Applied Math
Table of Contents
●
Introduction and overview.
●
The Recipe Conversion process.
●
Compute the Working Factor.
●
Putting it all together.
●
Using the Recipe Conversion process.
●
Odds and Ends.
●
A sample problem illustrates other things to
consider when converting recipes.
Recipe Conversion:
Introduction
●
Many times you will find that an
often-used recipe has a yield that is either
too high or too low for your current
needs.
Yield:
20 cinnamon rolls
My current recipe:
What I want:
Yield:
When this happens, you will need to
determine the correct amount of each
ingredient in order to produce the desired
yield.
Recipe Conversion:
Introduction
The process of computing these
Recipe Conversion:
Introduction
●
You have probably converted recipes
before.
●
At home for example, it is not uncommon
2 cups flour x 2
1/2 package yeast x 2
1 tsp salt x 2
1 c water x 2
1 T sugar x 2
1 T butter x 2
Original
4 cups flour 1 package yeast 2 tsp salt
2 c water 2 T sugar 2 T butter
Doubled Recipe
2 cups flour 1 package yeast 1 tsp salt
1 c water 1 T sugar 1 T butter
Original
Recipe Conversion:
Introduction
●
Chances are you multiplied each
…or multiplied by 1/2 to cut it in half.
2 cups flour x 1/2
1/2 package yeast x 1/2
1 tsp salt x 1/2
1 c water x 1/2
1 T sugar x 1/2
1 T butter x 1/2
Original
1 cup flour
1/4 package yeast 1/2 tsp salt
1/2 c water 1/2 T sugar 1/2 T butter
Halved Recipe
2 cups flour 1 package yeast 1 tsp salt
1 c water 1 T sugar 1 T butter
Original
Recipe Conversion:
Recipe Conversion:
Introduction
●
When you multiply ingredient amounts by
numbers such as 2 or 1/2, you are using a
working factor
to convert the recipe.
●
A working factor indicates how many
Recipe Conversion
Determine Working Factor
●
There are two things you have to do in
order to convert recipes:
1.) Determine the working factor.
Follow along with the next three
examples to learn how to calculate the
working factor for any situation.
Recipe Conversion
Recipes used in commercial kitchens often
state the number of portions and the size
of each portion.
PESTO
12 portions at 2 oz each
Fresh Basil 2 qt Olive Oil 1.5 cups Pignoli 2 oz Garlic cloves 6 Salt 1.5 tsp Parmason Cheese 5 oz Romano Cheese 1.5 oz
Number of portions...
…size of each portion.
Recipe Conversion
●
Original Recipe:
Recipe Conversion
Determine Working Factor:
Sample Problem 1
●
New Recipe:
12 portions @ 6 oz. each
30 portions @ 6 oz. each
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
30 portions @ 6 oz. ea.
First determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
30 portions @ 6 oz. ea.
First determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
30 portions @ 6 oz. ea.
First determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
12
x 6 oz. =
72 oz.
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
30 portions @ 6 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
30 portions @ 6 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
30
x 6 oz. =
180 oz.
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
30 portions @ 6 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
30
x 6 oz. =
180 oz.
Yield Wt. =
72 oz
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
Yield Wt. =
72 oz
New Yield:
30 portions @ 6 oz. ea.
Yield Wt. =
180 oz
180 oz. ÷ 72 oz. =
2.5
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
Yield Wt. =
72 oz
New Yield:
30 portions @ 6 oz. ea.
Yield Wt. =
180 oz
The working factor is
2.5
. The new recipe
is 2.5 times larger than the original.
180 oz. ÷ 72 oz. =
2.5
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 1
Original Yield:
12 portions @ 6 oz. ea.
Yield Wt. =
72 oz
New Yield:
30 portions @ 6 oz. ea.
Yield Wt. =
180 oz
●
Original Recipe:
Recipe Conversion
Determine Working Factor:
Sample Problem 2
●
New Recipe:
12 portions @ 6 oz. each
36 portions @ 8 oz. each
Recipe Conversion
Determine Working Factor:
Sample Problem 2
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
36 portions @ 8 oz. ea.
First determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 2
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
36 portions @ 8 oz. ea.
First determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
12
x 6 oz. =
72 oz.
Recipe Conversion
Determine Working Factor:
Sample Problem 2
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
36 portions @ 8 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 2
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
36 portions @ 8 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
36
x 8 oz. =
288 oz.
