|
What if I said: |
||
| "I'm thinking of a number, and if you add 2 to it | ||
| you get 5. | ||
| What number am I thinking of?" | ||
| Well that one's not too hard. | ||
| We know that: | ||
|
3 + 2 = 5 |
||
| So the number I was thinking of was 3. | ||
| Math people are always asking questions like that | ||
| (Hey, that's what they do!) | ||
| So they wanted to come up with a quicker way | ||
| of saying stuff like: | ||
| "I'm thinking of a number. If you subtract 4 from it | ||
| you get 2. What number am I thinking of?" | ||
| At first, they got the bright idea to write: | ||
|
? - 4 = 2 |
||
|
And then ask: What's the "?" |
||
|
This particular "?" is 6, because 6 - 4 = 2 |
||
| Using a "?" for the number you were looking for | ||
| worked fine for easy problems, | ||
| but later harder problems they ran into troubles. | ||
| So they decided that instead of a "?" they'd use an "X". | ||
| So stuff like: | ||
|
? - 4 = 2 |
||
| was now written as: | ||
|
X - 4 = 2 |
||
| BUT IT STILL MEANS EXACTLY THE SAME THING. | ||
| OK, | ||
| I'm thinking of a number that if you add 2 to it, you get 6. | ||
| What number am I thinking of? | ||
| With a problem like this, | ||
| we can probably just look at it or count on our fingers | ||
| and say: | ||
|
If X + 2 = 6 then X = 4 |
||
|
Because 4 + 2 = 6 |
||
| But as the problems get more complex, | ||
| we start needing another way to get the answer. | ||
| To deal with hard problems, | ||
| we have a set of rules we can use | ||
| to find the thing we don't know (X). | ||
| So start with a problem like: | ||
|
X - 4 = 2 |
||
| and we want to wind up with: | ||
|
X = (something) |
||
| with the X all by itself, | ||
| The first trick to help us do this says: | ||
|
|
||
| So here, that means we add a 4 to each side | ||
| to "get rid of" the - 4 next to the X | ||
|
|
||
| Let's try a few more: | ||
| Examples: | ||
|
|
||
|
copyright 2005 Bruce Kirkpatrick |
