Printable math worksheets with fraction and ratio problems related to cooking recipes.

Problem Overview:

The task involves solving scaling problems by working up and down using the given recipes for Fruit Salad and Scones. The goal is to adjust the quantities of ingredients based on the number of people the recipe serves.

---

Step 1: Fruit Salad

#### Given Information:
- Original recipe serves 12 people.
- Ingredients for 12 people:
- 6 large oranges
- 20 strawberries
- 6 cups of pineapple chunks

#### Task:
Adjust the recipe to serve 4 people.

#### Solution Approach:
To scale down the recipe from 12 people to 4 people, we need to divide each ingredient quantity by the ratio of the original servings to the new servings:
\[
\text{Scaling factor} = \frac{\text{New servings}}{\text{Original servings}} = \frac{4}{12} = \frac{1}{3}
\]

Now, apply this scaling factor to each ingredient:

1. Oranges:
\[
\text{Original quantity} = 6 \quad \Rightarrow \quad \text{New quantity} = 6 \times \frac{1}{3} = 2
\]

2. Strawberries:
\[
\text{Original quantity} = 20 \quad \Rightarrow \quad \text{New quantity} = 20 \times \frac{1}{3} = \frac{20}{3} \approx 6.67 \quad (\text{round to } 7 \text{ if necessary})
\]

3. Pineapple Chunks:
\[
\text{Original quantity} = 6 \text{ cups} \quad \Rightarrow \quad \text{New quantity} = 6 \times \frac{1}{3} = 2 \text{ cups}
\]

#### Final Adjusted Quantities for 4 People:
- Oranges: 2
- Strawberries: 7 (rounded from 6.67)
- Pineapple Chunks: 2 cups

---

Step 2: Scones

#### Given Information:
- Original recipe serves 12 people.
- Ingredients for 12 people:
- 2 cups of flour
- 1 cup of sugar
- 1 teaspoon of baking powder
- 1/2 cup of butter
- 1/2 cup of milk
- 1 egg

#### Task:
Adjust the recipe to serve 6 people.

#### Solution Approach:
To scale down the recipe from 12 people to 6 people, we need to divide each ingredient quantity by the ratio of the original servings to the new servings:
\[
\text{Scaling factor} = \frac{\text{New servings}}{\text{Original servings}} = \frac{6}{12} = \frac{1}{2}
\]

Now, apply this scaling factor to each ingredient:

1. Flour:
\[
\text{Original quantity} = 2 \text{ cups} \quad \Rightarrow \quad \text{New quantity} = 2 \times \frac{1}{2} = 1 \text{ cup}
\]

2. Sugar:
\[
\text{Original quantity} = 1 \text{ cup} \quad \Rightarrow \quad \text{New quantity} = 1 \times \frac{1}{2} = 0.5 \text{ cup}
\]

3. Baking Powder:
\[
\text{Original quantity} = 1 \text{ teaspoon} \quad \Rightarrow \quad \text{New quantity} = 1 \times \frac{1}{2} = 0.5 \text{ teaspoon}
\]

4. Butter:
\[
\text{Original quantity} = 1/2 \text{ cup} \quad \Rightarrow \quad \text{New quantity} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \text{ cup}
\]

5. Milk:
\[
\text{Original quantity} = 1/2 \text{ cup} \quad \Rightarrow \quad \text{New quantity} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \text{ cup}
\]

6. Egg:
\[
\text{Original quantity} = 1 \quad \Rightarrow \quad \text{New quantity} = 1 \times \frac{1}{2} = 0.5 \quad (\text{half an egg})
\]

#### Final Adjusted Quantities for 6 People:
- Flour: 1 cup
- Sugar: 0.5 cup
- Baking Powder: 0.5 teaspoon
- Butter: 1/4 cup
- Milk: 1/4 cup
- Egg: 0.5 (half an egg)

---

Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Fruit Salad for 4 people:} \\
\text{- Oranges: 2} \\
\text{- Strawberries: 7} \\
\text{- Pineapple Chunks: 2 cups} \\
\\
\text{Scones for 6 people:} \\
\text{- Flour: 1 cup} \\
\text{- Sugar: 0.5 cup} \\
\text{- Baking Powder: 0.5 teaspoon} \\
\text{- Butter: 1/4 cup} \\
\text{- Milk: 1/4 cup} \\
\text{- Egg: 0.5 (half an egg)} \\
\end{array}
}
\]