Math for Grownups (13 page)

Sarah is ready to order the curtains. What dimensions will she need?

Looking at her sketch and considering the advice her friend gave her, she knows she needs to buy four panels that are 30" wide by 64" tall. Because the curtain rods will need to extend 5" past the molding on each side, her two curtain rods will have to be at least 40" long (5" on the left side of the window + 30" for the window width + 5" on the left side of the window = 40").

Sarah orders the curtains and hardware and pays extra for overnight delivery. Only one more early wake-up call with Sine! She plugs in her rechargeable drill before she goes to bed that night.

The next day Sarah’s package arrives, and she is ready. She’s strapped her tool belt around her waist and loaded it up with everything she needs—a retractable tape measure, cordless drill, sharpened pencil, drill bits, and a Phillips screwdriver.

Her drawing shows exactly where to position her curtain rods so that the curtains will fall exactly where they should. And before Sine is ready for his afternoon nap, Sarah has his new drapes installed.

It’s curtains for her early bird.

Math in the everyday world can be challenging for one big reason: There are too many darned steps! Even people with long attention spans and great spatial abilities can get lost in a matter of moments.

Some basic problem-solving skills can help out in a pinch.

1. Make a list.
If your head is swimming with numbers, do a brain dump. In other words, list everything you know about the problem. Then cross off what you don’t need.

2. Draw a picture.
It doesn’t take a Rembrandt to whip up a sketch of a room and label its dimensions.

3. Make a table.
Organizing the information so that it makes sense can point you to the perfect solution.

4. Look for clues.
Certain words will tell you what you need to do:
per
means “each,”
squared
means “times itself,” and even little old
is
means “equals” or “is equal to.”

5. Rewrite the problem.
Sometimes you just need to write things in a different way. And—surprise!—sometimes writing an equation with variables is just the thing.

6. Check your answer.
You don’t need to call up your algebra teacher to see if your answer is right. But it is a good idea to ask yourself, “Is this answer
reasonable
?”

In the Kitchen: Making More, Making Less—Recipe Math to the Rescue!

Ah, the sweet smells from the kitchen! Freshly baked bread, spicy garlic and onions, ginger cookies—and the whiff of smoke coming from your ears as you attempt to halve your great-grandmother’s biscuit recipe.

The kitchen is both a delight and a source of great frustration. The dozens of culinary magazines, television programs, and websites are testament to the true art and science of baking and cooking. And as you probably learned long ago, math plays a role. From adjusting recipes to converting measurements, a little bit of arithmetic can either make or break a dish.

But it’s not hard! If you can scramble an egg or even make toast, you can do basic kitchen math and reap the delicious benefits day after day.

Graham has a green thumb. When he planted a few tomato plants in his backyard, he had no idea that he’d be overwhelmed with the ruby-red fruits all summer long. His neighbors and coworkers are sick of them, and so is Graham. It’s time for a secret weapon: Mom’s spaghetti sauce.

See, Graham figures that he can stash a big batch of red sauce in the freezer and eat well all fall and winter long. He might even have enough to share, once everyone has forgotten the mounds of tomatoes he’s already given away. But first he has to figure out how to adjust the recipe.

His last tomato harvest yielded 25 tomatoes, and he’d like to use them all. But Mom’s recipe calls for 10 tomatoes. Clearly, he’ll need to increase the batch, but by how much? Twice? Three times? Something in between?

The answer may be clear to you. But if not, here’s another way to ask this question: 25 is how many times 10? Or 10 times what is 25?

25
=
10 • ?

Remember, we can substitute
x
for the question mark:

25
=
10 •
x

And we don’t need the multiplication sign:

25
=
10
x

Now all Graham needs to do is solve the equation. That will tell him the number by which he needs to multiply each ingredient amount in order to correctly alter the recipe.

If Graham has a bumper tomato crop, he’ll want to do something else with those saucy fruits, too. And canning is just the thing. In the winter, home-canned tomatoes are perfect for chili, lasagna, or more spaghetti sauce.

Fortunately, Graham has his mother’s canning recipes, as well. She says that about 7 tomatoes will fill one 1-quart jar.

Graham pokes around in his basement for some canning supplies. And he hits pay dirt—16 canning jars.

