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  • Hi and Welcome to Math Antics.

  • In the last video we learned how easy it is to add and subtract fractions that have the same bottom number.

  • We call thoselikefractions.

  • But often youll be asked to add or subtract fractions that have different bottom numbers, orunlikefractions.

  • And we learned that the only way we can do that is to change our fractions so that they DO have the same bottom number.

  • Alright thenhow do we do that? How can we change twounlikefractions into twolikefractions?

  • How do we get our fractions to have a ‘common denominator’?

  • The answer is, we need to use equivalent fractions! You remember what equivalent fractions are, right?

  • Theyre fractions that have the same value, but use different top and bottom numbers:

  • like 1 over 2 and 2 over 4. They both represent one half, but with different numbers.

  • Well, whenever we have two unlike fractions that we need to add, if we could find equivalent fractions to use instead,

  • AND if those new equivalent fractions had the SAME bottom numbers as each other, then we’d be all set.

  • We’d have twolikefractions and we could add them using our procedure.

  • Okay, but how do we find equivalent fractions that have a common denominator (or the same bottom number)?

  • Well, there’s two main ways of doing it.

  • In this video, were only gonna learn the first way of doing it,

  • and I like to call this wayfinding the easiest common denominator’.

  • In the next video, well talk about another method that some of you may have already heard about.

  • It’s calledfinding the least common denominator.’

  • Okay, so how does thiseasiest common denominator methodwork?

  • Well, even though this is an easy method, it might sound a little complicated at first.

  • But don’t worry. Itll make a lot more sense once youve seen a few examples.

  • In this method, the common denominator is always going to be the product of the bottom numbers.

  • In other words, it will be number you’d get if you multiplied the bottom numbers together.

  • Basically, all were going to do is take the two different bottom numbers, and make two differentwhole fractionsusing them.

  • Then, were going to move thewhole fractionto the opposite sides and multiply them by ourunlikefractions.

  • Doing this will give us two new equivalent fractions that will have the same bottom number.

  • Then we can add or subtract them easily.

  • Okay, let’s try a couple examples so we can see this method in action.

  • Let’s add the fractions 2 over 5 and 1 over 3.

  • These are NOT like fractions because they have different bottom numbers, so were going to change them.

  • And the common denominator we will uses is the product of the bottom numbers: 5 × 3 = 15.

  • We change them by multiplying each fraction by a ‘whole fraction’.

  • The firstwhole fractionis going to be 3 over 3, because 3 is the second fraction’s denominator,

  • and the secondwhole fractionis going to be 5 over 5 because 5 is the first fraction’s denominator.

  • Next, we multiply starting with our first fraction.

  • On the top: 3 × 2 = 6

  • And on the bottom: 3 × 5 = 15.

  • So our first fraction has become 6 over 15.

  • Now for the second fraction

  • On the top: 1 × 5 = 5

  • And on the bottom: 3 × 5 = 15.

  • So our second fraction has become 5 over 15.

  • Now we just add them using our procedure for addinglikefractions. We add the top numbers: 6 + 5 = 11.

  • And then we keep the same bottom number, which is 15.

  • So that means the answer to 2 over 5, plus 1 over 3, is 11 over 15.

  • That’s pretty easy, huh? Alright, let’s see one more example of this method.

  • Let’s add the fractions 7 over 8 and 3 over 10.

  • Our common denominator for this problem is going to be 80,

  • because that’s what we get when we multiply the denominators together: 8 × 10 = 80.

  • Well multiply our 7 over 8 by thewhole fraction’ 10 over 10.

  • And well multiply our 3 over 10 by thewhole fraction’ 8 over 8.

  • Then, when we do our multiplication, the 8 times 10 will give us 80 on the bottom of both fractions.

  • For the top of the first fraction we have: 7 × 10 = 70.

  • And the top of the second fraction we have: 3 × 8 = 24.

  • Now that we havelikefractions, we can just add the top numbers: 70 + 24 = 94.

  • And keep the bottom number the same: 80

  • So… 7 over 8, plus 3 over 10, equals 94 over 80.

  • Some of you see that this answer could be simplified.

  • Be sure to check out our videos on Mixed Numbers and Simplifying Fractions to see how you could do that for your final answer.

  • Alright, that’s the first way you can find the common denominator and change yourunlikefractions intolikefractions so you can add or subtract them easily.

  • Remember, practice is really important in math, so be sure to do the exercises for this section so you really get the hang of it.

  • After that, check out the next video and I’ll show you how to use a different method to find what we call the Least Common Denominator.

  • Thanks for watching and I’ll see you next time.

  • Learn more at www.mathantics.com

Hi and Welcome to Math Antics.

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數學反常學--共同點ECD (Math Antics - Common Denominator ECD)

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    Yassion Liu posted on 2021/01/14
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