WEBVTT
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The product of two rational numbers is negative 16 over nine.
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If one of the numbers is negative four over three, find the other number.
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So the first thing we’re gonna do is look at a couple of key terms.
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So we’ve got product, which means multiply.
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So if we find the product of two numbers, that means we’re multiplying them together.
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And then we’re also looking at the term, rational.
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And what this means is a number that can be written as a fraction with an integer as the numerator and an integer as the denominator, which is gonna help us when we’re gonna try and find the number that we’re looking for.
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So taking the information we’ve got from the question, what we can do is write it down.
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And we’ve got negative four over three multiplied by 𝑎 over 𝑏 equals negative 16 over nine.
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And it’s this 𝑎 over 𝑏 that we’re trying to find.
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Well, there are, in fact, a couple of ways we could solve this.
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So we’re gonna have a look at both of those.
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So first of all, what we could do is divide both sides by negative four over three.
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So when we do that, we’ll have 𝑎 over 𝑏 equals negative 16 over nine divided by negative four over three.
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So then what we can do is divide our fractions.
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And to do that, we can use our memory aid, KCF — keep it, change it, flip it — which is gonna give us 𝑎 over 𝑏 is equal to negative 16 over nine multiplied by negative three over four.
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So now, before we multiply, what we can do is divide through by any common factors.
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Well, first of all, we can divide numerators and denominators by four and then by three.
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So now what we’ve got is negative four over three multiplied by negative one over one.
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Well, a negative multiplied by a negative is a positive.
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So therefore, what we’re gonna get is 𝑎 over 𝑏 is equal to four over three.
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So therefore, we’ve found our missing number.
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And what we can do is check this by using the alternate method.
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And the alternate method is equating the numerators and denominators.
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Well, as we know, we’ve got negative four over three in the left-hand side and the result is negative 16 over nine.
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We know that a negative has to be multiplied by a positive to give us a negative result.
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So therefore, we know that 𝑎 over 𝑏 will be positive.
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So we could ignore the signs when we’re gonna equate the numerators and denominators.
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Well, if you equate the numerators, we’ve got four 𝑎 cause four multiplied by 𝑎 is equal to 16.
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So therefore, 𝑎 will be equal to four.
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So then if we equate the denominators, we’re gonna get three 𝑏 is equal to nine.
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So 𝑏 is equal to three.
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So therefore, 𝑎 over 𝑏 is gonna be equal to four over three, which is what we’ve got with the first method.