Recipe Conversion
Determine Working Factor:
Sample Problem 2
Original Yield:
12 portions @ 6 oz. ea.
New Yield:
36 portions @ 8 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
36
x 8 oz. =
288 oz.
Yield Wt. =
72 oz
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 2
Original Yield:
12 portions @ 6 oz. ea.
Yield Wt. =
72 oz
New Yield:
36 portions @ 8 oz. ea.
Yield Wt. =
288 oz
288 oz. ÷ 72 oz. =
4
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 2
Original Yield:
12 portions @ 6 oz. ea.
Yield Wt. =
72 oz
New Yield:
36 portions @ 8 oz. ea.
Yield Wt. =
288 oz
The working factor is
4
. The new recipe is
4 times larger than the original.
288 oz. ÷ 72 oz. =
4
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 2
Original Yield:
12 portions @ 6 oz. ea.
Yield Wt. =
72 oz
New Yield:
36 portions @ 8 oz. ea.
Yield Wt. =
288 oz
●
Original Recipe:
Recipe Conversion
Determine Working Factor:
Sample Problem 3
●
New Recipe:
30 portions @ 4 oz. each
20 portions @ 5 oz. each
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
First determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
First determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
First determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
30
x 4 oz. =
120 oz.
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
20
x 5 oz. =
100 oz.
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
Now determine the yield weight (total
weight) of each recipe.
# of portions x portion size = yield wt.
20
x 5 oz. =
100 oz.
Yield Wt. =
120 oz
100 oz. ÷
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Yield Wt. =
120 oz
100 oz. ÷ 120 oz.=
0.833
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Yield Wt. =
120 oz
The working factor is
0.833
.
100 oz. ÷ 120 oz.=
0.833
Recipe Conversion
Determine Working Factor:
Sample Problem 3
Original Yield:
30 portions @ 4 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Calculate the
working factor
by dividing
New Yield Wt. by the Old Yield Wt.
Yield Wt. =
120 oz
Recipe Conversion
Determine Working Factor:
Practice Problems
●
For practice, compute the working factor
for these two situations.
1.) Original Recipe: 35 portions at 5 oz each.
New Recipe: 20 portions at 5 oz each.
2.) Original Recipe: 40 portions at 6 oz each.
New Recipe: 50 portions at 4 oz each.
Recipe Conversion
Determine Working Factor:
Practice Problems
Original Yield:
35 portions @ 5 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
Yield Wt. =
175 oz
Yield Wt. =
100 oz
Practice Problem 1:
Recipe Conversion
Determine Working Factor:
Practice Problems
Original Yield:
35 portions @ 5 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
Yield Wt. =
175 oz
Yield Wt. =
100 oz
Practice Problem 1:
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Recipe Conversion
Determine Working Factor:
Practice Problems
Original Yield:
35 portions @ 5 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
Yield Wt. =
175 oz
Yield Wt. =
100 oz
Practice Problem 1:
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Recipe Conversion
Determine Working Factor:
Practice Problems
Original Yield:
35 portions @ 5 oz. ea.
New Yield:
20 portions @ 5 oz. ea.
Yield Wt. =
175 oz
Yield Wt. =
100 oz
Practice Problem 1:
New Yield Wt. ÷ Original Yield Wt. = Working Factor
The working factor is
0.57
.
Recipe Conversion
Determine Working Factor:
Practice Problems
Original Yield:
40 portions @ 6 oz. ea.
New Yield:
50 portions @ 4 oz. ea.
Yield Wt. =
240 oz
Yield Wt. =
200 oz
Practice Problem 2:
Recipe Conversion
Determine Working Factor:
Practice Problems
Original Yield:
40 portions @ 6 oz. ea.
New Yield:
50 portions @ 4 oz. ea.
Yield Wt. =
240 oz
Yield Wt. =
200 oz
Practice Problem 2:
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Recipe Conversion
Determine Working Factor:
Practice Problems
Original Yield:
40 portions @ 6 oz. ea.
New Yield:
50 portions @ 4 oz. ea.
Yield Wt. =
240 oz
Yield Wt. =
200 oz
Practice Problem 2:
New Yield Wt. ÷ Original Yield Wt. = Working Factor
Recipe Conversion
Determine Working Factor:
Practice Problems
Original Yield:
40 portions @ 6 oz. ea.
New Yield:
50 portions @ 4 oz. ea.
