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Rational number operations | Worked example

Sal Khan works through a question on dividing fractions from the Praxis Core Math test.

Video transcript

- [Instructor] We are asked, what is the value of 2 6/7 divided by 3 1/3? And we're told to give our answer as a fraction. So, pause this video and see if you can figure this out. Alright, so, the first thing I would wanna do, if I have to divide fractions, is to not have them expressed as mixed numbers like this. So, let's convert these from mixed numbers into what you could consider to be more pure fractions. Sometimes, folks would call them improper fractions because the numerator will be bigger than the denominator. So, 2 6/7 is the same thing as two plus 6/7, which is the same thing, two is the same thing as 14/7. 14/7 plus 6/7. If you're wondering why did I say 14/7, well, I wanted them to have the same denominator. So, I wanted a seven in the denominator. And so, how many sevenths will make two? Well, I'd need two times seven up here, so that's where I got 14/7 from. So, 14/7 plus 6/7, well, I have a common denominator here, so we're speaking in terms of sevenths. So, I have 14 of something plus six of something, well, now I'm going to have 20/7. So, this first mixed number, I could rewrite as 20/7. And then that's going to be divided by this second mixed number. And so, 3 1/3, I can do the same idea. That's the same thing as three plus 1/3. Now, three, if I want three in the denominator, how many thirds is three? Well, three is 9/3. Another way to think about it, I just took this denominator and I multiplied it by three to get nine. Or you could say nine divided by three is three. So, 9/3 plus 1/3 is going to be equal to 10/3. So, I've just rewritten this quotient, I guess you could say, as 20/7 divided 10/3. And now, we just have to remember how to divide fractions. If I divide by a fraction, that's the same thing as multiplying by its reciprocal. So, this is going to be equal to 20 divided by seven times the reciprocal of this. The reciprocal of 10/3 is 3/10. And that is going to be equal to, there's several ways that we could tackle this. We could try to simplify first or that we could multiply and then simplify. I like to simplify first. Where we see in our numerator, we have a 20; in our denominator, we have a 10; if we divide both of those by 10, the 20 becomes a two, the 10 becomes a one. So, we have two times three in the numerator, which is six; and then seven times one in the denominator, seven. Just as a refresher, when multiplying fractions, you just multiply the numerators and you multiply the denominators. The other way you could've done this, you could've just said 20 times three, which would've been 60, over 70 times 10, which is 70. And then, if you wanted to simplify this in some form, you could divide both the numerator and the denominator by 10, and you would get what we got right over there.