WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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We are going over mixed numbers and improper fractions and how to switch between the two.
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If we look at fractions, there is three different kinds.
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There is the mixed number, proper fractions, and improper fractions.
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Mixed number is a fraction with a whole number.
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If I have 1 and 1/2, the number in the front, 1, is a whole number and then 1/2 is a fraction.
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The whole number with a fraction is called a mixed number.
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Another example would be 5 and 3/4; that is called a mixed number.
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A proper fraction is a fraction where the top number is smaller than the bottom number.
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3/4 with no whole number, just 3/4, that would be a proper fraction.
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Keep in mind that proper fractions, because the top number,
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the numerator, is smaller than the denominator, these fractions are smaller than 1
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because if you ate 3 out of 4 pieces, then you ate less than the whole thing.
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A proper fraction would be a fraction that is smaller than 1.
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Improper fraction would be the opposite.
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It is when the top number, the numerator, is bigger than the denominator.
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Like 4/3, this is an improper fraction; again there is no whole number.
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If there was a whole number, it would be called a mixed number.
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An improper fraction, the top number is bigger than the bottom number.
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If you ate 4 pieces out of 3, then you actually ate more than 1.
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You ate 1; and you ate a little more.
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Improper fractions are actually bigger than 1.
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Mixed number we know is bigger than 1 because you have a whole number and you have a fraction.
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And improper fractions are bigger than 1.
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Since proper fractions are smaller than 1, we can't do anything to that one.
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That one, we can't change; that one has to stay the way it is.
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But since mixed number and improper fractions are both bigger than 1,
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we can actually change them from mixed number to improper fraction and improper fraction to mixed number.
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For you to be able to switch between, let's start with this one--mixed number to improper fraction.
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If I have a mixed number, 2 and 1/2, again that is a mixed number
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because you have a whole number in the front and you have...this is like a proper fraction.
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It is a whole number with a proper fraction.
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Together it is called a mixed number.
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If I want to switch a mixed number to make it look like an improper fraction,
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the first thing I am going to do is take this number on the bottom which is the denominator.
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Multiply it to the whole number; it would be 2 times 2 which is 4.
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Then you are going to add the top number--plus 1.
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Again take the bottom number, 2, multiply it to the whole number, and add it to the top number.
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It is 2 times 2 which is 4; plus 1 is 5.
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That number is going to be the top number of your improper fraction.
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It is going to be the numerator; 5 over... the denominator stays the same.
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The denominator of the improper fraction is going to be the same as the denominator of your mixed number.
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That does not change; 5/2.
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Again the top number, the numerator, is bigger than the denominator.
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We have no whole number.
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From a mixed number, we just change that to an improper fraction.
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Again denominator times the whole number; then add the top number.
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If you are going to go the other way, you are going to go from an improper fraction
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and change it to a mixed number, say I have 10/3.
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We know this is an improper fraction because the top number, the numerator, is bigger than the denominator.
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In this case, I want to see how many times the bottom number can fit into the top number.
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How many times can the bottom number go into the top number?
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I know 3 times 3 is 9.
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That means the 3 fits into 10 three times because 10 is bigger than 9.
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I am going to write that number as my whole number because mixed number again has a whole number.
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You are figuring out the biggest multiple of 3 that fits into 10.
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Again 3 goes into 10 three times which makes it a 9.
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How many do I have left over then?
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If 3 times 3 is 9, but this number is 10, I have 1 left over.
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My leftover is going to be the top number of the fraction.
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Again my denominator has to stay the same; the denominator here is 3.
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The denominator here is going to stay 3.
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Again to change from an improper fraction to a mixed number,
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you are going to see how many times the bottom number will fit into 10.
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It fits in there three times with 1 left over.
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Then denominators both stay the same.
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Here are some examples.
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This is an improper fraction because again the top number is bigger than the bottom number.
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We know this is bigger than 1.
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Since this is an improper fraction, I want to change it to a mixed number.
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I don't have to, but if I want to, I can switch it over.
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In order to switch it, I see how many times the bottom number will fit into the top number.
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How many times does 3 fit into 5?
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3 times 1 is 3; 3 times 2 is 6; but 6 is too big.
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Only one time; that becomes my whole number.
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If 3 fits into 5 one time, how many do I have left over?
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3 times 1 is 3; I have 5 here; my leftover is 2.
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What goes down here as my denominator?--the same denominator.
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From improper fraction, I can change it to this mixed number.
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These mean the same thing.
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This fraction is the same fraction as this one right here.
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You are just writing it in different form.
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This example here, this fraction is... can you guess?
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Good, it is a mixed number because we have a whole number with a proper fraction.
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Here, since this is a mixed number, I can change it to an improper fraction.
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I take my denominator; I multiply it to my whole number.
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Then I add it to my numerator.
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It is 2 times 4 which is 8; plus 1.
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That is 9 over... my denominator stays the same as a 2.
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4 and 1/2 is the same thing as 9/2.
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Here is another example; this right here is a mixed number.
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We can change it to an improper fraction.
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You take the 4, the denominator; you are going to multiply it to the 5.
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Then you are going to add the top.
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It is 20; plus 3 is 23; it is 23.
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Then the denominator stays the same; the denominator is 4.
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5 and 3/4 is the same thing as 23/4.
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Another example, 6/7; the top number is smaller than the bottom number.
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If I look at this and ask myself how many times does 7 go into 6?
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It doesn't go into it at all.
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6 is smaller than 7; 7 doesn't fit into 6.
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This fraction is a proper fraction; this is a proper fraction.
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I can't switch it over to the other types of fractions.
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I can't change this to a mixed number.
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I can't change it to an improper fraction.
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This fraction is smaller than 1; it is called the proper fraction.
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This fraction here, the top number is bigger than the bottom number.
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This is an improper fraction; therefore we can change it to a mixed number.
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Again I ask myself how many times does 8 fit into 19?
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8 times 1 is 8; 8 times 2 is 16; 8 times 3 is 24.
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This number right here is 19; 8 fits into 19 only two times.
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That becomes a whole number.
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If 8 times 2 is 16, how many are left over?
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We do 19; subtract the 16; I have 3 left over.
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My denominator stays the same as an 8.
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19/8 is the same thing as 2 and 3/8.
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This fourth example, this fraction right here is called a mixed number
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because we have a whole number and we have a proper fraction.
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Since I have a mixed number, I can switch this over.
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I can change this to make it look like an improper fraction.
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The first thing I do here is I take the denominator of 5.
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I am going to multiply it to the whole number.
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Then I take that number and add it to the top number, the numerator.
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I do 5 times 8 which is 40.
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I am going to add the top number; it is going to be 44.
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That goes in the numerator of my improper fraction.
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Then the denominator has to stay the same.
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The denominator for this fraction is 5; it is going to stay a 5 here.
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This is an improper fraction because the top number is bigger than the bottom number.
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8 and 4/5 would be the same thing as 44/5.
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