Recipe ScalingUsing Ratios and Proportions to adjust recipe size.

Recipe Scaling is all about using your favorite recipe:

For 200 rather than the 4 it was written for:

And still having it turn out!

Like a Champ!

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.

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

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.

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

entAmtOldIngredientAmtNewIngredi

OldYieldNewYield

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

dc

ba

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 

..

entAmtOldIngredientAmtNewIngredi

OldYieldNewYield

2116

25 x

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

OldYieldNewYield

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.

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

OldYieldNewYield

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.

5.44

18

OldYieldNewYield

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

Let’s work a recipe:•Recipe yields 4 portions and we want 10:• New Yield/Old Yield =•10/4 = •2.5 = Conversion Factor = CF

5.24

10

OldYieldNewYield

•Ingredients: Old Qty: CF: New Qty:•Flour 2 cups x 2.5 = ______•Water 8 floz. x 2.5 = ______•Egg 2 each x 2.5 = ______•Baking Powder 1 tsp. x 2.5 = ______•Cinnamon 2 tsp. x 2.5 = ______

It turned out!

Bon Appétit