Recipe Scaling

1. Recipe Scaling Using Ratios and Proportions to adjust recipe size.

2. Recipe Scaling is all about using your favorite recipe:

3. For 200 rather than the 4 it was written for:

4. And still having it turn out!

5. Like a Champ!

6. You Already Know How to do this! • How would doubling a recipe be done? • How would that look on paper? • Multiply all of the ingredients by 2. • Or if a recipe yielded 4 portions and you needed it for 8 portions: 8/4 = 2 • Here the recipe is increasing in size so you need to multiply it by a number bigger than 1.

7. Let’s try it a different direction: • How about halving a recipe? • And how would this look on paper? • Divide ingredients by 2, or multiply by 0.5. • If the recipe yields 6 portions and you need 3: 3/6 = ½ or 0.5 • Here the recipe is decreasing in size so you need to multiply it by a number smaller than 1. • You have just used ratios

8. Understanding Recipe Scaling is an exercise in understanding: Ratios and Proportions: • Ratio – compares two quantities of the same unit by division. • 20 portions to 5 portions gives a ratio of 20:5 = 20/5 = 20 ÷ 5 = 4 • A Proportion occurs when two ratios are equal.

9. The Proportions we will be using in recipe scaling are built something like this:

10. To solve a proportion you will use the Cross Product Property: then ad = bc Numerator of the first, times Denominator of the second = Denominator of the first, times Numerator of the second

11. Example: Cross Product • Old Recipe 6 ptns., New Recipe 25 ptns. • Old Yield: Flour 1 ½ oz: then: • Cross Multiply: 6x = (25 ∙ 1 ½) • Then solve for “x”: 6x = 37.5 oz • New Yield: x = 6.25 or 6 ¼ oz

12. Arrive at a ratio: • Now that you understand what a proportion is let’s arrive at a ratio that will be easier to work with in the kitchen: • If you solve, or reduce the fraction: • Then you can multiply this result by your old recipe’s ingredients’ quantities • To arrive at the new recipe’s ingredients’ quantities. • Example: 4/2 = 2 = doubling • Or: 3/6 = 0.5 (1/2) = halving

13. When working with multiple ingredient recipes: • Arrive at the ratio • Then multiply it by each ingredient • Will be a faster method of applying the principles learned on the previous page for each ingredient. • As the proportions will be the same for each ingredient.

14. In the kitchen this ratio is referred to as a Conversion Factor; • Ratios shown in previous examples = Conversion Factor = • Once we have arrived at the Conversion Factor (Ratio) • This is then multiplied by each of the old recipe quantities to arrive at the new quantities: • Old Quantity × Conversion Factor = New Quantity

15. Example: Conversion Factor • The original recipe calls for 4 portions and the new recipe needs to be 18 portions: • Conversion Factor = • Now each ingredient quantity is multiplied by the Conversion Factor (4.5). • And the Units are adjusted to the largest usable unit.

16. Example: Application of Conversion Factor • Conversion Factor = 4.5 • Old recipe: Water 2 ¾ cups • 2 ¾ (2.75) cups ∙ 4.5 = 12.375 cups = 12 3/8 cups • Adjusted to largest usable unit = 3 qts.+3/8 c. • New recipe: Water= 3 quarts + 3/8 cup

17. Let’s work a recipe: • Recipe yields 4 portions and we want 10: • New Yield/Old Yield = • 10/4 = • 2.5 = Conversion Factor = CF • Ingredients: Old Qty: CF: New Qty: • Flour 2 cups x 2.5 = ______ • Water 8floz. x 2.5 = ______ • Egg 2 each x 2.5 = ______ • Baking Powder 1 tsp. x 2.5 = ______ • Cinnamon 2 tsp. x 2.5 = ______

18. It turned out!Bon Appétit