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