Number Sense: Drill Set 6, Problem 4. On a number line, the distance between the integers -12 and 10 can be expressed by which of the following?
|Basic Operations||Absolute Value|
|CAHSEE Math||Number Sense|
|Number Sense||Absolute value|
OK, this question is really just asking about
number lines and absolute values.
For starters, we have to draw a little picture.
The number line looks like this... and the -12 is here.
The positive 10 is here...
and you can see that there are 22 hops, skips, or jumps between the two points.
So now we just have to figure out which of our answer choices equals 22...
...keep in mind that those straight line bar thingies, otherwise known as absolute value symbols...
...will take the positive value of anything inside of them.
Let's just brute force our way through the problem...
...and we see that A is -12 plus ten and it gets us back to only 2 skips away from the origin.
Remember we need 22. Distance skipping, not a sprint.
OK, B. We go 10 forward then 12 backward -- and we're only 2 skips away from the origin.
If we apply the absolute value function, we are 2 forward of the origin instead of 2 behind
it, but that doesn't help us either way.
Now try C. Twelve steps back then 10 more -- then the absolute value function moves
us 22 steps in the positive direction -- and voila -- we have our answer. Woot.
Just to be sure we aren't missing something, check D and that's -12, which becomes positive 12.
...but then we subtract 10 and again only get 2 skips away from the origin.
So the answer is C. Done.
Doesn't it feel... freeing to find the right answer?