Question

The recipe calls for 7 cups of pasta for every 4 cups of cheese. Show those quantities on the double number line.

Answer 1

To represent the quantities of pasta and cheese on a double number line, we will mark the amounts of pasta and cheese in relation to each other based on the given ratio of 7 cups of pasta for every 4 cups of cheese.

Here’s how we set it up:

1. **Identify the ratio**: For every 7 cups of pasta, we have 4 cups of cheese. This can be expressed as the pairs: (7, 4).

2. **Express multiples of the ratio**: We can create more combinations based on the ratio. For example:
- 1st ratio: 7 cups pasta – 4 cups cheese
- 2nd ratio: 14 cups pasta – 8 cups cheese (2 times the first)
- 3rd ratio: 21 cups pasta – 12 cups cheese (3 times the first)
- 4th ratio: 28 cups pasta – 16 cups cheese (4 times the first)

3. **Create the double number line**: You can visualize it like this:

```
Pasta (cups): 0 7 14 21 28
|------|------|------|
Cheese (cups): 0 4 8 12 16
```

**In this representation:**
- Each point on the pasta line corresponds to a value on the cheese line based on the ratio of 7:4.
- This allows you to easily see the relationship between the quantities of pasta and cheese in the recipe.