## Hungry for Math: The Math of Food

# Introduction

Imagine you are getting ready for the big game by preparing your delicious dip recipe. Everyone is excited and the guest list is growing by the hour. Your place, with its delicious dip, is the place everyone wants to be. Your recipe is made to serve 8 but now it needs to feed 24. With some simple math you can scale your recipe to meet the demands of your new popularity. Modifying recipes is just one way math can help in the kitchen. In this week’s article we will explore a variety of other ways math impacts our work in the kitchen and the food we eat.

# Unexpected Guests

Let’s get back to this dip you are making for the big game. While your made from scratch onion dip is known throughout your neighborhood, it is actually a recipe from Food Network’s Alton Brown. (See the references if you actually want to know how to make it) In the time you have been reading this your Aunt Myrtle had some plans fall through and wants to come over for the game and try this delicious dip everyone has been talking about. Aunt Myrtle also wants to bring her bridge club with her. She knows it is a lot of people but promises to pay for any extra supplies needed for such a large group. Now your party is up to 40 people.

You might say well, I have five times as many guests as I planned, so I can just multiply all of the ingredients by 5. And then you look at the recipe and see that most of the ingredients are expressed as fractions. 1/2 teaspoon of this, 1 and 1/2 cups of that. Fractions can give people trouble well into adulthood so let’s break down what we need to do.

The first thing we need to remember is that any number can be expressed as a fraction. 5 is the same as 5/1.

Second, we can remember some rules for multiplying two fractions. We multiply the numbers on top and that becomes the new top. We multiply the numbers on bottom and it becomes the new bottom.Numbers like 1 and 1/2 we might need to change into a fraction like 3/2 so we can do the same operation on everything.

So 1/2 teaspoon becomes 5/2 teaspoons and 1 and 1/2 cups becomes 15/2 cups. Now these numbers look rather strange. This is because we usually use whole numbers with a remainder when expressing fractions, just like we did with 1 and 1/2 cups earlier. 5/2 teaspoons becomes 2 and 1/2 teaspoons and 15/2 cups becomes 7 and 1/2 cups.

# Cookie Overload

It is the next day after your massive party. Your math skills save the day and let you remain the king of dip. You and your family get a sweet tooth and want to make cookies. You pull out grandma’s old recipe and then you realize the her recipe makes six dozen cookies. That is just way too many cookies for your family of three. So instead of six dozen, three dozen might be more appropriate. (you will have enough to share with your mechanic Marvin and your florist Fern)

Just as we can multiply recipes to make them serve more people, we can also divide them to serve fewer people. As long as the proportion or ratio of each ingredient is the same we can reduce or expand our recipe.

Let’s look at our process again. We’ll express numbers 1 and 1/4 cups sugar as 5/4 cups sugar. We will still multiply, but this time we will multiply by 1/2, which is the same as dividing by 2. We get a new value of 5/8 cups sugar or a little more than half a cup.

# Clock Work Kitchen

After your foray in crazy dip production and sweet baking success, time passes and you just stick to exact recipes to avoid any extra math in your life. Then Thanksgiving lands in your lap. Aunt Myrtle called again. She will be coming over to celebrate Thanksgiving with you and your family. We are not sure why Aunt Myrtle always insists on inviting her self over, but it works out well for our discussion. Aunt Myrtle lives for tradition and she will expect a turkey with all of the fixings. So you go to the store and buy a 13 pound frozen turkey a week before Thanksgiving. You’ve cooked dip and cookies before, how hard can a turkey be?

Lucky for you, you read the label and see the turkey people say the turkey needs to thaw 24 hours in the refrigerator for every 5 pounds. You realize you’ll have to start prepping for this meal three days before you need to cook it!

As the big day arrives you answer the fifth call this week from Aunt Myrtle. Aunt Myrtle’s last call was to remind you that she doesn’t like the generic brand of cranberry sauce and that dinner should be at 3:00 PM for tradition sake. You look back at the turkey directions and realize the cooking time is based on the size of the turkey. The labels says 20 minutes per pound at 350 degrees Fahrenheit. You get out a pencil. 13 pounds times 20, 260 minutes. There are sixty minutes in an hour so it is going to take 4 hours and 20 minutes for the turkey to cook! You work backwards and you figure out you need to get the turkey in the oven by 10:30 on Thanksgiving morning. You do similar calculations and form a plan for when the potatoes, stuffing and green bean casserole need to go in. The meal is a success and Aunt Myrtle approves of your meal offerings, even if you didn’t have enough sense to get a hair cut before she arrived.

# One More Slice of Pie

You begin to doze on the couch anticipating Aunt Myrtle will soon depart now that dinner has completed. Aunt Myrtle tells you that it is just too dark outside for her to be driving and insists she stay at your house over night. As you prepare the guest room you see that Aunt Myrtle is lugging a suitcase from the trunk of her Cadillac. You start to ponder how convenient it is for her to have an overnight bag with her but decide to let it go.

Later that night your stomach is grumbling so you decide to get another piece of pie. “Who eats dinner at 3:00 PM? 8:30 rolls around and it is like you never ate dinner” you mumble to your self. As you are standing at the fridge enjoying your pie, Aunt Myrtle startles you as you suddenly see her illuminated by the light of the refrigerator. She is just standing there in her full length night gown and curlers. Then she says to you “More pie? My dear, you are really starting to fill in that sweater. Would you like me to make you a new one?” You pause to process what she said. “Did she really just say that?” you think to yourself. But then you wipe the meringue off your chin and put the drumstick down and ponder her words. While she lacks tact, and general control of her gas, she may have a point. So the next day you start an exercise plan to shed those pounds.

You look up on the internet that one pound of fat equals 3500 calories. You also read that safe weight loss is about 1-2 pounds a week. You cooked a 13 pound turkey, how hard could losing a single pound be? You walk each day in the week for thirty minutes. Some more research tells you that someone your size burns 200 calories by walking for 30 minutes. You multiply it out and figure you burned 1400 calories this week. You were on track with your diet but there was the one time you slipped and ate one brownie, well one ROW of brownies for 500 calories. You run the numbers and find that you only burned an extra 900 calories that week. The amount is not even half a pound. You use your improved math skills to make better choices in the coming weeks and make progress on your goals. With all of this new health surge you even find the energy to paint your house a different color. Aunt Myrtle ends up not being able to find your house for a good six months. Six. Blissful. Months.

# Conclusion

Even if you don’t have an Aunt Myrtle in your life, you can use math to tackle different problems with cooking and food. You can use math to increase the number of servings, decrease the number of servings, plan cooking tasks and to understand the impacts of diet and exercise. Check out the references and videos below to keep learning.

# References

- Onion Dip From Scratch by Alton Brown http://www.foodnetwork.com/recipes/alton-brown/onion-dip-from-scratch-recipe.html
- Soft and Chewy Chocolate Chip Cookie Recipe http://www.food.com/recipe/soft-and-chewy-chocolate-chip-cookies-48356
*Cooking with Math*on Math Central from the University of Regina http://mathcentral.uregina.ca/beyond/articles/Cooking/Cooking1.html- Real Life Math | Chef http://www.pbslearningmedia.org/resource/mkaet.math.rp.chef/real-life-math-chef/

# Videos