Math for Grownups
Authors: Laura Laing
Tags: #Reference, #Handbooks & Manuals, #Personal & Practical Guides
FOR
GROWNUPS
Relearn the Arithmetic You
Forgot from School So You Can:
Calculate how much that raise will
really amount to (after taxes)
Figure out if that new fridge will actually fit
Help a third grader with his fraction homework
Convert calories into cardio time
LAURA LAING
BS, Math Educator
Copyright © 2011 by F+W Media, Inc.
All rights reserved.
This book, or parts thereof, may not be reproduced in any
form without permission from the publisher; exceptions are
made for brief excerpts used in published reviews.
Published by
Adams Media, a division of F+W Media, Inc.
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www.adamsmedia.com
ISBN 10: 1-4405-1263-9
ISBN 13: 978-1-4405-1263-6
eISBN 10: 1-4405-2689-3
eISBN 13: 978-1-4405-2689-3
Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1
Library of Congress Cataloging-in-Publication Data
Laing, Laura.
Math for grownups / Laura Laing.
p. cm.
Includes index.
ISBN 978-1-4405-1263-6
1. Mathematics-Popular works. I. Title.
QA93.L27 2011
510-dc22
2011010369
This publication is designed to provide accurate and authoritative information with regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional advice. If legal advice or other expert assistance is required, the services of a competent professional person should be sought.
—From a
Declaration of Principles
jointly adopted by a Committee of the
American Bar Association and a Committee of Publishers and Associations
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This book is available at quantity discounts for bulk purchases.
For information, please call 1-800-289-0963.
For my three favorite mathematicians:
Dad, Gina, and Zoe.
Contents
INTRODUCTION
:
Everyday Math: Easier Than Running Out of Paint
1 AT THE STORE:
Deal or No Deal?
2 AT THE DEALERSHIP:
Leasing vs. Buying, New vs. Used—You Do the Math
3 ON THE MARKET:
Buying a House by the Numbers
4 AT HOME:
Will Your New Fridge Fit?
5 IN THE KITCHEN:
Making More, Making Less—Recipe
Math to the Rescue!
6 IN THE YARD:
If a Train Leaves Omaha at 8 A.M.
,
How Much Lawn Edging Do You Need?
7 IN THE CRAFT ROOM:
Measure Twice, Cut Once
8 AT THE BANK:
Income Minus Expenses Equals Happiness (or Misery)
9 IN THE GYM:
How Many Miles on the Treadmill to
Burn Off One Doughnut?
10 ON THE ROAD:
When Will You Get There and
How Much Will You Spend?
Introduction
Everyday Math: Easier Than Running Out of Paint
The numbers game plays a starring role in almost every part of daily life, from making dinner to planning a weekend getaway. Heck, you need math to order a pizza.
Even people who don’t sweat math problems—namely, mathematicians!—sometimes have trouble with the calculations we face in everyday life. So it’s no wonder that those of us who have already forgotten what we learned in high school (or, worse, never liked math and didn’t do well in it) can sometimes stare at a math problem and not have the faintest idea what to do about it.
But luckily you don’t have to be Stephen Hawking (or even be proficient with a scientific calculator) to use math in ordinary situations. Remember, it’s only a tool. (And it’s not even one that requires safety glasses or special training so you won’t cut off the tip of your left index finger.) It’s a language that describes how our world fits together. Math enables us to make predictions and quick decisions. Math helps us feel powerful and confident.
Here’s the honest truth: Adding fractions is no harder than signing up for the office football pool or buying airline tickets online or remembering how to create a folder on your computer desktop. It may just
seem
more challenging.
The truth is that very few people in the world can’t do math. You are not one of them. Here’s the thing—most math doesn’t require you to remember how to find the slope of a line (or even to remember what slope is). The everyday stuff is a combination of basic arithmetic and your innate understanding of how to speak the language of numbers, shapes, and measurements.
Yep, innate. You were born with curiosity about the world around you. Math is just one way to describe that world. And, like it or not, it’s a pretty important way.
So unless you don’t care what’s in your bank account or whether your new elliptical machine will fit through the door of your exercise room, you’re going to have to do some math.
And you might as well think you’re good at it, right? (Because, guess what? You are.)
