WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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This lesson is on multiplying fractions; that includes mixed numbers.
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If you are multiplying fractions and you do have mixed numbers,
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then make sure to change them to improper fractions first.
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I am going to do a few examples here.
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But if you don't remember how to do that, just go back
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to the previous lesson on switching between mixed numbers and improper fractions.
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Once all of your fractions are either proper fractions or improper fractions,
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then you are going to take the numerators which are the top numbers, multiply them together.
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If we have A/B, A/B which are variables, they are going to represent numbers.
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If this is a fraction, a number over number, times another fraction, C/D,
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then you are going to take this top number, multiply it to this top number.
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You get AC.
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Then you are going to take your denominator, B, and multiply it to the other denominator, D.
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It becomes AC/BD.
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Don't get confused between multiplying and adding and subtracting fractions.
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Remember when we add or subtract fractions, you have to make sure that these denominators are the same.
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For your answer, your denominator is going to be the same as well.
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But in this case when you are multiplying fractions, you are just going to multiply the denominators together.
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Here are some examples, 2/3 times 3/4.
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2/3, that is not a mixed number; 3/4 is not a mixed number.
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I can go ahead and multiply them.
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2/3... I am just going to write it out again... 3/4.
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You can do 2 times 3 which is 6 over... 3 times 4 which is 12.
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6/12, they have a common factor; they have a common factor of 2.
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Or the greatest common factor, the biggest factor that they have in common, is 6.
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I can just divide the top number by 6 and then divide the bottom number by 6.
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This is going to become 1/2; 1/2 is going to be the answer.
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Another way when you have the problem like this,
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I can go ahead and simplify straight from here and get my answer as 1/2.
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I can do what is called cross cancelling.
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If I have a 3 down here and a 3 up there, then I can cross this out because they are the same.
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They can cancel each other out.
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2/4, there is a common factor between 2/4 which is 2.
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I can just divide this by 2; that becomes a 1.
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4 divided by 2 becomes a 2; I can simplify it that way.
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Make sure if you are going to simplify two numbers,
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one of the numbers has to be on the top, one of the numerators.
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Another one has to be on the denominator.
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It doesn't matter if one is on the top up here and the other one is a denominator here
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or one is numerator up here and then the other one is a denominator here.
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As long as one number is the numerator and the other number is the denominator, you can cross cancel them.
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If you multiply 1 times... this is just a 1.
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Then 3 cancels out to make a 1; 1 times 1 is 1.
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1 times 2 is 2; either way you get the same answer.
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In the other example here, I have 1 and 2/5 times 2 and 3/5.
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These numbers, these fractions, are mixed numbers; I have a whole number in the front.
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I have to change this fraction from a mixed number to an improper fraction, 1 and 2/5.
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If I want to change this to an improper fraction, I take my bottom number, my denominator.
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Multiply it to my whole number; it is going to be 5 times 1.
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Then add the numerator; 5 times 1 is 5; plus 2 is 7.
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This becomes 7/5; I have another mixed number here, 2 and 3/5.
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I multiply my denominator to my whole number and then add my numerator.
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5 times 2 is 10; I add the 3; that is 13; 13/5.
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Instead of multiplying this number, the mixed number, I am going to multiply 7/5 times 13/5.
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This is a 5 right here; this is a 5 right here.
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I can't cancel those out because those are both numerators.
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Remember if I want to cancel or simplify numbers, one of them has to be the denominator.
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Another one has to be a numerator; in this case, they are both denominators.
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5 to 13, nothing can simplify; I can't cancel anything out.
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I am just going to go ahead and multiply my numerators.
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7 times 13 is... you can use your calculator if you want.
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7 times 13 is 91 over... 5 times 5 is 25.
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If you look at this, they are not going to have any common factors, 91/25.
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That is an improper fraction, but you can just leave it like that.
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This will be my answer, 91/25.
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Another example, we have 6/5 times 3/4.
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6/5... let me rewrite this problem.
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6/5 is an improper fraction because we know that 6 is bigger than the denominator.
