Free Math for Grownups by Laura Laing Page A

of painting it, she’s decided to upholster it with a huge piece of purple velvet. The girl has ambitious plans
and
an amazing sense of style.)
    How does she figure out how much paint she needs? She divides the total square footage by 350, which is the number of square feet that 1 gallon of paint is supposed to cover.
    544 / 350 = 1.55 gallons
     
    But remember, midnight blue will probably require two coats, so Narcissa multiplies by 2.
    1.55 • 2 = 3.1 gallons
     
    No paint store will sell her that exact amount, so Narcissa rounds up and buys 4 gallons of midnight blue paint.
    But she
could
do something else. Remember, there are 4 quarts in 1 gallon. Another way to put this: 1 quart is 0.25 gallon. In this situation, she could buy 3 gallons and 1 quart, because 3.25 gallons (3 gallons + 1 quart) is larger than 3.1 gallons (the amount of paint she needs).
    Now all Narcissa needs is the velvet.
Windows to the Mind
     
    If you’re looking around your living room right now, envisioning what it would look like in midnight blue, you’ve probably spotted something we didn’t take into consideration in our above calculation: doors and windows. Because Narcissa isn’t going to paint the windows in her room (unless she’s
really
into Goth) and probably not the doors, either, shouldn’t she consider subtracting out the square footage of the windows and doors in order to reach a more exact calculation of how much paint she’ll need? If she needs to be extra careful about her purchase, sure.
    Luckily, the experts have figured out two simple rules:
    Most doors are about 20 ft 2
    Most standard windows are 15 ft 2
    Narcissa has 4 windows and 2 doors, so she does these calculations:
Doors
2 • 20 = 40 ft 2
Windows
4 • 15 = 60 ft 2
    So, if we add 40 + 60, we’ll see that the windows and doors take up 100 ft 2 of the room—area that she’s not going to paint. So she can subtract that from the total she found earlier:
    544 - 100 = 444 ft 2
     
    And she can divide by 350 again to find out how many gallons it will take to cover 444 square feet:
    444 / 350 = 1.27
     
    Then she needs to multiply by 2 (for the two coats of paint):
    1.27 • 2 = 2.54
     

Length•Width
     
    You may have noticed that Narcissa used the formula for the area of a rectangle to find the total square feet in each wall.
    A = lw
    A is the area of the wall
    l is the length of the wall
    w is the width of the wall
    Then she added the areas of all the walls to find the
surface area
of her walls.
    In school, you probably spent some time finding the total surface area of solids, such as prisms and pyramids. In these cases, you found the area of each side and then added them together. But sometimes you want the surface area of only some sides—like the walls of a room, but not the ceiling or floor. In this case, you only need to add the areas of the sides that you’re interested in.
    If you think of a room as a three-dimensional figure (specifically, a rectangular prism), it’s easy to see how this would work for all types of 3-dimensional shapes.
    No funny-looking glasses required.
    Narcissa should be just fine with 2½ gallons of paint (in other words, 2 gallons and 2 quarts). That’s quite a bit less than her original calculation!
Switching Up
     
    When Bruno picks up Narcissa to go to the paint store, he looks at her calculations. “You did this wrong,” he mutters glumly.
    Narcissa grabs the paper from his gloved hand and looks again.
    “No I didn’t!” she hollers.
    “Look,” Bruno says, “I remember that Dear Aunt Sally stuff, and you’ve done the math in the wrong order. You have to
multiply
before you
divide
.”
    He grabs the paper from Narcissa’s hand, fishes a stubby pencil from the front pocket of his black jeans, and scribbles down some numbers.
    444 ft 2
    2 coats of paint
    444 • 2 = 888 ft 2
    888 / 350 =
    He stops and scratches his long goatee with the nub of his pencil. “Huh.”
    Narcissa gloats. “See, I did it right,” she says.