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Current time:0:00Total duration:4:33

Topic B: Multiplication and division of integers and rational numbers

Video transcript

let's do a few examples multiplying fractions so let's multiply negative 7 times 3 over 49 so we just you might say well I don't see Fras have a fraction here this looks like a the second integer we just have to remind yourself that the negative 7 can be rewritten as negative 7 over 1 times 3 over 49 now we can multiply the numerators so the numerator is going to be negative 7 times 3 and the denominator is going to be 1 times 49 1 times 49 and this is going to be equal to 7 times 3 is 21 and have a negative one of their signs is negative so a negative times a positive going to be a negative so this is going to be negative 21 you could view this as negative 7 plus negative 7 plus negative 7 and that's going to be over that's going to be over 49 and this is the correct value but we can simplify it more because 21 and 49 both share 7 is a factor that's their greatest common factor so let's divide both the numerator and the denominator by 7 divide the numerator and the denominator by 7 and so this gets us negative 3 in the numerator and in the denominator we have 7 so we could view it as negative 3 over 7 or you could even do this negative 3/7 let's do another one let's take five ninths five ninths times I'll switch colors more on this one that was a little monotonous going all red there five ninths x times 3 over 15 so this is going to be equal to we multiply the numerators so it's going to be 5 times 3 5 times 3 in the numerator and the denominator is going to be 9 times 15 9 9 times 15 9 times 15 we could multiply them out but just leaving it like this you see that there is already common factors in the numerator in the denominator both the numerator and the denominator they're both divisible by 5 and they're both divisible by three which essentially tells us that they're divisible by 15 so we can divide the numerator and the denominator by 15 so divide the numerator by 15 which is just like dividing by five and then dividing by three so we'll just divide by 15 divided by 15 and this is going to be equal to well 5 times 3 is 15 divided by 15 you get 1 in the numerator and in the denominator 9 times 15 divided by 15 well that's just going to be that's just going to be 9 so it's equal to 1/9 let's do another one what would negative 5 9 times negative 3 over 15 be well we've already figured out what positive five ninths times positive 3 over 15 would be so now we just have to care about the sign if we were just multiplying the two positives it would be 1 over 9 but now we have to think about the fact that we're multiplying a negative times a negative now we remember when you multiply a negative times a negative it's a positive the only way that you get a negative is if one of those two numbers that you're taking the product off is negative not 2 if both are positive it's positive if both are negative it's positive let's do one more example let's take let's take five I'm using the number 5 a lot so let's let's do let's do 3 over 2 just to show that this would work with improper fractions 3 over 2 times negative negative 7 over 10 negative 7 over 10 I'm arbitrarily picking colors and so our numerator is going to be 3 times negative 7 3 times negative 7 and our denominator is going to be 2 times 10 2 times 10 2 times 10 so this is going to be the numerator positive times a negative is a negative 3 times 7 negative 7 is negative 21 negative 21 and the denominator 2 times 10 that is just 20 so this is negative 21 over 20 and you really can't simplify this any further