WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com; this next lesson is on subtracting integers.
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The previous lesson was on adding integers.
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What we are going to do first in order to subtract integers is
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use a two-dash rule to change the subtraction problem to an addition problem
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because adding integers is always a lot easier than subtracting integers.
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We are going to use the two-dash rule.
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What that is is in order to change the minus sign to a plus sign, you are going to add a dash to it.
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For example, if I have 3 minus 5, first step, I have to make two dashes.
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The first dash is to make this minus sign a plus sign.
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That is the whole point--to change the minus to a plus.
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I am going to use the first dash to make that a plus.
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Then I have to make two of them.
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My second one will be to make this a negative.
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My subtraction problem is now an addition problem.
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Another example, if I have 3 minus -5.
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This is a minus; this is a negative.
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The first dash is going to make this minus a plus.
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Since I have to make two dashes, this is already a negative.
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My second dash would be to make that a positive.
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3 minus -5 would be the same as 3 plus 5.
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If I have -3 minus 5, this right here would be just a -3.
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That is not a minus problem.
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The minus is right here because it is -3 minus the 5.
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When you use a two-dash rule, you are not going to be using it for negative signs.
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All you are doing is changing the subtraction problem to an addition problem.
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You are not going to use two-dash rule for this one up here.
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But you are just using it for the minus sign; it will be one, two.
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That is your subtraction problem to an addition problem; then you just add the integers.
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If you remember from last lesson, when we add integers,
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if we have the same sign here, if it is the same sign,
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if this is a negative and this is a negative, then we can combine these numbers.
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We can add the numbers which is 8; or take the absolute value.
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Remember absolute value takes the distance from 0.
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-3 is 3 from 0.
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Absolute value must be a positive number because distance...
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if you are looking at how far away -3 is from 0... here is 0, 1, 2... here is -3.
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How many units away from 0 is it?--it is 3.
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Whenever you measure distance, it cannot be a negative; it has to be a positive.
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The absolute value of -3 is 3; the absolute value of -5 is 5.
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If you add those, it is going to be 8.
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But then be careful because you have to give it the same sign.
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This is a negative; this is a negative.
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Then this is going to be a negative; -3 plus -5 is -8.
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If you look at these problems right here or this one, let's do this one first.
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This one doesn't have a sign in front it.
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But it is a positive because numbers are going to be either positive or negative.
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If there is no negative sign in front of it, then it has to be a positive.
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This is a +3 plus a +5.
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That is just the same thing as 3 plus 5 which is 8 or +8.
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For this one, their signs are different; this is a +3 plus a -5.
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Since their signs are different, again you take the absolute value.
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This is 3; absolute value of this is 5.
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Instead of adding them, you are going to subtract them.
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You are going to find the difference; that is 2.
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Then you take the number with the greater absolute value which is this one right here.
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Get that sign; give it to this one; the answer is -2.
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If you don't remember how to do this or if you want to look at a few more examples,
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we are going to do a few more here for this lesson.
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But you can also go back to the lesson on adding integers.
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The first set of examples is to rewrite the subtraction problem to an addition problem.
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This one, the first one is 5 minus 9.
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We want to use the two-dash rule.
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The two-dash rule is strictly just used to make a subtraction problem to an addition problem.
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Later when you start getting really comfortable with these kind of problems, you won't have to use the two-dash rule.
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The two-dash rule is just to make the problems a lot easier.
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For here, the first dash I am going to make is to make that minus into a plus.
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That is the first one.
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My second one that I have to make will be to make that one a negative.
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Now we have 5 plus -9.
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Now that it is a plus problem, we have to add these two integers.
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But they have different signs; this is +5; this is a -9.
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We take the absolute value; the absolute value of 5 is 5.
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The absolute value of -9 is 9; remember their signs are different.
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So we find their difference.
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Absolute value of 5 plus absolute value of -9 is going to be...
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I am sorry... this is a minus; let me just make that a minus.
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This is going to be 4; it is a 4.
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But remember again you have to figure out which one...
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If this is a 5 and this is a 9, this is the bigger number.
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You look at the sign that goes with that number; it is a negative.
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You are going to give that negative sign to the answer; it is -4.
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This next problem, we have a minus negative; it is -10 minus a -4.
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Again the first dash will be to make this one into a plus.
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The second dash... for this problem, we made it into a negative.
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But it is already a negative; we have to make that into a plus.
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Again you are not going to use the two-dash rule for this negative sign up here.
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It is only to make this a plus.
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Whenever you do the two dash rule, it has to be right in there.
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-10 plus 4; this is -10 plus 4; that is the same thing.
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Plus positive is the same thing as just plus.