You don’t have to know calculus to figure out how to lower your monthly mortgage payments. You don’t have to remember the Pythagorean Theorem to lose a few extra pounds. And you don’t have to do long division in your head to buy paint for your new house.
You do need to have an open mind and a sense of humor. After all, it’s only math.
At the Store: Deal or No Deal?
Unless you just hit the Lotto jackpot, you’re probably looking for ways to save a little cash at the register. Whether you’re buying groceries or the perfect knickknack for your newly decorated living room, keeping more money in your wallet can be a real challenge. The key is to plan ahead and stay sharp.
What’s more important: finding your server’s tip to the penny or getting out of the restaurant with your sanity intact? We all know some of those folks who obsessively use a calculator to find the tip on their morning bagel and coffee, but how much fun are they? (And how much fun are they having?)
Estimation is your best friend. Need to split the lunch bill with your best friends? Estimate. Need to know how far apart to plant your begonias? Estimate. Want to know how long it will take you to get to Grandma’s house for Thanksgiving dinner? Estimate.
When you estimate, you create math problems that are simple to solve in your head. You round numbers so that they’re easy to add, subtract, multiply, or divide. You evaluate what you can do well and apply those strategies to the problem at hand. In short, you look for ways to do mental math.
But you are not guessing. In some instances, you’re finding a range of possible solutions that make sense. (What’s my ETA?) In other situations, you’re merely figuring out the answer to a yes-or-no question. (Can I afford to buy those designer shoes?) And sometimes you just don’t need to have the answer down to the penny. (How much can I expect to pay each month for my mortgage?)
Mathematicians and scientists estimate all the time—even when they’re looking for an exact answer. Estimating helps you judge your solution, and this in turn can keep you out of embarrassing situations (like arriving at the party way too late)
and
hot water (like paying more than you can afford for your not-so-smart phone).
Estimating can really pay off when you’re in a hurry. And let’s face it, who doesn’t want to get out of the grocery store as quickly as possible? The cart’s squeaky wheel would drive Buddha to distraction.
It’s the day before Thanksgiving, and your mother needs five things from the grocery store: pumpkin pie spice, eggs, mini-marshmallows, a jar of olives, and a can of jellied cranberry sauce. Your head hurts from Great-Uncle Pete’s incessant shouting, so you gladly volunteer, grabbing the list and a $20 bill from Mom’s purse as you head out the door.
Head pounding, you race through the store, find what you need, and end up on the pharmacy aisle. Hey, do you have enough money left for a $4.69 container of aspirin?
Here’s what you have in your cart:
• Pumpkin pie spice: $3.15
• Eggs: $3.17
• Mini-marshmallows: $1.15
• Olives: $4.98
• Cranberry sauce: $1.19
When you were in elementary school, you may have learned to estimate by doing the problem and then rounding. But that kind of defeats the purpose, doesn’t it? Instead, try rounding first and
then
doing some quick mental math.
$3.15
→ $3
$3.17
→ $3
$1.15
→ $1
$4.98
→ $5
$1.19
→ $1
$4.69
→ $5 (that’s the aspirin)
Now you can add up the rounded numbers, speedy quick, to get $18. That’s less than the $20 bill you have shoved in your pocket. But wait, there’s more!
If you’re shopping in a state that charges a sales tax, $20 may not cover it all. Let’s just say that the sales tax is 5%. In a rush, and with a screaming headache, how on earth can you find that calculation quickly—and somewhere near accurately?
Remember how to find 10% of a number in your head? Move the decimal point to the left one space: 10% of $10.00 would then be $1.00; 10% of $18.00 would be $1.80.
If you can do that, you can certainly find 5%. Here’s how:
10% of $18.00 is $1.80, right?
And 5% is half of 10%, right?
So half of $1.80 is $0.90.
That means your sales tax will be just about $1, and the $20 in your pocket will cover it all.
Whew. That pounding in your temples will be gone in no time.
You Shouldnt Believe Them
Myth 1: There’s Only One Way to Skin a Math Problem
Here’s the great news. Our brains are designed to solve problems. We do it all the time.
When your kid swears to you that 30 minutes is plenty of time to shower, finish his homework, clear the dinner table,
and
squeeze in one last video game, your brain says, “No way.” And your brain is right, even though you didn’t have to sit down and calculate that answer.
