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To solve this problem, let’s start by analyzing the given information and breaking down each part:

### Given Information
- **Ratio of garlic powder to salt**: \( 4 \) grams of garlic powder to \( 16 \) grams of salt.

We need to:
1. Determine two unit rates based on this ratio.
2. Calculate the amount of garlic powder needed if \( 12 \) grams of salt are used.

### Part (a): Finding Unit Rates
The ratio \( 4 : 16 \) can be simplified by dividing both numbers by their greatest common divisor, which is \( 4 \):
\[
4 : 16 = 1 : 4
\]
This means for every \( 1 \) gram of garlic powder, \( 4 \) grams of salt are used.

#### Unit Rates:
1. **First unit rate**: How many grams of salt per gram of garlic powder?
   - From \( 1 : 4 \), we get that for each \( 1 \) gram of garlic powder, there are \( 4 \) grams of salt.

2. **Second unit rate**: How many grams of garlic powder per gram of salt?
   - Inverting the ratio \( 1 : 4 \) gives \( \frac{1}{4} \) grams of garlic powder per gram of salt.

So the two unit rates are:
- **4 grams of salt for each 1 gram of garlic powder**
- **1/4 grams of garlic powder for each 1 gram of salt**

### Part (b): Calculating Grams of Garlic Powder for 12 Grams of Salt
We need to find out how much garlic powder is needed if \( 12 \) grams of salt are used. Using the unit rate of \( \frac{1}{4} \) grams of garlic powder per gram of salt:
\[
\text{Garlic powder} = 12 \times \frac{1}{4} = 3 \text{ grams}
\]

### Final Answers
1. **Part (a)**:
   - First unit rate: \( 4 \) grams of salt per \( 1 \) gram of garlic powder.
   - Second unit rate: \( \frac{1}{4} \) grams of garlic powder per \( 1 \) gram of salt.

2. **Part (b)**:
   - \( 3 \) grams of garlic powder are needed for \( 12 \) grams of salt.

Would you like further details or have any questions?

### Related Questions
1. How would you determine the unit rate if the ratio were 5 grams of garlic powder to 20 grams of salt?
2. What would be the unit rate if the ratio was given in larger amounts, like 40 grams of garlic powder to 160 grams of salt?
3. If the amount of salt is doubled, how does that affect the amount of garlic powder needed?
4. How do you convert other ratios into unit rates?
5. Can you express the unit rate in different forms, such as a decimal?

### Tip
Always simplify ratios by dividing both terms by their greatest common divisor to make calculating unit rates easier.

A pizza parlor makes batches of pizza dough. They use a ratio of 4 grams of garlic powder to 16 grams of salt. Give two different unit rates using this relationship. How many grams of garlic powder are needed if 12 grams of salt are used?

Learn how to calculate unit rates and proportions using the example of pizza dough ingredients, with a 4:16 garlic powder to salt ratio. This problem involves simplifying ratios and determining quantities based on unit rates, suitable for students in Grades 5-6.

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