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This is an improper fraction.
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This is a proper fraction because the numerator is smaller than the denominator.
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It doesn't matter; we can still multiply it the same way.
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From here, I can either just multiply it out.
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If you don't feel like checking to see if numbers can cancel or can reduce,
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you can just multiply and then simplify your answer.
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Or you can see if you can simplify any of these numbers.
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5 and 3, they have no common factors; the greatest factor is 1.
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We have to leave those numbers.
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But 4 and 6; 4 and 6 have the common factor of 2.
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I can divide each number by 2 and just simplify that way.
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4 divided by 2 is 2; 6 divided by 2 is 3.
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When you cross cancel numbers, you have to make sure you are going to divide by that same number.
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4 and 6, I have to divide by 2 to both numbers.
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4 divided by 2; it becomes 2; 6 divided by 2; that becomes 3.
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3 times 3 is 9; 5 times 2 is 10.
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9/10, there are no common factors besides 1; that is my answer.
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The next problem is 4 and 1/4 times 5/3.
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This is a mixed number; I need to change that.
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4 times 4, 16; add the 1; that is 17; 17/4 times 5/3.
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Again here I need to check to see if any numbers can cancel out.
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I can't because 17 and 3 have no common factors.
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5 and 4 have no common factors besides 1 of course.
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I can just multiply 17 times 5.
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If you want to do that on the side, let's just do a little multiplication right here.
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7 times 5 is 35; 5 times 1 is 5; plus 3 is 8.
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Again when you have a double digit times a single digit, you are just going to do 7 times 5.
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You are going to put that number, the 3... because it is 35.
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The 3 goes up there; the 5 goes down here.
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Then 5 times this number, 5; you are going to add this number right here.
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5 times 1 plus 3; it becomes 8.
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17 times 5 is 85 over... 4 times 3 is 12; this is my answer.
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Some more examples; I want you guys to try to do these problems on your own.
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You can just pause the video; look at these problems, write them out, and try them.
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After you are done, you can play it again and just check your answers that way.
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This problem, 7/8 times 3 and 2/9.
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7/8 is a proper fraction; and we have a mixed number, 3 and 2/9.
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Times... I need to change this.
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It is 9 times 3 which is 27; plus 2 is 29; 29/9.
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Remember the denominator has to stay the same.
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When you are changing it from a mixed number to an improper fraction, you are going to keep the denominator.
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7 and 9, do they have any common factors?--no.
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8 and 29?--no, they have no common factors.
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You are going to do 7 times 29; let's do that right here.
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29 times 7; 9 times 7 is 63; the 6 goes up here.
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The 3 goes down here below lined up with the 9 and the 7.
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7 times 2 is 14; plus 6 is 20.
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There is no number to carry over.
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You are just going to write both numbers down here, 20; it becomes 203.
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203; 8 times 9 is 72; that is your answer.
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This is an improper fraction; you can leave it like that.
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Or you can change it to a mixed number if you would like.
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If you would like to do that, you would just take the 72.
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See how many times it will fit into 203; you can do that by dividing.
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You could just do 203 divided by 72 and see how many times it will go into there.
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Then you find how many leftovers you have.
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The leftover becomes your numerator; 72 becomes your denominator.
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But otherwise just leave it like this, improper fraction.
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The next example, 5/4 times 9/11.
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Since we are multiplying these fractions, they are both...
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5/4 is improper; 9/11 is a proper fraction; we can go ahead and multiply that
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Let's see; can we cancel anything?
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5 and 11, they have no common factors besides 1.
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4 and 9 have no common factors besides 1.
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5 times 9 is 45; 4 times 11 is 44; that is an improper fraction.
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But we can still leave it like that; that is our answer, 45/44.
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The last couple of examples, we have 3 and 3/7 times 6 and 1/4.
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These are both mixed numbers.
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Remember when we multiply fractions, we have to make sure that the fractions are not mixed numbers.
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We have to change these mixed numbers to make it an improper fraction.
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3 and 3/7, to change this to a mixed number, again I take the denominator of 7.