But brains are like fingerprints—each one is unique. You may have an uncanny ability with maps, while your husband may not be able to find his way out of a paper bag. Or you may be able to read 600 words a minute but have trouble calculating percents.
The key is to find out how
your
brain solves problems.
Here’s a quick test. Without using a pencil and paper or a calculator, quickly solve this problem:
56
+
25
=
?
Now ask someone else to find the answer, but don’t tell her how you did it. Then ask her about her process. It’s quite possible that she did it differently than you did.
Here are just three ways to find the answer:
Method 1: 56
+
25
=
?
50
+
25
=
75 and 56
-
50
=
6
6
+
75
=
81
so 56
+
25
=
81
Method 2: 56
+
25
=
?
60
+
25
=
85 and 60
-
56
=
4
85
-
4
=
81
so 56
+
25
=
81
Method 3: 56
+
25
=
?
50
+
20
=
70 and 6
+
5
=
11
70
+
11
=
81
so 56
+
25
=
81
There are many more approaches, but notice that not one of them requires you to do this:
If you want to line everything up, add the ones digits, carry the 1, and then add the tens digits, go for it. There’s nothing wrong with that process either.
But you should feel free to try something new. You’re not being graded, and no one is asking you to show your work.
Myth 2: Memorization Is Math’s BFF
So you say you’re no good at math because you can’t remember what 7 times 8 is? Or you claim there’s no way you can reduce your mother’s enormous chicken casserole recipe, because you don’t remember how many pints there are in a quart of milk?
Here’s a little secret: You don’t have to have these facts down cold in order to use math.
Sure, your fourth grade teacher drilled those multiplication tables into your head. And your middle school math tests included recalling dozens of conversion facts. But since then, you’ve packed that space between your ears with lots of other useful information—like how to ask where the bathroom is in Spanish and where ESPN is on your cable lineup.
It’s completely understandable if you struggle with some basic math facts. And it’s completely unnecessary to dig out the flash cards to review.
Instead, use your smarts to figure out arithmetic facts or formulas that you’ve forgotten. For example: You probably can remember what 10 times 8 is, and you can use that fact to figure out 9 times 8. (10 times 8 is 80, so subtract 8 from 80 to get 72. Voila! That’s 9 times 8.)
See, it’s much more important to remember the foundation of the times tables—that 9 times 8 just means 9 groups of 8s—than to remember the facts themselves well into your eighties. (And if you do? That’s great too!) When you understand
why
arithmetic works, you can make up for most any math fact that you’ve forgotten.
Still stumped? Head to the web. You can find out how to do
anything
these days by typing a few search terms into a browser. With a click of the mouse, you can access a variety of conversion tables or calculators to choose from. Or a video showing how to find the area of a triangle. The really cool thing is that these instructions are often provided by regular folks, not mathematicians. So you probably have a good shot at finally understanding them. (No offense, math geeks.)
Myth 3: Using a Calculator Is Cheating
Your elementary teacher didn’t let you use a calculator to find 6 times 7—and for good reason. She wanted you to learn that fact by heart.
But she’s not around anymore.
You wouldn’t expect a plumber to fix your pipes without a wrench. And you shouldn’t expect to do all math computations with paper and pencil—or in your head. There’s no shame in turning to some really great tools to solve your everyday math conundrums. And a calculator is one of them.
The math you do as an grownup is very, very different from what you did as a kid. In math class, you were learning basic ideas, which often meant putting calculators and computers aside. Through that process, you came to understand the foundation of mathematics—how the times tables worked or why adding a negative number is the same as subtracting a positive number.
And now that you have those fundamental concepts humming along with every other idea you use on a daily basis—like language and basic geography—you should feel free to use whatever tools you have at your disposal, whether it’s a cheap desktop calculator or your sister, who has that spooky talent for multiplying three-digit numbers in her head.
Look, there are going to be times when you need to do some mental math (figuring out whether a “Big Sale!” means you really can afford that new jacket) or scribble some calculations on a piece of paper (cutting a recipe in half). But if you want to use a calculator, go right ahead. If you need to call your dad for math help, have at it.
