WEBVTT

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Find the sum 3 1/8 + 3/4 + ( -2 1/6)

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Let's just do the first part first,

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This is pretty straightforward.

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We have two positive numbers, let me draw a

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number line , we are going to start with 3 1/8,

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this is 0, then we have 1, 2, 3 and then you have 4.

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3 1/8 is going to be right about there

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so let me just draw its absolute value

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3 1/8, is going to be 3 1/8ths to the right of 0

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So it is going to be exactly that distance

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from 0 to the right.

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The length of this arrow, you could view it as 3 1/8th.

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Now, whenever I like to deal with fractions

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especially when I have different denominators

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i like to deal them with improper fractions,

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it makes the addition, and the subtraction,

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and actually the multiplication and divison a lot easier.

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So 3 1/8 is the same thing as

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8 times 3 is 24 plus one is 25 over 8.

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which is the same thing as 3 1/8.

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Another way to think about it,

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3 is 24 over 8,

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and then add 1/8 to that,

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so that you get 25/8.

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So this is our starting point.

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To that we are going to add 3/4,

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we are going to move another 3/4

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to the right, this length of this is 3/4

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So plus 3/4.

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Where does this put us,

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so both of these are positive intergers,

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so we can just add them,

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we just have to find the like denominators

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we have 25/8 + 3/4. That's the same thing as,

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we have to find the common denominator here,

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the common denominator, or the least common multiple

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of 4 and 8 is 8, so it's going to be something over 8.

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To get from 4 to 8, we multiplied by 2,

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so we have to multiply 3 by 2 as well.

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So we get 6,

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so 3/4 is the same thing as 6/8.

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So we have 25/8, and we're adding 6/8 to that,

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that gives us 25 plus 6 is

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31, over 8.

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So this number right over here is 31/8

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And it makes sense, because 32/8 will be 4,

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so it should be a litte bit less than 4

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So this number right over here is 31/8

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or the length of this arrow,

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the absolute value of that number

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is 31/8.

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If you want to write it as a mixed number, it would be

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3 7/8.

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Now to that we want to add a -2 1/6.

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So we're going to add a negative number.

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So think about what -2 1/6 is going to be like.

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Let me do this in a new color, do it in pink.

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-2 1/6. So we're gonna subtract, or,

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I guess we should say we are going to add a -1,

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add a -2, and then a -1/6.

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So -2 1/6, we can literally draw it like this.

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-2 1/6, we can draw it with an arrow

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that looks something like that,

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so this is -2 1/6.

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There are a couple of ways to think about it,

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we could just say,

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when you add this arrow, this thing is moving to the left.

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We could put it over here

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and you would get straight to -2 1/6.

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But we're adding this -2 1/6,

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it is same thing as subtracting a 2 1/6;

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we're moving 2 1/6 to the left.

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And we're going to end up with a number

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whose absolute value is going to

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look something like that.

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It is actually going to be to the right,

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so it's not only going to be its absolute value,

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the absolute value is going to be the number,

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since it's going to be a positive number.

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So let's just think about what it is.

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This value right here,

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which is going to be the answer to our problem,

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is going to be the difference of 31/8 and 2 1/6.

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And it's a positive difference,

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because we're dealing with a positive number.

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So we just take 31/8, and

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from that, we will subtract 2 1/6.

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So this orange value is going to be 31/8

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minus 2 1/6.

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So 2 1/6 is the same thing as

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6 times 2 is 12 plus 1 is 13.

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-13/6, and this is equal to --

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once again we're going to get

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the common denominator over here -

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and it looks like 24 will be the common denominator.

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This is the 31/8, and this is the 2 1/6.

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So 31/8, over 24, you have to multiply by 3

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to get the 24 over here,

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so we multiply by 3 on the 31,

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that gives us 93.

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And then to go from 6 to 24,

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you have to multiply by 4,

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I'll do that in another color,

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so you have to multiply by 4 up here as well.

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So 4 times 13, let's see.

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4 times 10 is 40, 4 times 3 is 12,

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so that's 52.

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So this is going to be equal to

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93 minus 52 over 24, and that is,

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3 minus 2 is 1, 9 minus 5 is 4.

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So it is 41/24, positive.

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You can see that here,

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just by looking at the number line.

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This right here is 41/24, and it should be

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a little bit less than 2,

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because 2 would be 48/24.

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So this would be 48/24, and it makes sense

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because we're are a little bit less than that.