Yield Wt. =
240 oz
Yield Wt. =
200 oz
Practice Problem 2:
New Yield Wt. ÷ Original Yield Wt. = Working Factor
The working factor is
0.833
.
Recipe Conversion
Sample
Problem 1
●
Now that you can compute the working
factor for any situation, let’s put it all
together and convert a recipe.
PESTO
12 portions at 2 oz each
Fresh Basil 2 qt Olive Oil 1.5 cups Pignoli 2 oz Garlic cloves 6 Salt 1.5 tsp Parmason Cheese 5 oz Romano Cheese 1.5 oz
PESTO
4 portions at 2 oz each
Fresh Basil ? qt Olive Oil ? cups Pignoli ? oz Garlic cloves ?
First, determine the working factor.
PESTO
12 portions at 2 oz each
Fresh Basil 2 qt Olive Oil 1.5 cups Pignoli 2 oz Garlic cloves 6 Salt 1.5 tsp Parmason Cheese 5 oz Romano Cheese 1.5 oz
PESTO
4 portions at 2 oz each
Fresh Basil ? qt Olive Oil ? cups Pignoli ? oz Garlic cloves ?
Salt ? tsp Parmason Cheese ? oz Romano Cheese ? oz
Original:
12 portions x 2 oz ea. = 24 oz
New:
4 portions x 2 oz ea. = 8 oz
Working Factor:
8 ÷ 24 =
0.333
Recipe Conversion
Then, multiply each ingredient by the working
factor.
PESTO
4 portions at 2 oz each
Fresh Basil 0.7 qt Olive Oil 0.5 cups Pignoli 0.7 oz Garlic cloves 2
Salt 0.5 tsp Parmason Cheese 1.7 oz Romano Cheese 0.5 oz
PESTO
12 portions at 2 oz each
Fresh Basil 2 qt Olive Oil 1.5 cups Pignoli 2 oz Garlic cloves 6 Salt 1.5 tsp Parmason Cheese 5 oz Romano Cheese 1.5 oz
PESTO
12 portions at 2 oz each
Fresh Basil 2 qt x 0.333
Olive Oil 1.5 cups x 0.333
Pignoli 2 oz x 0.333
Garlic cloves 6 x 0.333
Salt 1.5 tsp x 0.333
Parmason Cheese 5 oz x 0.333
Romano Cheese 1.5 oz x 0.333
Recipe Conversion
Sample
Problem 1
PESTO
4 portions at 2 oz each
Fresh Basil 0.7 qt Olive Oil 0.5 cups Pignoli 0.7 oz Garlic cloves 2
Salt 0.5 tsp Parmason Cheese 1.7 oz Romano Cheese 0.5 oz
PESTO
12 portions at 2 oz each
Fresh Basil 2 qt Olive Oil 1.5 cups Pignoli 2 oz Garlic cloves 6 Salt 1.5 tsp Parmason Cheese 5 oz Romano Cheese 1.5 oz
PESTO
12 portions at 2 oz each
Fresh Basil 2 qt x 0.333
Olive Oil 1.5 cups x 0.333
Pignoli 2 oz x 0.333
Garlic cloves 6 x 0.333
Salt 1.5 tsp x 0.333
Parmason Cheese 5 oz x 0.333
Romano Cheese 1.5 oz x 0.333
Recipe Conversion
Sample
Problem 1
All of these results are
less
than
the original amounts. This is
expected since we are
reducing
Let’s try another one.
Gazpacho
12 portions at 6 oz each
Tomatoes 2 1/2 lbs Cucumbers 1 lbs Onions 8 oz Green Peppers 4 oz Crushed Garlic 1/2 tsp Bread Crumbs 2 oz Tomato Juice 1 pt Red Wine Vinegar 3 oz Olive Oil 5 oz Salt to taste
Red Pepper Sauce to taste Lemon Juice3 Tbsp
Gazpacho
36 portions at 8 oz each
Tomatoes ? lbs Cucumbers ? lbs Onions ? oz Green Peppers ? oz Crushed Garlic ? tsp Bread Crumbs ? oz Tomato Juice ? pt Red Wine Vinegar? oz Olive Oil ? oz Salt to taste
Red Pepper Sauce to taste Lemon Juice? Tbsp
Recipe Conversion
Original:
12 portions x 6 oz ea. = 72 oz
New:
36 portions x 8 oz ea. = 288 oz
Working Factor:
288 ÷ 72 =
4
Determine the working factor.
