Ratios - MathBitsNotebook(Jr) - Free Printable

The image shows a table with two columns:

- Cups of Water
- Cups of BBQ Sauce

And the values are:

| Cups Water | Cups BBQ Sauce |
|------------|----------------|
| 2 | 5 |
| 4 | 10 |
| 6 | 15 |
| 8 | 20 |
| 10 | 25 |

There are arrows indicating how the numbers change from row to row, with multipliers like ×2, ×3, and ×4.

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Step 1: Understand the Pattern

Let’s examine how the Cups of Water and Cups of BBQ Sauce relate.

#### For Water:
- 2 → 4 → 6 → 8 → 10
- This is increasing by 2 each time.
- Alternatively:
- 2 × 1 = 2
- 2 × 2 = 4
- 2 × 3 = 6
- 2 × 4 = 8
- 2 × 5 = 10

So, Water = 2 × (row number)

#### For BBQ Sauce:
- 5 → 10 → 15 → 20 → 25
- Increasing by 5 each time.
- Or:
- 5 × 1 = 5
- 5 × 2 = 10
- 5 × 3 = 15
- 5 × 4 = 20
- 5 × 5 = 25

So, BBQ Sauce = 5 × (row number)

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Step 2: Find the Relationship Between Water and BBQ Sauce

We can express both in terms of the row number:

- Water = 2n
- BBQ Sauce = 5n

So, we can write:
> BBQ Sauce = (5/2) × Water

Or:
> BBQ Sauce = 2.5 × Water

Alternatively, for every 2 cups of water, you need 5 cups of BBQ sauce.

This is a ratio of:
> Water : BBQ Sauce = 2 : 5

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Step 3: Interpret the Arrows

The green arrows on the left show how the water increases:
- From 2 to 4: ×2
- From 2 to 6: ×3
- From 2 to 8: ×4

Similarly, yellow arrows on the right:
- From 5 to 10: ×2
- From 5 to 15: ×3
- From 5 to 20: ×4

So, both quantities are scaled by the same factor.

For example:
- If you multiply water by 3 (2 → 6), you also multiply BBQ sauce by 3 (5 → 15)
- If you double water (2 → 4), you double BBQ sauce (5 → 10)

This confirms that the ratio is constant.

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Final Answer and Explanation

✔ The relationship between cups of water and cups of BBQ sauce is proportional.

- The ratio is 2:5 (water to BBQ sauce).
- So, for every 2 cups of water, you need 5 cups of BBQ sauce.
- You can scale this up or down using the same multiplier.

#### Example:
If you want 12 cups of water:
- 12 ÷ 2 = 6 → so multiply the BBQ sauce by 6
- 5 × 6 = 30 cups of BBQ sauce needed.

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Summary:

- Ratio: 2 cups water : 5 cups BBQ sauce
- Proportional relationship: BBQ Sauce = (5/2) × Water
- The arrows show scaling by the same factor (×2, ×3, ×4), preserving the ratio.

✔ This is a direct proportion with constant ratio 2:5.