I Used to Know That_ Stuff You Forgot From School - Caroline Taggart [17]
MATH
Remember when you used to harangue your parents about why you needed to know “this stuff”? It was only later that you found out why as you wrestled with the challenges of chemistry, engineering, physics, architecture or more ordinary kinds of problems such as figuring your income tax and balancing your checkbook. That math you found so useless as a child is not so useless after all, is it? But perhaps over the years you have found yourself floundering for some of those rules and answers you might have known if you hadn’t been doodling on your notebook during class. Well, flounder no more.…
Arithmetic
Arithmetic is all about sums—adding, subtracting, multiplying, and dividing—each with its own vocabulary:
• If you add two or more numbers together, their total is a sum. So 7 is the sum of 4 + 3.
• With subtraction you find the difference between two numbers. The difference between 9 and 7 is the smaller number subtracted from the larger: 9 - 7, and the difference is 2.
• If you multiply two or more numbers together, the answer is a product. So 30 is the product of 6 x 5.
• With division you divide a divisor into a dividend and the answer is a quotient. If there is anything left over, it is called a remainder. So 15 divided by 2 gives a quotient of 7 with a remainder of 1.
☞ LONG MULTIPLICATION
If you are old enough to have taken math exams without the aid of a calculator, you will have learned the times tables. The easiest one is the 11 times table because it goes 11, 22, 33, 44, and so on—but it all goes a bit wrong after 99. Many people learn by rote up to 12 x 12 = 144; beyond that a person really needs to understand what they are doing. For example:
After the number 9, you have to use two digits. The right-hand digit in any whole number represents the units; to the left are the tens and then the hundreds and so on. So 63 is made up of 6 tens, or 60, plus 3 units. And in this problem, you need to multiply 147 by each of those elements separately.
Start from the right: 3 x 7 = 21, so you write down the 1 and “carry” the 2 to the next column;
3 x 4 = 12, plus the 2 you have carried = 14. Write down the 4 and carry the 1;
3 x 1 = 3, plus the 1 you carried = 4.
So 3 x 147 = 441.
To multiply 147 by 60, put a 0 in the right-hand column and multiply by 6 (because any number multiplied by 10 or a multiple of 10 ends in 0);
6 x 7 = 42, so write down the 2 and carry 4;
6 x 4 = 24, plus the 4 you have carried = 28. Write down the 8 and carry 2;
6 x 1 = 6, plus the 2 you have carried = 8.
So 60 x 147 = 8,820;
63 x 147 is therefore the sum of 60 x 147 (8,820) and 3 x 147 (441), which equals 9,261.
Or
Songwriter and mathematician Tom Lehrer plays a tune about New Math, in which he does his problem in base 8. If you do a search on Youtube.com for Lehrer’s New Math, you’ll see why this section avoids that technique.
☞ LONG DIVISION
Division is multiplication in reverse, so start with 9,261 and divide it by 63.
If you have a divisor of 12 or less, the times tables does or did the work for you: You know or knew that 72 divided by 8 was 9, without having to work it out. But with a number larger than 12, you need to be more scientific:
With division you work through the number from left to right.
You can’t divide 63 into 9, for the simple reason that 63 is larger than 9. So look at the next column. You can divide 63 into 92—once—so you write a 1 at the top of the sum. But it doesn’t go into 92 once exactly—there is a remainder, which is the difference between 92 and 63; in other words, 92 minus 63, which is 29.
Carry 29 forward into the next column and put it in front of the 6 to give you 296. Does 63 go into 296? Yes, it must, because 296 is bigger than 63, but how many times? Well, look at the left-hand figures of the two numbers and you’ll see something that you can solve using the times table: