So far in this course we seen the operations of addition, subtraction, multiplication and division. We've also looked at some other symbols like parenthesis and brackets. There's actually another type of symbol we're going to learn. It looks like this. Now, I'm not going to tell you what this means, we're actually going to try and figure that out together. So, let's try and figure this out through a story I asked 4 people at udacity, how many candies were in a jar. The person with the closes guess got to keep the whole jar. Here's what they said, Katie said 743, Kogure said 728, Andy said candies in the jar. Knowing this information, who won the jar.
Okay, so we want someone with the closest answer to the number of candies in the jar. So I could do the number of candies in the jar minus the number of candies guessed. So for Katie there were 734 candies in the jar minus 743, her guess. I have +734 and -743. I know that this number is more negative. It's 9 more negative, so I have -9. For Kogure I had guess, and I got 6. For Andy he was off by with these results. We want to know who's the closest to the number of candies in the jar. Katie's guess was off by 9. She guessed 743 and she was actually over by negative sign means we were over our guess. Kogure was 6 candies off. She was under, she guessed 728. 728 is less than mean that she was under. Andy guessed 714 and that was 20 candies away from the answer. Kathleen was also over. She guessed 746, so she was 12 units above. The positive and negative mean something in this context. The negatives mean that we were above the guess, like Katie and Kathleen. For Kogure and Andy however, they guessed below the number of candies in the jar. So they wound up with a positive answer, based on our model. Remember, I shouldn't really care about the negative and positives here. I just want to know, who was the closest to the number of candies in the jar. I'm only concerned with how far away everyone's guess was from 734. I don't care if the result was negative or positive. If I want to know the absolute difference, I should use absolute value. This is the symbol we saw at the start of this lesson. Absolute value is the distance from 0. It just says how far away we are from 0. So Katie's guess was really 9 candies off. Kogure's guess was 6 candies off. Andy's guess was units off. Notice that the absolute value took the positive result of all the numbers. Let's look at this in another example.
So the true meaning of absolute value is the distance from 0. Let's take a closer look at this. If I had the absolute value of 6, I would want to know the distance of here's 0 and here's 6. If I count the distance from 0 to 6, I know I go 1, 2, 3, the absolute value of 6 is 6. For -9 I want to find the distance of -9 from 0. Here's 0 and here's -9. If I count the distance, or units, from 0 to -9, I know that I'll go 9 units all together. So, this distance is 9. The absolute value of -9 is 9. For absolute value, I know that absolute value will always be positive. I'm referring to distance.
Let's try a quiz. I want you to find the absolute value of these numbers. You can put your answer in these boxes.
Okay for the first one I'm at 5, positive units away from 0, so I get 5. -8 is right here, I know it's 8 units away from 0. So this answer is +8. Remember the distance, or the absolute value, is always positive. Here's -5. And just like the first one, that's also 5 units from 0. So I get 5. For 5+2, I'm going to move 5 units to the right. So I'd be right here at 5. And then I'm going to go 2 more to the right because I have 5+2. So I end up at 7. Whenever you have expressions inside absolute value, you want to simplify them first, just like parentheses and brackets. I would have is 7. For 2-5, I'm going to start by going +2. Notice that when a sign isn't present, it's always positive, so +2. Then I have to move 5 units to the left. 1, 2, 3, 4, have the absolute value of -3. I'm trying to find the distance of -3 from 0. And I know that's just 3 units. Alright, nice job on that quiz.
Let's try out this quiz. I want you to find the value of this expression. I have -|8-5^2|. You can put your answer in this box. Good luck.
When solving this problem I'm going to start within the absolute value bars. Remember, I have a negative one on the outside, and then, I need to do the exponent first. So I have 8-25. 8-25 is -17. So I have negative one times the absolute value of -17. The absolute value of -17 is positive So I have -117. Remember, when I do the absolute value of a number, I want the positive result or the distance from zero and I don't have to put the absolute value bars anymore. -117 is -17. If you got -17, nice work.
For the second problem, I have, two times the absolute value of the negative of five squared times negative two minus one times the quantity six minus six squared. You can put your answer in this box here.
Okay, for this 3rd problem I have the negative of the absolute value of 3 ^ 3 or ^ 2 and this quantity is cubed, or raised to the 3rd power. Remember start with the inside parentheses first and then work your way out. You can put your answer in this box here. Good luck.
For this fourth problem, I have the negative of the absolute value of the quantity (-3 5)^2 - 10^2. And again, put your answer right here.
For our last problem, I have the quantity of (4-10)^2+3^2 minus the absolute value of five times the quantity negative four times 1 plus 2, and this whole quantity in the brackets is squared. I know this seems like a lot, but if you work carefully and start from the parentheses you can figure this out. Good luck.