Authors: Laura Laing
Tags: #Reference, #Handbooks & Manuals, #Personal & Practical Guides
Math for Grownups (19 page)
That means you’ll use ½ fluid ounce per 1 gallon of water for your sprayer.
Using math in everyday life is nothing like solving those rows of algebra equations you had in high school. Formulas and equations don’t magically fall from the sky. And even if you don’t need an equation, how do you know when to do even the simple stuff, like add, subtract, multiply, or divide?
Simple. Read the clues.
Each math problem has some clues in it that tell you exactly what to do. You just need to know what they are. Here’s a short list of words and phrases that serve as clues to the five most commonly used operations.
Addition:
sum, total, in all, perimeter
Subtraction:
difference, how much more, exceed
Multiplication:
product, total, area, times
Division
: share, distribute, quotient, average, half, ratio
Equals:
same as, is the same amount, costs
Gary has just bought a great house. It even has a pond in the backyard! There’s not much landscaping to be done, but the pond is empty, and Gary would like to put in a few of those big goldfish he’s seen at the Japanese restaurant downtown.
Gary doesn’t even know that these fish are called koi. But he is smart enough to call One Fish, Two Fish, the local experts in aquariums and garden ponds.
“How big is your pond?” says the guy who answers the phone. Gary has no idea.
“Well, what shape is it? Round? Kidney? Rectangular?”
Aha! A question Gary can answer. “It’s round,” he beams.
The fishmonger explains that Gary needs to know the surface area of the pond before he can purchase the fish. That’s because the surface area determines how many fish can survive in a pond.
Gary hangs up and grabs his tape measure. He’s not quite sure how he can find surface area, but he knows that his pond is circular. If he measures from one side to the other, he’s sure to get something he can use.
The width of the pond is 10 feet. But from that measurement, how can Gary find the surface area?
Even though the pond itself is three-dimensional, the surface area of the water is the area of the circle itself. And the area of a circle is found with this formula:
A
=
πr
2
With dim memories of “pi are square” ringing in his mind, Gary recalls that
π
can be estimated by using 3.14. He also recalls that
r
is the radius of the circle. But he doesn’t know what the radius is.
Then Gary has another
aha!
moment. He measures the
diameter
of the pond, which is twice the radius. If the diameter is 10 feet, then the radius of the pond is 5 feet. Now he can use the formula.
A
=
π
• 5
2
Should Gary multiply
π
and 5 first or square 5 first? Another
aha!
moment. Gary remembers the order of operations—exponents are calculated before multiplication is performed.
A
=
π
• 25 ft
A
= 3.14 • 25 ft
A
= 78.5 ft
2
Gary knows now that the surface area of the water in his pond is 78.5 ft
2
. He calls One Fish, Two Fish back. The guy on the phone tells him a little more about the fish he’s interested in.
- If he needs to round the surface area, he should round down. (It’s better to have too few fish than too many.) So that 78.5-ft
2
measurement should be rounded down to 78 ft
2
, not up to 79 ft
2
. - . Gary should purchase half an inch (or ½ inch) of koi per square foot of surface area.
- The shop has 12-inch koi for sale.
Between Gary and the fish guy, the math is a breeze:
½ • 78
=
39 inches of fish
39
/
12
=
3.25, or (again rounding down) 3 fish
By the end of the spring, Gary’s pond is swimming with gorgeous koi, which love eating mosquitoes and somehow escape the clutches of the neighbor’s cat.
There’s no need to feel penned in by the elementary rounding rules you memorized all those years ago—such as “round up if the next digit is 5 or greater” or “round down if the next digit is less than 5.” Sometimes rounding up makes more sense than rounding down, and vice versa—no matter what your math book said.
Take Gary’s fish, for example. Normally, he would round 78.5 up to 79. But as his fish expert recommended, it’s better to have more space for the fish than to crowd too many fish into too small a habitat.
Then again, if your teenage son decides to put away 50% of his lawn-mowing earnings, he’ll save a lot faster if he rounds all of his deposits up to the nearest dollar, rather than down.
Just one more example of the flexibility of math.
In the Craft Room: Measure Twice, Cut Once
Some folks are the crafty type. They play with paper, fabric, beads, wood. They can recreate the Mona Lisa in glitter or make their own ceramic dishes. On birthdays and holidays, they give handmade soaps (created from herbs they’ve grown in their own garden, naturally), knitted tea cozies, and birdfeeders that resemble Westminster Abbey.
At a craft fair, they’re the ones examining the wares carefully—not to buy, mind you. No, they’re mentally taking them apart, in order to re-create them at home, perhaps out of completely different materials.
They have an attic full of fringe, fabric, and foam, just waiting for the right project. And they know all the differences between white glue, wood glue, and rubber cement.
You hate them.
But even though there’s much to envy, there’s no need for hard feelings. There’s room in the world for all sorts of crafters. Maybe you’re only interested in putting your grandmother’s sewing machine to work hemming up all those pants your taller sister gave you. Or you may want to learn how to make new candles from the stubs you have stuck in your utility drawer.
Whatever your goals, math sneaks into most projects in the craft room. So grab your glue gun and a sharp pair of scissors. Let’s get crafty.
Knitting and crocheting have hit the big time. With weekly knitting circles and yarn shops cropping up like mushrooms after a long rain, you can’t even go to church without hearing the clicking of needles. Who knew that granny squares could be hip again?
The geometry of yarn work is pretty simple, especially if you’re making a scarf or a blanket. (Rectangles are simple.) Every good knitter and crocheter has a few easy math skills at the tips of her needles and hooks.
Last week, Ann found the most gorgeous yarn on sale at her favorite yarn shop, Knits for Ewe. And she has just the project for it—a simple crocheted scarf.
The problem is that the sale wasn’t really that wonderful. She could afford only 4 skeins of it, and her pattern calls for 6 skeins.
No matter. She can make the scarf smaller for her goddaughter, Jasmine, who just turned 5. It’ll make a great gift when she visits Jasmine and her family in November. Ann decides to leave the width of the scarf the same and reduce the length.
But how can she change the pattern? Her best bet is to do a little math.
Proportions are just the thing in this situation. They are ideal for showing the relationships among four numbers. (A ratio is a way to compare two numbers; proportions are just ratios on steroids.)
Her pattern tells Ann the relationship between the number of skeins and the length of the finished scarf. (She’s already checked her gauge, so she knows she can trust the size.) The pattern calls for 6 skeins of yarn, and the finished scarf will be 66 inches long.
Ann writes that information as a ratio:
She has 4 skeins of yarn, but she doesn’t know how long her scarf should be. Therefore, she creates another ratio to represent this information, using
s
as her stand-in for the length of the shortened scarf:
Now she’s ready to create the proportion, and it is
Ann looks carefully at the equation she’s created. Does it really express an equality? She needs the numerators to be “like items” (the numbers of skeins) and the denominators to be “like items” (the lengths of the scarves). Satisfied, she moves on.
To solve the proportion, Ann just needs to cross multiply. She’ll have to multiply the numerator of the first ratio by the denominator of the second ratio and the numerator of the second ratio by the denominator of the first ratio. (That’s a lot easier
done
than
said
, actually!)
Now she can solve for
x
by dividing each side of the equation by 6.