CAHSEE Math 6.4 Number Sense

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 OperationsAbsolute Value
CAHSEE MathNumber Sense
LanguageEnglish Language
Number SenseAbsolute value

Transcript

00:20

OK, this question is really just asking about

00:23

number lines and absolute values.

00:26

For starters, we have to draw a little picture.

00:28

The number line looks like this... and the -12 is here.

00:32

The positive 10 is here...

00:34

and you can see that there are 22 hops, skips, or jumps between the two points.

00:38

So now we just have to figure out which of our answer choices equals 22...

00:43

...keep in mind that those straight line bar thingies, otherwise known as absolute value symbols...

00:49

...will take the positive value of anything inside of them.

00:52

Let's just brute force our way through the problem...

00:54

...and we see that A is -12 plus ten and it gets us back to only 2 skips away from the origin.

01:02

Remember we need 22. Distance skipping, not a sprint.

01:05

OK, B. We go 10 forward then 12 backward -- and we're only 2 skips away from the origin.

01:13

If we apply the absolute value function, we are 2 forward of the origin instead of 2 behind

01:18

it, but that doesn't help us either way.

01:20

Now try C. Twelve steps back then 10 more -- then the absolute value function moves

01:26

us 22 steps in the positive direction -- and voila -- we have our answer. Woot.

01:34

Just to be sure we aren't missing something, check D and that's -12, which becomes positive 12.

01:39

...but then we subtract 10 and again only get 2 skips away from the origin.

01:44

So the answer is C. Done.

01:46

Doesn't it feel... freeing to find the right answer?