WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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The next lesson is on dividing fractions including fractions that are mixed numbers.
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In the same way that we multiply fractions,
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when we divide fractions, we have to make sure that we have no mixed numbers.
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If you do have mixed numbers, make sure to change them to an improper fraction.
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When you have a fraction A/B and you are dividing it by another fraction C/D,
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what you are going to do is take the second fraction and you are going to flip it.
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You are just going to make this number, the top number, the bottom number.
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Then the bottom number becomes your top number.
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When you do that, you are going to change the division to a multiplication sign.
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Now your problem becomes A/B times D/C.
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You are going to multiply the fractions the same way.
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Again take the second fraction and flip it.
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When you flip it, it is going to go from dividing to multiplying.
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Let's do a few examples; 2/3 divided by 3/4; I have no mixed numbers.
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I can go ahead and work with these fractions right here, 2/3.
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I am going to switch this sign to a multiplication sign because I am going to take this fraction right here.
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My 4, my denominator, becomes my numerator; my numerator becomes my denominator.
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Don't forget; if you flip the first fraction, you are going to get it wrong.
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Make it is not the first fraction; it is the second fraction that you flip.
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From here, I am going to multiply my numerators.
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2 times 4 is 8; 3 times 3 is 9.
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2/3 divided by 3/4 is 8/9.
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The next example, 1 and 2/5 divided by 2 and 3/5.
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Both of my fractions are mixed numbers.
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I have to make sure to change them to improper fractions before I go ahead and divide them.
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When you change it from a mixed number to an improper fraction, you take the bottom number 5.
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Multiply it to your whole number and add the top number.
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You are going to go 5 times 1 is 5; plus 2 is 7.
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It is 7/5 divided by... 5 times 2 is 10, plus 3 is 13; 13/5.
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Look at how I kept the division sign.
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I can only switch it to multiplication when I flip my top and bottom numbers.
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For now, I didn't flip it yet.
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All I did was just convert this mixed number to an improper fraction.
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I had to keep this sign.
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My next step, I am going to make it a multiplication problem by flipping these.
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My 5 now goes on the top.
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My 13 is going to go on the bottom.
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Remember from last lesson, if I have this problem right here, I can see if a number from the top
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and a number from the bottom can reduce, can simplify if they have common factors.
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7 and 13 have no common factors because they are both prime.
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7 is a prime number; 13 is a prime number.
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The only common factor between them would be 1.
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This 5 and the 5 up here, they have a common factor of 5.
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They are the same numbers so their common factor would be itself.
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I can simplify these numbers by dividing their common factor of 5.
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I am going to take this 5; divide it by 5 which is 1.
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Then this number divided by 5; that also becomes 1.
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Now I can multiply the top numbers together and then multiply my bottom numbers together.
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7 times 1 is 7; 1 times 13 is 13; that is my answer.
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Some more examples, 6/5 divided by 3/4.
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Since none of these are mixed numbers, I can go ahead and just work with those.
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Since I am dividing, I can now multiply after switching these.
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It becomes 4/3; again you can just multiply them.
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Just do 6 times 4, 24, over 5 times 3 which is 15; then simplify that fraction.
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Or you can simplify the problem--this is the problem--by seeing if any numbers have common factors.
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Again 6 and 4, this number 6 and this number 4 have a common factor of 2 because they are both even numbers.
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But I can't cancel those out because they are both on the top.
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Whenever you cancel numbers out, make sure that one of them is on the top and one of them is on the bottom.
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I can only do maybe 5 and 4.
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But they don't have any common factors besides 1.
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6 and 3 have a common factor of 3.
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3 divided by 3 is 1; 6 divided by 3 is 2.
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Make sure you divide both numbers by that same factor.
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Now I am going to multiply; 2 times 4 is 8.
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5 times 1 is 5; that is an improper fraction.
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But I can leave it like; that is my answer.
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The next example, 4 and 1/4 divided by 5/3.
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I have a mixed number; I need to convert that.
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4 times 4 is 16; plus 1 is 17; 17/4 divided by 5/3.
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I didn't change it yet because I didn't flip this fraction.
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17/4 times 3/5; make sure it is the second fraction that you flip.
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From here, let's see, 17 with 5; no, they don't have any common factors.
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4 with 3?--nope, no common factors besides 1.
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I have to just solve it out; 17 times 3; and then 4 times 5.
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17 times 3; let's do that problem.
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7 times 3 is 21; the 2 up here; 1 down here.
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Multiply these two and then add that number.
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3, 5; 51 over... 4 times 5 is 20; this is my answer.
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You can change it to a mixed number if you would like.
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All you are going to do is see how many times 20 is going to fit into 51.
