Free Math for Grownups by Laura Laing Page B

“888 divided by 350 is 2.54. Hah!”
    Why are both of them right? Because it doesn’t matter whether you multiply first or divide first.
    In other words, PEMDAS = PEDMAS (Please Excuse Dark Moods And Songs).
    Remember what I said about there often being different ways to reach the same answer?

Hit the Floor
     
    In the morning, it can be awfully tough to crawl out of bed—and when the hardwood floor is freezing, Micah dreads the thought of leaving his cocoon of blankets.
    He decides it’s time to put in some fluffy shag carpet, with a pile so deep that he won’t be able to see his toes. Heaven!
    But Micah doesn’t trust those guys at Budget Carpet. Sure, their prices can’t be beat, but he’s certain they’re making up the difference by overestimating the amount of carpet customers need. He decides to figure out how much carpet he’ll need, before
they
start measuring.
    In short, he needs to know the area of his floor. This would be no problem if his floor were a perfect square—or a rectangle. But it’s not! He has an L-shaped room: the main part, plus an alcove.
    Micah takes some measurements and draws a sketch of his room. Then, squinting, he realizes that his L-shaped room is actually 2 rectangles. That gives him an idea for how to solve his problem. All he has to do is find the area of each of these rectangles and then add them together. Violà! He measures the main part of the room. The length is 15 feet, and the width is 33 feet. He calls the area of this part of the room Area 1, or
A
1 :
    A 1 = 15 • 33
    A 1 = 495 ft 2
    Next he measures the alcove, which is a square that measures 25 feet
by 25 feet. He calls the area of this part of the room Area 2, or
A
2 :
    A 2 = 25 • 25
    A 2 = 625 ft 2
    To figure the total amount he needs, or
A
, he adds together
A
1 and
A
2 :
    A = A 1 + A 2
    A = 495 + 625
    A = 1,120 ft 2
    So Micah needs 1,120 ft 2 of carpeting. What if he wants to carpet his walk-in closet, too? Then he just needs to find the area of the floor and add that to the 1,120 ft 2 he already knows he needs.

Wall to Wallet
     
    What’s the price tag of that gorgeous shag carpet that Micah wants to install? Budget Carpet has a deal for $10.99 per square yard. So he needs to do a little more math to see whether he can actually afford this luxury. His floor is 1,120 ft 2 . How many square yards is that?
    There are 3 feet in a yard, so the calculation is pretty simple. Just divide the number of square feet that you need by 9.
    Wait! Why 9? Don’t you divide by 3?
    Nope. Remember, you’re working with squared units. There are 3 feet in a yard, so there are 9 square feet in a square yard. (Yep, all you’ve done is squared 3—that is, multiplied itself by itself—to get 9.)
    Micah breaks out his trusty calculator and comes up with
    1,120 / 9 = 124.44444444…
     
    Because the decimal is less than ½, he should round down, right? Not so fast. When ordering materials, it’s always best to round up; that way you have a little extra, just in case, instead of not enough. So it looks like Micah might want to order 125 square yards of carpet.
    That means he’ll pay
    $10.99 • 125
    $1,373.75
    And that doesn’t include the installation fees.
    Maybe buying an area rug or a nice pair of wool socks is a better plan.

Subversive Numbers
     
    When Micah was calculating the area of his bedroom, why did he use the little number at the bottom right corner of his variables? Remember how he referred to Area 1 as
A
1 and to Area 2 as
A
2 ? That little number is called a subscript, and it’s how Micah distinguished between the area of his main room and the area of his alcove. In other words,
    A 1 is the area of the main room.
    A 2 is the area of the square.
    A is the total area of the floor.
    But why not use completely different letters? Why not call the area of the main room
m
, the area of the alcove
a
, and the total area
T
?
    You certainly could. But
A
is useful, because it shows that all three results represent