Culinary Math Training Kit - Free Printable

Let me work through this problem step by step.

The worksheet shows two recipes that need to be adjusted:

Recipe 1: Angel Food Cake (increase)
- Yield: 12 → New Yield: 30
- Ingredients:
- Egg whites: 1½ cups
- Cream of tartar: 1 teaspoon
- Sugar: 1½ cups
- Vanilla extract: 1 teaspoon
- Salt: ¼ teaspoon
- Flour (sifted): 1 cup

Recipe 2: Spice Food Cake (decrease)
- Yield: 72 → New Yield: 30
- Ingredients:
- Shortening: 1¾ cups
- Cream of tartar: 1 teaspoon
- Milk: 1½ cups
- Extract: 1 teaspoon
- Salt: ¼ teaspoon
- Flour (sifted): ? cup (looks like it might be cut off)

Wait, let me re-read the image more carefully. The second recipe says "Spice Food Cake (decrease) Yield: 72, New Yield: 30"

Let me calculate the conversion factors:

Recipe 1: Angel Food Cake
- Original yield: 12
- New yield: 30
- Conversion factor = New Yield / Original Yield = 30/12 = 2.5

Now multiply each ingredient by 2.5:
- Egg whites: 1½ cups × 2.5 = 3.75 cups = 3¾ cups
- Cream of tartar: 1 tsp × 2.5 = 2.5 tsp = 2½ tsp
- Sugar: 1½ cups × 2.5 = 3.75 cups = 3¾ cups
- Vanilla extract: 1 tsp × 2.5 = 2.5 tsp = 2½ tsp
- Salt: ¼ tsp × 2.5 = 0.625 tsp = ⅝ tsp
- Flour (sifted): 1 cup × 2.5 = 2.5 cups = 2½ cups

Recipe 2: Spice Food Cake
- Original yield: 72
- New yield: 30
- Conversion factor = 30/72 = 5/12 ≈ 0.4167

Now multiply each ingredient by 5/12:
- Shortening: 1¾ cups × 5/12 = (7/4) × (5/12) = 35/48 cups ≈ 0.729 cups
- 35/48 is approximately ¾ cup (actually 35/48 = 0.729, which is close to ¾ = 0.75)
- Let me keep it as a fraction: 35/48 cups

Actually, let me reconsider. In culinary math, we typically round to the nearest cooking fraction. Common cooking fractions are: ¼, ⅓, ½, ⅔, ¾, and whole numbers.

- Shortening: 1¾ × 5/12 = 7/4 × 5/12 = 35/48 cups
- 35/48 ≈ 0.729 cups
- Nearest cooking fraction: ¾ cup (0.75) or ⅔ cup (0.667)
- 0.729 is closer to ¾ (0.75) than to ⅔ (0.667)
- Difference from ¾: |0.729 - 0.75| = 0.021
- Difference from ⅔: |0.729 - 0.667| = 0.062
- So ¾ cup is closer

- Cream of tartar: 1 tsp × 5/12 = 5/12 tsp ≈ 0.417 tsp
- Nearest cooking fraction: ½ tsp (0.5) or ⅓ tsp (0.333) or ¼ tsp (0.25)
- 0.417 is closest to ½ tsp (0.5)? Let's check:
- |0.417 - 0.5| = 0.083
- |0.417 - 0.333| = 0.084
- |0.417 - 0.25| = 0.167
- Actually ½ tsp and ⅓ tsp are almost equally close, but ½ is slightly closer
- Hmm, but in practice, ⅓ tsp might be more commonly used. Let me think...
- Actually 5/12 = 0.4167, and ½ = 0.5, ⅓ = 0.333
- 0.4167 - 0.333 = 0.0837
- 0.5 - 0.4167 = 0.0833
- So ½ tsp is very slightly closer (by 0.0004)
- I'll go with ½ tsp

- Milk: 1½ cups × 5/12 = 3/2 × 5/12 = 15/24 = 5/8 cups = 0.625 cups
- Nearest cooking fraction: ⅔ cup (0.667) or ½ cup (0.5)
- |0.625 - 0.667| = 0.042
- |0.625 - 0.5| = 0.125
- So ⅔ cup is closer

- Extract: 1 tsp × 5/12 = 5/12 tsp ≈ 0.417 tsp
- Same as cream of tartar above: ½ tsp

- Salt: ¼ tsp × 5/12 = 5/48 tsp ≈ 0.104 tsp
- Nearest cooking fraction: ⅛ tsp (0.125) or just a pinch
- |0.104 - 0.125| = 0.021
- So ⅛ tsp is closest

- Flour (sifted): The image is cut off, but it looks like it might say something. Let me assume it's visible. Looking at the image description again, it seems like the flour amount might be cut off. Let me assume it's a reasonable amount. Actually, looking more carefully at typical spice cake recipes with yield 72, the flour might be around 4-5 cups. But since I can't see it clearly, I'll note that the calculation would follow the same pattern.

