}
\][/tex]

So, there are 8 tablespoons in [tex]$\frac{1}{2}$[/tex] cup.

### Part 2: How many teaspoons are in 8 tablespoons?

1. According to the problem, there are 3 teaspoons in 1 tablespoon.
2. To find out how many teaspoons are in 8 tablespoons, we multiply the number of tablespoons by the number of teaspoons per tablespoon:

[tex]\[
8 \text{ tablespoons} \times 3 \text{ teaspoons per tablespoon} = 24 \text{ teaspoons}
\][/tex]

Therefore, there are 24 teaspoons in 8 tablespoons.

### Part 3: How many teaspoons are in [tex]$\frac{1}{2}$[/tex] cup?

1. From Part 1, we found out that [tex]$\frac{1}{2}$[/tex] cup is equivalent to 8 tablespoons.
2. Since we already know that there are 24 teaspoons in 8 tablespoons from Part 2, we can conclude that:

[tex]\[
\frac{1}{2} \text{ cup} = 24 \text{ teaspoons}
\][/tex]

To summarize:
- [tex]$\frac{1}{2}$[/tex] cup is equal to 8 tablespoons.
- 8 tablespoons is equal to 24 teaspoons.
- Therefore, [tex]$\frac{1}{2}$[/tex] cup is also equal to 24 teaspoons.