Video: Solving Rational Number Problems Involving Fractions

The product of two rational numbers is −16/9. If one of the numbers is −4/3, find the other number.

02:28

Video Transcript

The product of two rational numbers is negative 16 over nine. If one of the numbers is negative four over three, find the other number.

So the first thing we’re gonna do is look at a couple of key terms. So we’ve got product, which means multiply. So if we find the product of two numbers, that means we’re multiplying them together. And then we’re also looking at the term, rational. 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. So taking the information we’ve got from the question, what we can do is write it down. And we’ve got negative four over three multiplied by 𝑎 over 𝑏 equals negative 16 over nine. And it’s this 𝑎 over 𝑏 that we’re trying to find.

Well, there are, in fact, a couple of ways we could solve this. So we’re gonna have a look at both of those. So first of all, what we could do is divide both sides by negative four over three. So when we do that, we’ll have 𝑎 over 𝑏 equals negative 16 over nine divided by negative four over three. So then what we can do is divide our fractions. 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. So now, before we multiply, what we can do is divide through by any common factors. Well, first of all, we can divide numerators and denominators by four and then by three.

So now what we’ve got is negative four over three multiplied by negative one over one. Well, a negative multiplied by a negative is a positive. So therefore, what we’re gonna get is 𝑎 over 𝑏 is equal to four over three. So therefore, we’ve found our missing number. And what we can do is check this by using the alternate method. And the alternate method is equating the numerators and denominators. Well, as we know, we’ve got negative four over three in the left-hand side and the result is negative 16 over nine. We know that a negative has to be multiplied by a positive to give us a negative result. So therefore, we know that 𝑎 over 𝑏 will be positive. So we could ignore the signs when we’re gonna equate the numerators and denominators.

Well, if you equate the numerators, we’ve got four 𝑎 cause four multiplied by 𝑎 is equal to 16. So therefore, 𝑎 will be equal to four. So then if we equate the denominators, we’re gonna get three 𝑏 is equal to nine. So 𝑏 is equal to three. So therefore, 𝑎 over 𝑏 is gonna be equal to four over three, which is what we’ve got with the first method.

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