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That is going to be your whole number.
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How many you have left over is your numerator; keep the same denominator of 20.
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Let's just do that; 20 is going to fit into 51 two times.
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If you do it two times, it is 51 divided by 20.
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It is going to fit in there two times; that becomes 40.
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I have 11 left over; I can write it like this.
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Or I can write it like... 2 is my whole number; I have 11 left over... over 20.
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Either fraction, improper or mixed number, is going to be your answer.
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You can leave it this way; or you can write it this way.
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Few more examples, 7/8; you can divide and then change this fraction.
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9 times 3 is 27; add the 2; that is 29/9.
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I am going to do 7/8 times 9/29.
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8 and 9 have no common factors; 7/9 have no common factors.
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I can go 9 with 29; I can compare those two.
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But nothing has any common factors for me to simplify or to reduce.
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I am going to multiply; 9 times 7 is 63; 29 times 8.
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29 times 8; 9 times 8 is 72; 8 times 2 is 16.
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Plus 7 is 23; that is 232.
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I know they have no common factors because none of these were able to reduce.
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This will be my final answer.
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The next example, 5/4 divided by 9/11; that is my problem.
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Before I start cancelling numbers out, I have to make sure I change this to a multiplication problem first.
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5/4 times 11/9; don't forget to flip this one.
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Let's see; 11 with 9--no; 11 with 4--no; 5 with 9--no.
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None of these have any common factors for me to cross cancel numbers out.
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5 times 11 is 55; 4 times 9 is 36; that is my answer.
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The next couple of examples, I have 3 and 3/7 divided by 6 and 1/4.
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These are both mixed numbers; I have to convert them to improper fractions.
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I take my denominator of 7, multiply it to my whole number, and then add the numerator.
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7 times 3 is 21; plus 3 is 24;
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Then 4 times 6 is 24; plus 1 is 25.
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Make sure you keep the same denominator.
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Now I can go ahead and divide these fractions.
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For me to divide fractions, I have to take my second fraction and flip it.
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My top number is going to become my bottom number.
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My bottom number will become the top number; let's write it right here.
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Once I flip it, I am going to change my sign to multiplication.
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It is going to be 24/7 times 4/25.
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Make sure you flip the second one and not the first one.
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If you flip the first one, you are going to get the wrong answer.
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It is 24/7 times 4/25.
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You are going to see if you can cancel any of these numbers out.
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Make sure that one number is the numerator and another number is in the denominator position.
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7 with 4, they have no common factors because 7 is a prime number.
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24 and 25 also have no common factors.
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You are going to have to multiply the top numbers and then multiply the bottom numbers together to get your answer.
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24 times 4; 24 times 4; 4 times 4 is 16.
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I put the 1 right here; 6 down there.
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4 times 2 is 8; add the 1; 9; this becomes 96 over... 25 times 7.
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5 times 7 is 35; I put the 3 up here; 5 right there.
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7 times 2 is 14; plus 3 is 17; this is 175.
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Since none of these were able to reduce or cross cancel, I know that this is my answer.
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The next example, 2 and 4/5 divided by 10/3.
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10/3 is an improper fraction; I can leave that as it is.
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This one I have to convert; 5 times 2 is 10.
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Plus the 4 is 14; 14/5 divided by 10/3.
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I am going to flip the second fraction so that the top number and my bottom number switch positions.
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That changes this division to multiplication; 14/5 times 3/10.
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From here, now that it is a multiplication problem, I can see if any numbers will cross cancel.
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5 and 3 have no common factors because they are both prime numbers.
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14 and 10 have a common factor.
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Before we do that, let me just point out... 5 and 10, I have a common factor of 5.
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5 goes into both of these numbers.
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But remember you can't cancel those out because they are both denominators.
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They are both on the bottom.
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When you cancel numbers out, you have to make sure that
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one of them is on the top and another one is on the bottom.
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Since 14 is on the top and 10 is on the bottom, I can cross cancel those numbers out.
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A common factor between 14 and 10 is 2 because they are both even numbers.
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I am going to take both numbers and divide it by that common factor.
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Since the common factor is 2, I am going to divide this number by 2.
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That is 5; then take the 14, divide it by 2; that becomes 7.
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You have to make sure that you are going to divide by the same factor.
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There are no more; 7 and 5, they have no common factors.
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I can go ahead and multiply them.
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7 times 3 is 21; 5 times 5 is 25; that is your answer.
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Make sure when you divide fractions, number one, convert all mixed numbers to improper fractions.
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Then you are going to switch the second fraction.
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The top number becomes the bottom number; the bottom number becomes the top number.
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Then you are going to multiply those fractions together.
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That is it for this lesson; thank you for watching Educator.com.