| Algebra is a way of figuring, just as arithmetic is. | | | | side by side. All of these are called equations. |
| Both algebra and arithmetic are branches of the | | | | An equation is a statement that two things are |
| science of mathematics. Algebra is the branch of | | | | equal. There are many rules governing equations, |
| mathematics that is studied next after arithmetic. | | | | and when you know them you can "solve" |
| It begins as a kind of shorthand. Suppose you | | | | problems by finding unknown numbers. Algebra |
| have the simple job of adding 4 and 2 together: 4 | | | | goes on to study powers, roots, and series of |
| 2 6 You could also write this: 4 + 2 = 6 and if | | | | numbers. A pon er of a number is the product, or |
| you spelled out the numbers, it would look like | | | | result, you get when you multiply the number by |
| this: Four + Two = Six In algebra you might write | | | | itself, one or more times. It is expressed by an |
| F + T = S -using the first letters of the words to | | | | exponent, a small number written after and higher |
| stand for the numbers, just as George Arthur | | | | than the number. Thus, 32 (when you read it |
| Jones might write his name G. A. Jones. Now | | | | aloud, you say "three squared") means 3 X 3, or |
| suppose you knew that F meant 4, and S meant | | | | 9; 2r> means 2 X 2 X 2 X 2 X 2, or 32 (it is read |
| 6, but you didn't know what T meant. You could | | | | "two to the fifth power"). |
| easily figure out that T must mean 2, because no | | | | A root is the opposite of a power. It is a number |
| other number could be added to 4 to make 6. | | | | that must be multiplied by itself to produce a |
| But this would not be easy to do in your head if F | | | | given number. It is written with a radical sign, as \ |
| and T were numbers like 3,471 or 142,857. | | | | C4 (read "the cube root of 6 4 " ); the answer |
| The purpose of algebra is to put calculations into a | | | | here is 4, since 43 (4 X 4 X 4) is 64. When the |
| form that makes it just as easy to solve | | | | sign is used without a little number, it means |
| problems with big numbers as with small ones, | | | | square root, as V 25 = 5. A series is a group of |
| and with numbers you don't know as with | | | | numbers related by some rule. In an arithmetic |
| numbers you do know. We will go back now to | | | | series, such as 1, 4, 7, 10..., a constant number |
| the first example in which F stood for Four and T | | | | (here, 3) is added to each term to give the next. |
| stood for Two and S stood for Six. E would | | | | In a geometric series, such as 1, 2, 4, 8..., each |
| stand for Eight. Now we could write: S _ F = T ( | | | | term is multiplied by a constant number (here, 2) |
| 6 - 4 = 2) F - r T = T (4 -b 2 = 2) F X T = E ( | | | | to produce the next. Series often provide the |
| 4 X 2 = 8) In algebra, instead of F X T = E you | | | | best way to find out the value of important |
| would write F T = E, because the multiplication | | | | unknown numbers in physics and other sciences. |
| sign is not used when two symbols are placed | | | | |