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We're asked to add 4/9 and 11/12[br]and to write our answer

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as a mixed number, and then[br]simplify and write our answer

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as a mixed number.

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So here we have two fractions[br]we're adding together, but we

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have different denominators.

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So whenever you add fractions,[br]the first thing you have to do

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is check the denominators.

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If they're the same, you can[br]add, but if they're different

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like this, you have to make[br]them have the same

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denominator.

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So what we have to do is find[br]a number that both 9 and 12

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will divide into, and that[br]will be our common

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denominator, and you'll see[br]why both 9 and 12 have to

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divide into it.

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So let's think about what that[br]number is, and there's two

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ways of coming up with that[br]what we could call a least

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common multiple, the smallest[br]multiple of both 9

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and 12 that is common.

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One way is just to kind of look[br]at the multiples of 9 and

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see if any of them are[br]divisible by 12.

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So if you start with 9--[br]we can do it over here.

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So you have 9, that's[br]not divisible by 12.

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18 isn't divisible by 12.

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27 isn't divisible by 12.

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36, well, that is[br]divisible by 12.

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That is 12 times 3.

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So 9 goes into 36 and[br]12 goes into 36.

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So what we want to do is write[br]a common denominator.

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So we're going to write 4/9 as[br]something over 36, and we're

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going to write 11/12 as[br]something over 36.

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Now, to turn your 9 into[br]a 36, you have to

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multiply it by 4, right?

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9 times 4 is equal to 36.

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Now, you can't just multiply[br]the denominator by 4.

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You also have to multiply the[br]numerator by the same thing.

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So if you multiply the numerator[br]by 4, you get 4

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times 4 is 16.

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So 4/9 is the exact same[br]thing as 16/36.

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If you wanted to simplify this[br]one to 4/9, you divide the

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numerator and the denominator[br]by 4.

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Now, we do the same[br]thing over here.

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36, 12 times 3, so we're[br]multiplying 12 by 3 to get 36.

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Well, if we did that to the[br]denominator, we also have to

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do that to the numerator,[br]so 11 times 3 is 33.

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And just like that, we've now[br]rewritten each of the

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fractions so that they have[br]the same denominator.

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Both of their denominators[br]is 36.

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So now we're ready to add.

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If you add these two things,[br]we'll have 36, because we're

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considering kind of parts of[br]36 or fractions of 36, and

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then we have 16 plus 33[br]in the numerator.

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Let me write that down.

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16 plus 33 in the numerator.

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And 16 plus 33 is what?

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6 plus 33 would be 39[br]and then you have

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another 10, so it's 49.

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So it's equal to 49/36.

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Now, can we simplify this?

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49, it's 7 squared, so it has[br]1, 7 and 49 as factors.

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This has 1-- it has a bunch[br]of numbers, but it's not

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divisible by 7, so this is[br]actually in simplest form, but

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this is an improper fraction.

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The numerator is larger[br]than the denominator.

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So let's write it as[br]a proper fraction.

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To do that, we divide[br]36 into 49.

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36 goes into 49 how[br]many times?

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Well, it only goes one[br]time, so it equals 1.

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And how much will[br]be left over?

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If I divide 36 into 49 one time,[br]or 1 times 36 is 36,

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then I have 13 left[br]over to get to 49.

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So it's 1 and 13/36.

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And you can do that manually,[br]if you like you.

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You'd say 36 into 49.

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36 goes into 49 one time.

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1 times 36 is 36, and[br]then you subtract.

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9 minus 6 is 3.

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4 minus 3 is 1.

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You have a remainder of 13.

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So that's our answer:[br]1 and 13/36.

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