CHAPTER 11

ABSOLUTE VALUE...

Have you heard of Absolute Value? Well, it is the distance a number is from nil. For example, |2| (absolute value of 2) is equal to 2. Try it on a number line! Simple, huh?

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What do you think |-2| is? If you said -2, then try again. Try it on a number line this time. What did you get? 2 would be correct. The reasoning is that absolute value is the distance from 0.

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THINK!!!!!

TIME TO HONE THOSE SKILLS!

• |7|
• |-68|
• True or False: |8| > |-9|
• |-787868779986.673738|

OPERATIONS

The rules for multiplication and division of integers are the following:
-2 x -2 = +4
-2 x +2 = -4
+2 x +2 = +4
+2 x -2 = -4
See a pattern? If they are the same sign then the answer is positive. If the signs are different then the answer is negative.

Those rules apply to both multiplication and division, but not addition or subtraction. We'll get into them later. But do you know how to deal with exponents? For example, -2 squared is -(2x2) which is -4. But parentheses hold some say in this. (-2) squared is (-2) x (-2) which is +4. PARENTHESES POWER!

The addition and subtraction rules are simple. 17 + (-7) is the same as 17 - 7. This is true because the plus and the negative sign multiply, and as you already know, makes minus. -17 + 7 gets a bit hairy, but if you do it on a number line, you can easily get -10. These rules can be combined to get -17 + (-7) which is -17 -7. This can be taken further and be simplified to -24.
Or, -17 -(-7) is -17 + 7, which you know. Simple, right?

TIME TO HONE THOSE SKILLS!

• -76 -(-76)
• 2 + (- 43)
• 15/-3
• 14 x -17
• -2 x -7

VELOCITY AND SPEED

Do you know what speed is? It is how fast an object is moving. But can speed be negative? No, but velocity can. Speed is just how fast something is going, so if you think about it, it's logical it's only positive. Velocity has the direction built-in, so if an object is traveling downwards at 50 mph (speed) then the velocity would be -50 mph.

TIME TO HONE THOSE SKILLS!

• Velocity is -8382 feet per second. Find the speed.
• Speed is 618 mph. Can you tell the direction?
• What direction is an object traveling if it is at -737 mph (velocity)
• Why do you think speed doesn't show direction?

GOOD LUCK!