Gazpacho
12 portions at 6 oz each
Tomatoes 2 1/2 lbs Cucumbers 1 lbs Onions 8 oz Green Peppers 4 oz Crushed Garlic 1/2 tsp Bread Crumbs 2 oz Tomato Juice 1 pt Red Wine Vinegar 3 oz Olive Oil 5 oz Salt to taste
Red Pepper Sauce to taste Lemon Juice3 Tbsp
Gazpacho
36 portions at 8 oz each
Tomatoes ? lbs Cucumbers ? lbs Onions ? oz Green Peppers ? oz Crushed Garlic ? tsp Bread Crumbs ? oz Tomato Juice ? pt Red Wine Vinegar? oz Olive Oil ? oz Salt to taste
Red Pepper Sauce to taste Lemon Juice? Tbsp
Recipe Conversion
Multiply each ingredient by the working factor.
Gazpacho
12 portions at 6 oz each
Tomatoes 2 1/2 lbs Cucumbers 1 lbs Onions 8 oz Green Peppers 4 oz Crushed Garlic 1/2 tsp Bread Crumbs 2 oz Tomato Juice 1 pt Red Wine Vinegar 3 oz Olive Oil 5 oz Salt to taste
Red Pepper Sauce to taste Lemon Juice3 Tbsp
Gazpacho
36 portions at 8 oz each
Tomatoes 10 lbs Cucumbers 4 lbs Onions 32 oz Green Peppers 16 oz Crushed Garlic 2 tsp Bread Crumbs 8 oz Tomato Juice 4 pt Red Wine Vinegar12 oz Olive Oil 20 oz Salt to taste
Red Pepper Sauce to taste Lemon Juice12 Tbsp
Gazpacho
12 portions at 6 oz each
Tomatoes 2 1/2 lbs x 4
Cucumbers 1 lbs x 4
Onions 8 oz x 4
Green Peppers 4 oz x 4
Crushed Garlic 1/2 tsp x 4
Bread Crumbs 2 oz x 4
Tomato Juice 1 pt x 4
Red Wine Vinegar 3 oz x 4
Olive Oil 5 oz x 4
Salt to taste
Red Pepper Sauce to taste Lemon Juice3 Tbsp x 4
Recipe Conversion
Sample
Problem 2
Recipe Conversion
Practice Problem
●
Try this one on your own. When you are
done, click to see the answers.
Hungarian Potatoes 25 portions at 4 oz each
Butter 4 oz Onion 8 oz
Paprika 2 tsp Tomato Concasse 1 lb Potatoes, pld 5 lb Chicken Stock 1 qt Salt to taste
Pepper to taste Chopped Parsley 1/2 cup
Hungarian Potatoes 15 portions at 4 oz each
Butter ? oz Onion ? oz
Paprika ? tsp Tomato Concasse ? lb Potatoes, pld ? lb Chicken Stock ? qt Salt to taste
The working factor for this problem is
0.6
.
Hungarian Potatoes 25 portions at 4 oz each
Butter 4 oz Onion 8 oz
Paprika 2 tsp Tomato Concasse 1 lb Potatoes, pld 5 lb Chicken Stock 1 qt Salt to taste
Pepper to taste Chopped Parsley 1/2 cup
Hungarian Potatoes 15 portions at 4 oz each
Butter 2.4 oz Onion 4.8 oz
Paprika 1.2 tsp Tomato Concasse 0.6 lb Potatoes, pld 3 lb Chicken Stock 0.6 qt Salt to taste
Pepper to taste Chopped Parsley 0.3 cup
Hungarian Potatoes 25 portions at 4 oz each
Butter 4 ozx 0.6
Onion 8 oz x 0.6
Paprika 2 tsp x 0.6
Tomato Concasse 1 lb x 0.6
Potatoes, pld 5 lb x 0.6
Chicken Stock 1 qt x 0.6
Salt to taste
Pepper to taste Chopped Parsley 1/2 cup x 0.6
Recipe Conversion
Recipe Conversion
Odds & Ends
●
Let’s take a few moments to look at a few
We will work through one more problem to
illustrate these issues.
Lemon Pie Yield: 9 pies
(Partial List of Ingredients)
Water 4 lbs
Granulated Sugar 3 lb 6 oz Salt 1/2 oz
Lemon Gratings 3 oz Egg Yolks 12 oz
Original Recipe
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water ? lbs
Granulated Sugar ? lb ? oz Salt ? oz
Lemon Gratings ? oz Egg Yolks ? oz
New Recipe
First, let’s compute the working factor
.