Wait, let me look at the image description again. It says "Flour (sifted): ? cup" - the amount isn't clearly visible. Let me proceed with what I can see and note that the flour amount needs to be multiplied by 5/12 as well.

Actually, looking at the image more carefully, I think the flour amount for the second recipe might be cut off or not fully visible. Let me provide the answers for what I can clearly see.

Let me verify my calculations once more:

Recipe 1: Angel Food Cake
Conversion factor = 30/12 = 2.5

- Egg whites: 1.5 × 2.5 = 3.75 = 3¾ cups ✓
- Cream of tartar: 1 × 2.5 = 2.5 = 2½ tsp ✓
- Sugar: 1.5 × 2.5 = 3.75 = 3¾ cups ✓
- Vanilla extract: 1 × 2.5 = 2.5 = 2½ tsp ✓
- Salt: 0.25 × 2.5 = 0.625 = ⅝ tsp ✓
- Flour: 1 × 2.5 = 2.5 = 2½ cups ✓

Recipe 2: Spice Food Cake
Conversion factor = 30/72 = 5/12 ≈ 0.4167

- Shortening: 1.75 × 5/12 = 35/48 ≈ 0.729 cups → ¾ cup (nearest cooking fraction)
- Cream of tartar: 1 × 5/12 = 5/12 ≈ 0.417 tsp → ½ tsp (nearest cooking fraction)
- Milk: 1.5 × 5/12 = 5/8 = 0.625 cups → ⅔ cup (nearest cooking fraction)
- Extract: 1 × 5/12 = 5/12 ≈ 0.417 tsp → ½ tsp (nearest cooking fraction)
- Salt: 0.25 × 5/12 = 5/48 ≈ 0.104 tsp → ⅛ tsp (nearest cooking fraction)
- Flour: [amount not clearly visible] × 5/12

For the flour in recipe 2, since I can't see the original amount clearly, I'll note that it should be multiplied by 5/12 and rounded to the nearest cooking fraction.

Actually, let me reconsider the rounding for recipe 2. In culinary math, common cooking fractions are typically: ¼, ⅓, ½, ⅔, ¾. Let me be more precise:

- Shortening: 35/48 = 0.729
- ¾ = 0.75 (difference: 0.021)
- ⅔ = 0.667 (difference: 0.062)
- Nearest: ¾ cup ✓

- Cream of tartar: 5/12 = 0.417
- ½ = 0.5 (difference: 0.083)
- ⅓ = 0.333 (difference: 0.084)
- Nearest: ½ tsp (very slightly closer) ✓

- Milk: 5/8 = 0.625
- ⅔ = 0.667 (difference: 0.042)
- ½ = 0.5 (difference: 0.125)
- Nearest: ⅔ cup ✓

- Extract: Same as cream of tartar: ½ tsp ✓

- Salt: 5/48 = 0.104
- ⅛ = 0.125 (difference: 0.021)
- Nearest: ⅛ tsp ✓

Now I'm ready to provide the final answer.

Final Answer:

Recipe 1: Angel Food Cake (Yield: 12 → 30)
Conversion Factor: 2.5

| Ingredient | Quantity | Conversion Factor | New Quantity |
|------------|----------|-------------------|--------------|
| Egg whites | 1½ cups | 2.5 | 3¾ cups |
| Cream of tartar | 1 teaspoon | 2.5 | 2½ teaspoons |
| Sugar | 1½ cups | 2.5 | 3¾ cups |
| Vanilla extract | 1 teaspoon | 2.5 | 2½ teaspoons |
| Salt | ¼ teaspoon | 2.5 | teaspoon |
| Flour (sifted) | 1 cup | 2.5 | 2½ cups |

Recipe 2: Spice Food Cake (Yield: 72 → 30)
Conversion Factor: 5/12 (≈ 0.417)

| Ingredient | Quantity | Conversion Factor | New Quantity |
|------------|----------|-------------------|--------------|
| Shortening | 1¾ cups | 5/12 | ¾ cup |
| Cream of tartar | 1 teaspoon | 5/12 | ½ teaspoon |
| Milk | 1½ cups | 5/12 | ⅔ cup |
| Extract | 1 teaspoon | 5/12 | ½ teaspoon |
| Salt | ¼ teaspoon | 5/12 | teaspoon |
| Flour (sifted) | [original amount] | 5/12 | [original amount × 5/12, rounded to nearest cooking fraction] |

Note: For Recipe 2, the original flour amount wasn't clearly visible in the image. Apply the same conversion factor (5/12) and round to the nearest cooking fraction.