The problem is that the jars are different sizes. He brings them upstairs and puts them in groups: six 1-pint jars, eight 1-quart jars, and two 2-quart jars.

With these jars, how many tomatoes can he can?

First things first. The 2-quart jars are twice as big as the 1-quart jars. For each of those jars, Graham needs to double the number of tomatoes that can fit in a 1-quart jar.

2 • 7
=
14 tomatoes fit in a 2-quart jar

The pint jars are half the size of the quart jars. Because 7 tomatoes fit in a 1-quart jar,

½ • 7
=
3.5 tomatoes fit in a pint jar

Now he can estimate the number of tomatoes for each size jar.

six pint jars
→
6 • 3.5 = 21 tomatoes

eight quart jars
→
8 • 7 = 56 tomatoes

two 2-quart jars
→
2 • 14 = 28 tomatoes

And now he can add:

21
+
56
+
28
=
105 tomatoes

After the next heat wave, Graham should have plenty to do.

In
Chapter 2
, we reviewed how to isolate an unknown quantity (
x
), by doing the same thing to each side of the equals sign. We also reviewed the fact that the inverse of multiplication is division. Thus, to separate the
x
from 10
x
, we need to divide both sides of the equation by 10.

This means that Graham has 2.5 times as many tomatoes as the recipe calls for. If he wants to use all of the tomatoes—and he really, really does!—he’ll have to increase the amounts of all the ingredients by 2.5. In other words, he needs to multiply each ingredient amount by 2.5 before measuring.

But for all of Graham’s horticultural talents, he’s not big on using a calculator. He figures he can do the math in his head. And turns out he’s right. Remember that 2.5 is the same thing as 2½, so all Graham needs to do is this:

1. Double the original amount.

2. Find half of the original amount.

3. Add.

Let’s apply these steps to the ½ cup of olive oil that the original recipe calls for:

Double ½ cup
→
1 cup

Half of ½ cup
→
14; cup

1 cup
+
¼ cup
=
1¼ cups

And what about the carrots (Mom’s secret ingredient)?

Double 3 cups
→
6 cups

Half of 3 cups
→
1½ cups

6 cups
+
1½ cups
=
7½ cups

By evening, when the summer temperatures have fallen, Graham has a big pot of red sauce simmering on the stove—and not a single tomato left on his plants.

Cooking can be an adventure, especially if your 2-year-old has taken off with your measuring cups. Or what if you need 2 cups of whipping cream, which is sold only in pints or quarts?

That’s where a simple conversion chart can come in handy. Whether you’re adjusting a recipe or making do with limited tools, knowing a few conversions makes life in the kitchen much easier.

⅛ teaspoon or less = a pinch

3 teaspoons
=
1 tablespoon

4 tablespoons
=
¼ cup

5⅓ tablespoons
=
⅓ cup

8 tablespoons
=
½ cup

10⅔ tablespoons
=
⅔ cup

16 tablespoons
=
1 cup

2 cups
=
1 pint

4 cups
=
1 quart

2 pints
=
1 quart

4 quarts
=
1 gallon

Some fractions can be written two ways. The amount of olive oil that Graham needs in his altered version of Mom’s spaghetti sauce recipe is 1¼ cups. That’s a mixed number: It has a whole number (the 1) and a fraction (the ¼).

But that number can also be written entirely as a fraction. 1 cup is the same as 4∕4, right? (Imagine a pie cut into fourths. If you keep them all, you’re keeping the whole pie.) So 4∕4 plus ¼ is 5∕4. When you add fractions that have the same denominator (the bottom number), you just add the numerators (the top numbers) together and keep the denominator the same. So, ¼ is the same as 5∕4.

A fraction in which the numerator is larger than the denominator is called an improper fraction. If you have a mixed number such as 2¼, where the whole number is larger than 1, there’s another way to change a mixed number to an improper fraction.

First, multiply the whole number by the denominator of the fraction:

2¼ → 2 • 4 = 8

Then add that number to the numerator of the mixed number:

8
+
1
=
9

That number becomes the numerator of the improper fraction:

But what is the denominator? It’s the same as the denominator in the mixed number:

So, 2¼ = 9∕4.