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I don't have to put my positive sign.
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Again they have different signs.
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The absolute value of 10 minus the absolute value of 4 is 6.
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Which one has the greater number?
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The absolute value is going to be this one right here.
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You are going to take that same sign and give it to this.
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Be careful with the signs because you can get this number right.
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But if the sign is wrong, then the answer will be wrong.
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You have to make sure you have the correct sign along with the correct number.
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The next one, you are just finding the difference.
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Again we are going to use the two-dash rule to make that a plus and then there.
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They are different signs, a positive and negative sign.
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We are going to find the difference of their absolute values which is 7.
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You are going to give that a negative sign because the 11 is the greater absolute value.
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You are going to give that a negative.
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The next one, again you are going to make this a plus and then a plus.
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-5 plus 5; this is -5 plus 5;
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-5 plus 5, again they are different signs; you take the absolute value.
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That is 5; minus the 5 is 0; this is just 0.
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If you have +2 minus 2, that is 0.
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A -5 plus a 5, if you have opposites, then it will just be 0.
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Next one, 32 minus 9, make this a plus negative; they have different signs.
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I take the difference of the absolute values.
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This is 32, the absolute value; this is 39.
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If I find the difference of that, it is 7.
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With that negative sign belonging to the 39, to the greater value, that becomes a negative.
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For this, absolute value of -15 minus absolute value of -9.
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The absolute value of -15, how far is -15 from 0?--it is 15.
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You can also think of it, whenever you take the absolute value of something, it is just the positive of that number.
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If it is -15, then the positive of -15 is 15.
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Minus... this is not inside the absolute value sign.
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This doesn't change; this has to stay the same; absolute value of -9 is 9.
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15 minus 9, that is 6; we don't have to change this.
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If you want to, you can change this minus to a plus using the two-dash rule.
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But 15 minus 9, we know that that is just 6.
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The last couple examples; here we have -3 minus -8 plus 5.
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The first thing I want to do is -3 minus -8;
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I want to solve this first; but I have a minus.
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Remember we want to change our subtraction problems to additions problems.
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We do that by using the two-dash rule.
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For the two-dash rule, the first step will be to make that minus into a plus
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because that is the whole point of using it.
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The minus will change to a plus.
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Then I have to make one more little dash either to make this a negative or make it a plus
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because it already is a negative so I have to make that a plus.
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I change -3 minus -8 to -3 plus 8; -3 plus 8.
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Plus positive is the same thing as just plus; -3 plus 8.
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-3 plus 8, again they have different signs.
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This is a negative; this is a positive.
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I am going to take the absolute value.
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If it is different signs, then you are going to take the difference of the absolute values.
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-3, the absolute value of that, which is the distance from 0, how far away is -3 from 0?
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That is 3; this absolute value is 8.
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When you find how far apart they are from 8 and 3, the absolute values, you get 5.
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This is 5.
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You look at which number has the greater absolute value; that is 8.
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You are going to give it the same sign as that number.
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Since 8 is a greater number, it has the sign of a positive.
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You are going to give that 5 a positive sign.
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We don't have to write the positive sign.
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If you just don't write anything, then that is the same thing as giving it a positive sign.
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This right here became 5; then I have to do 5 plus this 5.
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My answer is going to be 10.
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The last example, this is 4 minus 10 minus a -9.
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I am going to solve that first.
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Again since it is a subtraction problem, 4 minus 10,
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I am going to change that subtraction to an addition problem by using the two-dash rule.
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The first dash will be to change this minus to a plus.
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My next dash is going to make that into a negative.
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Remember both dashes have to be within those two numbers.
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You can't make this number negative instead of this number.
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Both dashes you make are going to be within the two numbers.
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It is 4 plus -10; again their signs are different.
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This has no sign which means it is a positive; +4 plus -10.
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They have difference signs which means you are going to take the difference of the absolute values.
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This is 4; this is 10; their difference is going to be 6.
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This has the greater value; it has the sign of a negative.
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That is going to go there too.
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Then I am going to do that; -6 minus a -9.
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Again we have a minus problem.
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I am going to change this to addition by doing that; that is 1.
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It is already negative; I have to make that a +2.
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-6 plus +9, opposite signs; they are different signs so you find the difference.
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This is 6; this is 9; they are 3 units apart.
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Which one has the greater value?--the 9; that has a positive sign.
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This is going to be a positive sign; the answer is +3.
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That is it for this lesson on subtracting integers.
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If you want to go back and review over some more problems, the previous lesson on adding integers,
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that will probably help you freshen up a little bit for the next lesson.
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Thank you for watching; we will see you soon.