Multiplying Ratios

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You can multiply ratios by following a few basic steps. Get the facts about multiplying ratios with help from a mathematics educator in this free video clip.

Part of the Video Series: Mathematics Equations & More
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Video Transcript

Hi, I'm Jimmy Chang and we're here to talk about multiplying ratios. Now, more often than not, when you multiply ratios, you're multiplying two or more fractions together. So, we're here to talk about a couple of strategies that you can use when it comes to multiplying ratios and it often involves reducing the fractions, either at the end or along the way. So, here we go. Now, let's just say when you multiply two ratios, suppose you have 3/4ths, times, 2/5ths. Now one thing that you can do, is you can multiply first and reduce later. So, let's just go with that route. Now, as you know, with multiplying fractions, you need to multiply across. So 3 times 2 is 6, and then 4 times 5 is 20. Now, where you go from here is, just gotta ask yourself, can this fraction be reduced? So, what you want to think about is, look at the 6 and look at the 20, and ask yourself, well, do 6 and 20 have any numbers that they have in common? In this particular case, 6 and 20 both have a 2 as a factor. So what you can do, is reduce both numbers by the number 2. So, what you can think about is well, 6 divided by 2 is going to give you 3, and 20 divided by 2 is going to be 10. So, 6/20ths, is another way of saying 3/10ths. Just to keep in mind, if you reduce numbers you have to reduce both the numerator and the denominator. Now, the other approach is, you can reduce prior to finishing the problem. So, suppose you have something like, 2/3rds, times, 12/15ths. Now, what you want to think about is, may I cancel or reduce in terms of the numerator or in the denominators? So, in other words, looking at the numerators, will any of the numbers reduce with any of the denominators? You can, what we call, cross cancel or directly cancel. Now, as you can tell, 2 does not reduce into 3, and 2 does not reduce the 15, so nothing can be done with the 2 right now. But if you take a look at the 12, 12 and the 3 will reduce. In fact, 12 divided by 3 is going to give you 4. So, we're going to reduce. 12 divided by 3 is going to be 4, and 3 divided by 3 is going to be 1, and what's left over, 4, does not reduce the 15, so now what this does, is, if you reduce along the way, you don't have to reduce at the very, very end because you've already done the work. So, what you have to do now, is simply multiply across, with the modified numbers. So, 2 times 4 is going to give you 8, and 1 times 15, is going to be 15. So, in actuality, 2/3rds times 12/15ths, after the reductions, gives you 8/15ths. So, whether to reduce at the end or reduce along the way, it's completely up to you, as long as you get it in simplified form. So, I'm Jimmy Chang and that's multiplying ratios.

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