Dividing a Fraction by a Fraction

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Two fractions can be divided by one another the same way you can divide a whole number by another whole number. Learn about dividing a fraction by a fraction with help from a mathematics educator in this free video clip.

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Hi, I'm Jimmy Chang and we're here to talk about dividing a fraction by a fraction. Now, one of the things you want to keep, keep in mind, when it comes to dividing fractions it's actually a multiplication problem, except that you've gotta think about the denominator and the definition of what a reciprocal is. So, here's a couple of illustrations to show you. Suppose you have 2/5ths divided by 4/7ths. Now, dividing by 4/7ths, is actually another way of saying multiplying, and here's what we talk about. You take a look at the denominator which is 4/7ths and you're going to have to think about, what is the reciprocal? When we think about reciprocal, we're thinking about flipping the fraction. Now, the reciprocal of 4/7ths, if you flip it, it becomes 7/4ths. So, when you're dividing by 4/7ths, you're actually multiplying by the reciprocal of that, which is 7 over 4. Now, from here, you have a multiplication problem and then you can decide whether to multiply and reduce later or reduce now, and then multiply. So, in this particular case, maybe to save a little bit of time, let's see if we can reduce anything. As you can tell, the 2 and the 4 reduces by 2. So, 2 divided by 2 is 1, 4 divided by 2 is 2 and then you can multiply across. 1 times 7 is going to give you 7, and 5 times 2 is going to give you 10, so what that means here is, 2/5ths divided by 4/7ths is going to give you 7 over 10. Now, here's another example. Suppose you have 8/11ths, divided by, let's throw a negative in here, negative, 4/13ths. Same kind of idea. You take 8/11ths, but then you have to analyze the denominator, and you're dividing by a fraction, you're multiplying by the denominator's reciprocal, so the reciprocal of negative 4/13ths is negative 13 over 4. Same idea, you can multiply and reduce later, or you can reduce now and then multiply later. So looking at what we have, 8 and the 4 are reducible by 4 each. So, 8 divided by 4 is 2, 4 divided by 4 is 1, and then you multiply across. So, 2 times negative 13 is negative 26, 11 times 1 is 11 and so when you divide 8/11ths by negative 4/13ths, you will really get negative 26/11ths. So, I'm Jimmy Chang and there's a couple of examples on dividing a fraction by a fraction.

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