Math for Grownups (15 page)

But dependent variables are more like man’s best friend. Except for gnawing on your grandmother’s sofa, dogs can’t do much of anything on their own. Hunting for food? Nope. Cleaning up after themselves? No way. Surviving the loneliness when you leave the room for even a moment? Heaven forbid! In short, their happiness depends on you, you, you.

Dependent variables are the same way. Take the turkey example. The thawing time
depends on
the weight of the turkey. A larger turkey takes longer to thaw. A smaller turkey takes less time to thaw. So the time it takes a turkey to thaw is a dependent variable.

But the weight of the turkey is independent. You can buy a bird of whatever size you want. Be a rebel! Go for individual Cornish game hens. Or get a huge turkey so you can have plenty of leftovers. Think like your cat and do what makes you happy—independent of the whims and wishes of your friends and family.

But whatever you do, save some for the dog. Remember, she depends on you.

It’s the chance of her culinary lifetime. Gina has been invited to Paris to compete in a worldwide bake-off. She’s booked her flight, packed her supplies, and carefully adjusted her pecan-surprise toffee recipe to European-friendly metric units. To ensure absolute freshness, she will shell the pecans just hours before she’s expected to make her candies, and black strap molasses is being flown in from the Caribbean.

What could go wrong?

After enjoying a leisurely breakfast on her hotel room balcony, Gina strolls to the contest kitchen to get started. That’s when it hits her: She forgot her candy thermometer.

See, the trick to good toffee is cooking the molasses to the right temperature—307°F, to be exact. Without her thermometer, Gina has no chance.

But on her counter is the answer to her quickly muttered prayers. Along with a collection of spatulas, whisks, and measuring utensils is a shiny new candy thermometer.

Gina almost relaxes until she notices something odd. The thermometer only measures up to 200°. She’s in Paris, where temperatures are measured in the Celsius, not the Fahrenheit, temperature scale.

She’ll have to do some math to make this work.

Luckily, Gina has the conversion formula written in her
Welcome to Paris!
guidebook, which is helpfully tucked into her bag. In the conversion formula,
C
= degrees Celsius, and
F
= degrees Fahrenheit.

She needs the molasses to reach 307°F, so she substitutes and then does the calculations.

Gina scratches her head. She needs to remember how to multiply a whole number by a fraction. After a minute, she’s got it. All she needs to do is multiply the whole number by the numerator of the fraction.

She wants a decimal, rather than a fraction, so she divides.

C
= 152.777…, or 152.8

Feeling as though she narrowly missed a major kitchen catastrophe, Gina regains her composure in time to slice, simmer, and stir her way to victory.

It’s said that baking is a science, while cooking is an art. But actually, there’s a little of both in each venture. And both come in handy when you want to make changes in a recipe.

Increasing or decreasing a recipe’s yield (the amount it makes) is just a matter of multiplication or division. But substituting ingredients may take a little more thought. You can even develop your own recipes based on old favorites—if you know some basic fraction arithmetic.

Betty loves chocolate chip cookies. She’s used the same recipe for years and years, and now she’s looking for something a little different. After a trip to Hawaii for her 50th birthday, she’s inspired by the tropical flavors she tasted there—coconut and macadamia nuts, in particular.

At home once again, she pulls out her tried-and-true cookie recipe. The basic ingredients will have to stay the same, but she could substitute something for the chocolate chips. What if she used white chocolate chips, shredded coconut, and chopped macadamia nuts?

Her mouth waters, and she swears she can hear the faint strumming of a ukulele.

Betty’s recipe calls for 2 cups of chocolate chips. Her plan is to replace the chocolate chips with the three tropical-inspired ingredients. But if she uses 2 cups of white chocolate chips, 2 cups of shredded coconut,
and
2 cups of macadamia nuts, the cookie dough won’t stay together. Nope, she’ll have to stick with 2 cups total.

She gets out her pencil to do a little math. She has three ingredients that need to be divided so that they total 2 cups. She scribbles in the margin of her cookbook

That means she should add 2∕3 cup of each new ingredient (instead of the chocolate chips).

But Betty doesn’t trust her 50-year-old brain. This looks right, but is it? She can find out with some simple addition.

She remembers that as long as the denominators are the same, you can add fractions by adding just the numerators:

She’s done it! But wait, as much as she loves macadamia nuts, she loves coconut even more. What if she altered the ratios a little bit—for less macadamia flavor and more coconut flavor?

Betty thinks again. She could double the amount of coconut and halve the amount of macadamia nuts.

Double ⅔ cup of coconut
→
4/3 cup, or 1⅓ cup

Halve ⅔ cup of macadamia nuts
→
2/6 cup, or ⅓ cup

So Betty now figures she can use the following ingredients:

⅔ cup white chocolate chips

1⅓ cup coconut

⅓ cup macadamia nuts

Still not trusting herself, she decides to check her work.

Good thing she did, because 7∕4 = 21∕3. Her measurements are off by 1∕3. She looks carefully at the numbers and notices something. In order to have a total of 2 cups, she needs the numerators to add up to 6 (as long as she keeps the denominators the same).