Lemon Pie Yield: 9 pies
(Partial List of Ingredients)
Water 4 lbs
Granulated Sugar 3 lb 6 oz Salt 1/2 oz
Lemon Gratings 3 oz Egg Yolks 12 oz
Original Recipe
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water ? lbs
Granulated Sugar ? lb ? oz Salt ? oz
Lemon Gratings ? oz Egg Yolks ? oz
New Recipe
While the yields are expressed in a different
style, you will still divide new yield by old yield
to determine the working factor.
Lemon Pie Yield: 9 pies
(Partial List of Ingredients)
Water 4 lbs
Granulated Sugar 3 lb 6 oz Salt 1/2 oz
Lemon Gratings 3 oz Egg Yolks 12 oz
Original Recipe
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water ? lbs
Granulated Sugar ? lb ? oz Salt ? oz
Lemon Gratings ? oz Egg Yolks ? oz
New Recipe
The working factor:
Lemon Pie Yield: 9 pies
(Partial List of Ingredients)
Water 4 lbs
Granulated Sugar 3 lb 6 oz Salt 1/2 oz
Lemon Gratings 3 oz Egg Yolks 12 oz
Original Recipe
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water ? lbs
Granulated Sugar ? lb ? oz Salt ? oz
Lemon Gratings ? oz Egg Yolks ? oz
New Recipe
Original:
9 pies
New:
6 pies
Working Factor:
6
÷
9 =
0.667
How can you tell if the working factor you have
computed looks “reasonable”?
Working factors less than 1 occur when you are
reducing
recipes.
Original Quantity
Working Factor Result
5 lbs x
0.4
=
2 lbs
6 oz x
0.9
=
5.4 oz
1.5 tsp x
0.25
=
0.375 tsp
Watch what happens to each original quantity when it is
multiplied by a working factor smaller than 1.
How can you tell if the working factor you have
computed looks “reasonable”?
Original Quantity
Working Factor Result
In each example, the result is smaller than the
original quantity. This happens when you
multiply any quantity by a value less than
1
(one).
5 lbs x
0.4
=
2 lbs
6 oz x
0.9
=
5.4 oz
1.5 tsp x
0.25
=
0.375 tsp
Recipe Conversion
The opposite is true when you are increasing a
recipe: you should always get a working factor
larger than 1 (one).
5 lbs x
1.5
=
7.5 lbs
6 oz x
3.5
=
21 oz
1.5 tsp x
2
=
3 tsp
Working factors larger than 1 occur when you are
increasing
recipes.
Original Quantity
Working Factor Result
Recipe Conversion
Odds & Ends
The opposite is true when you are increasing a
recipe: you should always get a working factor
larger than 1 (one).
Each result is larger than the original quantity.
This is because the working factor is larger
than
1
.
5 lbs x
1.5
=
7.5 lbs
6 oz x
3.5
=
21 oz
1.5 tsp x
2
=
3 tsp
Original Quantity
Working Factor Result
To continue with this problem, you will multiply
each ingredient by 0.667.
Lemon Pie Yield: 9 pies
(Partial List of Ingredients)
Water 4 lbs
Granulates Sugar 3 lb 6 oz Salt 1/2 oz
Lemon Gratings 3 oz Egg Yolks 12 oz
Original Recipe
Lemon Pie Yield: 9 pies
(Partial List of Ingredients)
Water 4 lbs x 0.667
Granulated Sugar 3 lb 6 oz x 0.667
Salt 1/2 oz x 0.667
Lemon Gratings 3 oz x 0.667
Egg Yolks 12 oz x 0.667
Original Recipe
Here is a new problem! You cannot
multiply mixed units (lbs & oz) with
the working factor.
One solution is to convert 3 lb 6 oz
into ounces only:
3 lb x 16 = 48 oz
48 oz + 6 oz =
54 oz
To continue with this problem, you will multiply
each ingredient by 0.667.
Lemon Pie Yield: 9 pies
(Partial List of Ingredients)
Water 4 lbs x 0.667
Granulated Sugar 54 ozx 0.667
Salt 1/2 oz x 0.667
Lemon Gratings 3 oz x 0.667
Egg Yolks 12 oz x 0.667
Original Recipe
Now you will be able to continue.
Just multiply
54 oz
by 0.667
Tuning-up your final answers.
Complete the multiplication process.
