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Proportional relationship between orange juice and grape juice measured in cups, showing a consistent ratio.

A number line diagram showing the relationship between cups of orange juice and cups of grape juice, with orange juice increasing by 1 and grape juice increasing by 3 for each step.

A number line diagram showing the relationship between cups of orange juice and cups of grape juice, with orange juice increasing by 1 and grape juice increasing by 3 for each step.

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Show Answer Key & Explanations Step-by-step solution for: Working with Double Number Lines
Let’s look at the diagram carefully.

We have two number lines:

- Top line: “cups of orange juice” — goes from 0 to 4, with +1 between each step.
- Bottom line: “cups of grape juice” — goes from 0 to 12, with +3 between each step.

Each vertical line connects a value on the top (orange juice) to a value on the bottom (grape juice).

So let’s match them up:

- When orange juice = 0 → grape juice = 0
- When orange juice = 1 → grape juice = 3
- When orange juice = 2 → grape juice = 6
- When orange juice = 3 → grape juice = 9
- When orange juice = 4 → grape juice = 12

We can see a pattern: for every 1 cup of orange juice, you need 3 cups of grape juice.

That means the ratio is 1 : 3 (orange to grape).

Or, if you want to find how many cups of grape juice you need for any amount of orange juice, just multiply the orange juice cups by 3.

For example:
- 1 × 3 = 3 ✔️
- 2 × 3 = 6 ✔️
- 4 × 3 = 12 ✔️

This makes sense because the arrows show +1 on top and +3 on bottom — so it’s always multiplying by 3.

Final Answer:
The relationship is that for every 1 cup of orange juice, you need 3 cups of grape juice. So, cups of grape juice = 3 × cups of orange juice.
Parent Tip: Review the logic above to help your child master the concept of double line diagrams ratios worksheet.
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