WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com; this next lesson is on multiplying integers.
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When you multiply integers, it is very important to keep in mind that
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if one of the two numbers is negative, then your answer is going to be negative.
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If both numbers are negative, then your answer will be positive.
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Very different than when you add or subtract integers.
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Make sure you keep that rule in mind; this is very important.
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If only one number is negative, if you have one negative sign in the problem, then the answer will be negative.
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If you have two numbers, think of it as those two numbers cancel the negatives out.
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The product will be a positive; one number, then the answer will be negative.
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If it is two numbers, then the answer will be positive.
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If I am going to multiply let's say A and B together,
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if I multiply A times a ?B, then my answer is going to be... this is a positive.
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Remember there is no sign in front, then it is a positive.
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Positive times negative is going to be negative; this is ?AB.
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Or if I have ?A times ?B, we have two negatives signs.
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My answer will be a +AB.
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Let's do a few examples; the first one, -5 times 7; -5 times 7.
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We are going to multiply these numbers the same way; 5 times 7 is 35.
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I only have one negative sign.
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From the two numbers that I am multiplying, only one is negative.
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My answer will be a negative.
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This one, -8 times -4, I know that is a 32.
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I have two negative signs; two negatives signs gives me a positive.
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Another way to think of it, if you have an odd number of negatives in the problem,
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then your answer, your product will be a negative.
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If you have an even number of negatives, like 2, 4, 6, 8, then your answer would be a positive.
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Every two negatives cancel each other out to make a positive.
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Even if you are multiplying four numbers together and they are all negatives, you have four negative signs.
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That is going to give you a positive answer, a positive product.
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3 times -10; 30; I have only one negative sign; that is a negative product.
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What about this one?--this one, the answer is 60.
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If I multiply these two numbers, a positive and a positive.
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This doesn't change; this is just 12 times 5 is 60.
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There is no negative signs involved.
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20 times -12; 20 times 12 is 240.
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We have one negative sign right here; positive times a negative is a negative.
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This next one, 11 times 10 is 110.
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A negative sign times a negative sign, we have two negatives.
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That makes a positive; +110.
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Again when we are multiplying two numbers, we have only one negative sign.
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If only one of the numbers is negative, then the product will be a negative.
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If you have two negative signs, it is going to become a positive.
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In this problem, 7 times 9 is 63.
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I have a positive here; I have a negative here.
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I have one negative sign; that is going to make my answer a negative.
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This next problem, I have a few things I have to solve out.
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But the first thing I always solve out is parentheses.
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I must solve my parentheses first; this is order of operations.
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Order of operations says parentheses; I have parentheses right here.
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I am going to solve this out; that is -7 minus a 3.
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From the previous lesson on subtracting integers,
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I want to use the two-dash rule to make this subtraction problem into an addition problem.
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I am going to do that; keep this in parentheses.
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-7; make this a plus; then a negative; this becomes -7 plus a -3.
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They have the same sign; I add the numbers and keep that same sign.
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The absolute value of -7 is 7; plus the absolute value of -3 is 3.
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If I add those two numbers together, I get 10.
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But then since they are both negative, I have to keep that same sign.
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This rule is very different than multiplying integers.
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Always keep in mind what you are doing.
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Are you adding integers?--are you subtracting?--are you multiplying?
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The next lesson is going to be dividing integers.
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For each of them, think of the different rules; just keep practicing the problems too.
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This was -10; I still have another parentheses I have to solve out.
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This one right here is already an addition problem.
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We don't have to change this problem like we did this one because it is already a plus right here.
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The whole point of changing this was to make it a plus.
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A -15 plus 8, they have different signs.
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We are going to take the difference of their absolute values.
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-15, the absolute value of that would be 15.
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The absolute value of 8 is 8.
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If you find the difference of 15 and 8, that is 7.
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The sign, we take from this one, the 15; that sign is a negative.
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I give this a negative; just going to write this out again right here.
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-10 times a -7; 10 times 7 is 70.
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Then I have a negative times a negative; I have two negatives.
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That is going to make my answer, my product, a positive.
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Think of two negatives cancelling each other out; that is going to be +70.
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That is it for this lesson on multiplying integers; thank you for watching Educator.com.