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water 2.668 lbs
Granulated Sugar 36.018 oz
Salt 0.3335 oz
Lemon Gratings 2.001 oz
Egg Yolks 8.004 oz
New Recipe
Lemon Pie Yield: 9 pies
(Partial List of Ingredients)
Water 4 lbs x 0.667
Granulated Sugar 54 oz x 0.667
Salt 1/2 oz x 0.667
Lemon Gratings 3 oz x 0.667
Egg Yolks 12 oz x 0.667
Original Recipe
You may want to consider “cleaning up” your
answers.
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water 2.668 lbs
Granulated Sugar 36.018 oz
Salt 0.3335 oz
Lemon Gratings 2.001 oz
Egg Yolks 8.004 oz
New Recipe
This answer could be rounded
to 2.7 lbs.
This answer is pretty close to
36 oz.
You could also express this
answer as lbs and oz like it
was originally:
36 oz =
2 lbs 4 oz
This could be written as 0.3 oz.
This is close to 2 oz.
Round this to 8 oz.
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water 2.7 lbs
Granulated Sugar 36 oz
Salt 0.3 oz
Lemon Gratings 2 oz
Egg Yolks 8 oz
New Recipe
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water 2.7 lbs
Granulated Sugar 36 oz
Salt 0.3 oz
Lemon Gratings 2 oz
Egg Yolks 8 oz
New Recipe
You may wish to convert decimal answers to
fractional form. For example, convert each
decimal result below to the nearest 8th.
2.7 lbs to the nearest 8th is
2 6/8. If you’d like, you may
reduce this to
2 3/4
lbs.
0.3 oz converted to the nearest 8th
is
2/8
. This reduces to 1/4.
Lemon Pie Yield: 6 pies
(Partial List of Ingredients)
Water 2 3/4 lbs
Granulated Sugar 36 oz
Salt 1/4 oz
Lemon Gratings 2 oz
Egg Yolks 8 oz
New Recipe
Click on the information button below to
review this decimal-to-fraction technique.
Otherwise just click anywhere else to
continue.
Recipe Conversion
Odds & Ends
●
Ultimately, it is up to you to decide when
and how much rounding is appropriate.
●
Similarly, you must decide when to
convert decimal answers to fractional
form.
●
That decision will be based more on the types
of measuring equipment you have than
Final Practice Problem
●
Convert the following recipe.
●
When you are ready, click to see the
answers.
White Cream Icing Yield: 5 cakes
Emulsified Shortening 1 lb 4 oz Salt 1/4 oz
Dry Milk 5 oz Water 14 oz Powdered Sugar 5 lb
Original Recipe
White Cream Icing Yield: 3 cakes
Emulsified Shortening ? lb ? oz Salt ? oz
Dry Milk ? oz Water ? oz
The working factor is 0.6.
White Cream Icing Yield: 5 cakes
Emulsified Shortening 1 lb 4 oz Salt 1/4 oz
Dry Milk 5 oz Water 14 oz Powdered Sugar 5 lb
Original Recipe
Original:
5 cakes
New:
3 cakes
Working Factor:
3 ÷ 5 =
0.6
White Cream Icing Yield: 3 cakes
Emulsified Shortening ? lb ? oz Salt ? oz
Dry Milk ? oz Water ? oz
Powdered Sugar ? lb
New Recipe
Multiply each ingredient by the working factor.
White Cream Icing Yield: 5 cakes
Emulsified Shortening 1 lb 4 oz Salt 1/4 oz
Dry Milk 5 oz Water 14 oz Powdered Sugar 5 lb
Original Recipe
Mixed unit alert! Convert
1 lb 4 oz to
20 oz
.
Multiply each ingredient by the working factor.
White Cream Icing Yield: 5 cakes
Emulsified Shortening 20 oz x 0.6
Salt 1/4 oz x 0.6
Dry Milk 5 oz x 0.6
Water 14 oz x 0.6
Powdered Sugar 5 lb x 0.6
Original Recipe
White Cream Icing Yield: 3 cakes
Emulsified Shortening 12 oz
Salt 0.15 oz
Dry Milk 3 oz
Water 8.4 oz
Powdered Sugar 3 lb
New Recipe
Shown below is the finished recipe conversion.
White Cream Icing Yield: 3 cakes
Emulsified Shortening 12 oz
Salt 0.15 oz
Dry Milk 3 oz
Water 8.4 oz
Powdered Sugar 3 lb
