Questions on Dividing Fractions

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When dividing fractions it is common to have a few questions along the way. Get answers to questions on dividing fractions 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 discuss questions on dividing fractions. Now, one of the things you want to really keep in mind, and this is what sets apart, you know, fractions from other kinds of numbers, is that when you're dividing fractions, you're actually multiplying them. There's one fundamental step that you want to keep in mind and, that is, focus on the denominator. So, let's do an example and you'll see where this goes. Suppose you have 4/5ths, divided by, let's just say, 2/3rds. Now, when you're dividing a fraction, you, it's actually a multiplication exercise, because it involves taking the denominator, and thinking about it's reciprocal. So, if you're thinking about 2/3rds, the reciprocal of 2/3rds, is 3 halves. So, instead of dividing by 2/3rds, you're going to take 4/5ths and multiplying it by, 3 halves. Now at this particular point, you can either multiply first, and reduce later, or we can reduce along the way, and then multiply. Whatever's easier. But let's just go ahead and cross cancel, as they say, and the 4 and the 2, as you can tell is reducible, so we're going to reduce both numbers by 2, so 4 divided by 2 is 2, 2 divided by 2 is 1, and then you're going to multiply across. 2 times 3 is going to give you 6, and 5 times 1 is going to give you 5. So, in actuality, 4/5ths divided by 2/3rds, is really going to give you 6/5ths in the very, very end. Now let's do another quick example for you. Suppose you have 3/7ths and you're dividing by, let's just say, negative 2. Now if you're dividing by a whole number, what you want to think about is, take the denominator and write a fraction in it's place. So, negative 2, can be thought of, any whole number can be thought of as, that number over 1. So, 3/7ths divided by negative 2, is really dividing by negative 2 over 1, and once again you want to think about it's reciprocal. The reciprocal of negative 2 over 1, is negative 1 half. So this is really going to be 3/7ths, times negative 1 half. And then just go ahead and multiply across if you like, 3 times negative 1 is negative 3, and 7 times 2 is going to give you 14. So, 3/7ths divided by negative 2, is going to be negative 3/14ths. So, I'm Jimmy Chang and that's a couple of examples on questions on dividing fractions.

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