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Comparing Fractions 2

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    --
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    Use less than, greater than, or equal
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    to compare the two fractions 21/28, or 21 over 28, and 6/9,
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    or 6 over 9.
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    So there's a bunch of ways to do this.
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    The easiest way is if they had the same denominator,
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    you could just compare the numerators.
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    Unlucky for us, we do not have the same denominator.
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    So what we could do is we can find a common denominator
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    for both of them and convert both of these fractions
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    to have the same denominator and then compare the numerators.
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    Or even more simply, we could simplify them first and then
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    try to do it.
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    So let me do that last one, because I
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    have a feeling that'll be the fastest way to do it.
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    So 21/28-- you can see that they are both divisible by 7.
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    So let's divide both the numerator
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    and the denominator by 7.
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    So we could divide 21 by 7.
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    And we can divide-- so let me make the numerator--
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    and we can divide the denominator by 7.
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    We're doing the same thing to the numerator
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    and the denominator, so we're not
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    going to change the value of the fraction.
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    So 21 divided by 7 is 3, and 28 divided by 7 is 4.
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    So 21/28 is the exact same fraction as 3/4.
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    3/4 is the simplified version of it.
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    Let's do the same thing for 6/9.
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    6 and 9 are both divisible by 3.
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    So let's divide them both by 3 so we
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    can simplify this fraction.
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    So let's divide both of them by 3.
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    6 divided by 3 is 2, and 9 divided by 3 is 3.
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    So 21/28 is 3/4.
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    They're the exact same fraction, just written a different way.
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    This is the more simplified version.
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    And 6/9 is the exact same fraction as 2/3.
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    So we really can compare 3/4 and 2/3.
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    So this is really comparing 3/4 and 2/3.
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    And the real benefit of doing this is now this
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    is much easier to find a common denominator for than 28 and 9.
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    Then we would have to multiply big numbers.
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    Here we could do fairly small numbers.
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    The common denominator of 3/4 and 2/3
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    is going to be the least common multiple of 4 and 3.
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    And 4 and 3 don't share any prime factors with each other.
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    So their least common multiple is really
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    just going to be the product of the two.
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    So we can write 3/4 as something over 12.
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    And we can write 2/3 as something over 12.
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    And I got the 12 by multiplying 3 times 4.
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    They have no common factors.
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    Another way you could think about it is 4,
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    if you do a prime factorization, is 2 times 2.
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    And 3-- it's already a prime number,
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    so you can't prime factorize it any more.
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    So what you want to do is think of a number
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    that has all of the prime factors of 4 and 3.
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    So it needs one 2, another 2, and a 3.
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    Well, 2 times 2 times 3 is 12.
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    And either way you think about it,
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    that's how you would get the least common multiple
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    or the common denominator for 4 and 3.
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    Well, to get from 4 to 12, you've got to multiply by 3.
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    So we're multiplying the denominator by 3 to get to 12.
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    So we also have to multiply the numerator by 3.
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    So 3 times 3 is 9.
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    Over here, to get from 3 to 12, we
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    have to multiply the denominator by 4.
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    So we also have to multiply the numerator by 4.
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    So we get 8.
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    And so now when we compare the fractions,
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    it's pretty straightforward.
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    21/28 is the exact same thing as 9/12,
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    and 6/9 is the exact same thing as 8/12.
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    So which of these is a greater quantity?
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    Well, clearly, we have the same denominator right now.
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    We have 9/12 is clearly greater than 8/12.
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    So 9/12 is clearly greater than 8/12.
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    Or if you go back and you realize
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    that 9/12 is the exact same thing as 21/28,
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    we could say 21/28 is definitely greater than-- and 8/12
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    is the same thing as 6/9-- is definitely greater than 6/9.
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    And we are done.
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    Another way we could have done it-- we
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    didn't necessarily have to simplify that.
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    And let me show you that just for fun.
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    So if we were doing it with-- if we didn't think
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    to simplify our two numbers first.
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    I'm trying to find a color I haven't used yet.
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    So 21/28 and 6/9.
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    So we could just find a least common multiple
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    in the traditional way without simplifying first.
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    So what's the prime factorization of 28?
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    It's 2 times 14.
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    And 14 is 2 times 7.
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    That's its prime factorization.
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    Prime factorization of 9 is 3 times 3.
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    So the least common multiple of 28 and 9
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    have to contain a 2, a 2, a 7, a 3 and a 3.
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    Or essentially, it's going to be 28 times 9.
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    So let's over here multiply 28 times 9.
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    There's a couple of ways you could do it.
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    You could multiply in your head 28 times
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    10, which would be 280, and then subtract 28
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    from that, which would be what?
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    252.
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    Or we could just multiply it out if that confuses you.
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    So let's just do the second way.
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    9 times 8 is 72.
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    9 times 2 is 18.
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    18 plus 7 is 25.
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    So we get 252.
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    So I'm saying the common denominator here
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    is going to be 252.
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    Least common multiple of 28 and 9.
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    Well, to go from 28 to 252, we had to multiply it by 9.
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    We had to multiply 28 times 9.
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    So we're multiplying 28 times 9.
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    So we also have to multiply the numerator times 9.
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    So what is 21 times 9?
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    That's easier to do in your head.
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    20 times 9 is 180.
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    And then 1 times 9 is 9.
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    So this is going to be 189.
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    To go from 9 to 252, we had to multiply by 28.
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    So we also have to multiply the numerator by 28
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    if we don't want to change the value of the fraction.
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    So 6 times 28-- 6 times 20 is 120.
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    6 times 8 is 48.
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    So we get 168.
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    Let me write that out just to make
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    sure I didn't make a mistake.
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    So 28 times 6-- 8 times 6 is 48.
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    2 times 6 is 12, plus 4 is 16.
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    So right, 168.
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    So now we have a common denominator here.
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    And so we can really just compare the numerators.
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    And 189 is clearly greater than 168.
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    So 189/252 is clearly greater than 168/252.
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    Or that's the same thing as saying 21/28,
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    because that's what this is over here.
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    The left-hand side is 21/28, is clearly greater
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    than the right-hand side, which is really 6/9.
Title:
Comparing Fractions 2
Description:

u2_l1_t5_we2 Comparing Fractions

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Video Language:
English
Duration:
07:08
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