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I am going to multiply it to my whole number.
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It is going to be 7 times 3 which is 21.
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Then you are going to add the numerator, plus 3.
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It is 7 times 3 is 21; plus 3 is 24.
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You are going to keep the same denominator of 7.
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3 and 3/7 becomes 24/7; they are the same fraction.
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But you are changing it from a mixed number to improper fraction.
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We have to do this one because that is also a mixed number.
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6 and 1/4, I am going to multiply my denominator to my whole number.
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4 times is 6 is 24; add the 1; this is 25/4.
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Now that I converted this to an improper fraction and this one as well, I can now multiply those fractions.
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It becomes 24/7 times 25/4.
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From here, you can just multiply your numerators.
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24 times 25; get your answer; then 7 times the 4; get your denominator.
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Before you do that, you can just see if you can cross cancel any numbers.
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7 with 25, one has to be denominator; the other number has to be the numerator.
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7 and 25, do they have any common factors?
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I know that all the factors of 7 are just 1 and 7.
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It is a prime number; in that case, no.
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They do not have any common factors besides 1.
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4 and 24, 4 and 24, they are both even numbers.
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I know that since the factors of 4 are 2 and 4 and 4 goes into 26, I can reduce these numbers by 4.
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I am going to take these two numbers and divide both by 4.
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4 divided by 4 is 1; 24 divided by 4 is 6.
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Again when you simplify it, you have to make sure that one is on the top and another one is on the bottom.
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Then you are going to see what common factor they have and divide both numbers by that same factor.
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That is the most I can simplify; I need to multiply 6 times 25.
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You are just going to do that on the side; 25 times 6.
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5 times 6 is 30; you put the 3 up here; 0 down there.
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6 times 2 is 12; plus the 3 is 15.
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Since you have no numbers to bring it up, you write the whole number down there.
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150 over... 7 times 1 is 7; this is an improper fraction.
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But you can just leave it like that; that would be the answer.
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The next example, we have 2 and 4/5 times 10/3.
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2 and 4/5 is a mixed number; we have to change that.
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I am going to take my denominator, 5; multiply it to my whole number.
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It is 5 times 2 which is 10; then add the top number.
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That is 14; it will be 14/5 times 10/3.
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Again you can just do numerator times the numerator and get the numerator of your solution.
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5 times 3, that becomes your denominator.
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Or first you can just see if any of these numbers will cancel; let's see.
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14 and 10 have a common factor because they are both even numbers.
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But I can't cancel those out; I can't reduce those because they are both on the top.
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Remember if you want to reduce the numbers, you have to make sure
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that one is on the top and one is on the bottom.
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14 and 3 have no common factors.
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5 and 10 have a common factor of 5.
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I can take both numbers and divide it by that factor of 5.
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5 divided by 5 is 1; 10 divided by 5 is 2.
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You have to make sure that you are going to divide both numbers by that same factor.
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Then you are going to do 14 times 2.
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Now that everything is simplified here, we are going to go ahead and multiply.
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It is 14 times 2 is 28; 1 times 3 is 3.
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This becomes your answer; this is an improper fraction.
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If you want to change it to a mixed number, you can go back a few lessons
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to the lesson where I talk about how to change improper fractions to mixed numbers.
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Just to change this real quick, if you want to change this to a mixed number,
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I have to see how many times the 3 is going to fit into 28.
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How many times 3 fits into 28; I can do that by dividing.
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I do 28... this bar right here means divide.
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I can do 28 divided by 3; 28; I do 3.
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How many times does 3 go into 28?
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Let's see, 9; 9 times 3 is 27; I have 1 left over.
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You can leave it like this; this can be your answer.
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Or if you need to change it to a mixed number, you are going to see how many whole numbers.
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Since 3 fits into 28 nine times, 9 becomes your whole number.
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Then how many you have left over, I had 1 left over.
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That becomes your numerator; you are going to keep the same denominator.
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28/3 or 9 and 1/3, they are both your answers.
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That is it for this lesson; thank you for watching Educator.com.