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Comparing fractions

Comparing Fractions. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • leaf green style avatar for user Alexandria Murray
    Why did Sal, in the 54/81 problem at make a dot, erase it, and then write x?
    (115 votes)
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    • leafers tree style avatar for user Lauren
      well, the reason he did that because in some school districs they teach their students that a dot means to multiply (x). Its like a little easier shorter thing for them to write. If you have any more questions just ask me! :D
      (13 votes)
  • male robot hal style avatar for user Ethan
    Can't you simplify fractions even though you, like can't? Take 5/12, for example. Can't you simplify that using what you know about decimals? 🤔🤔🤔
    (1 vote)
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  • female robot ada style avatar for user Layla Fox
    Why would u have to do the 9 divided by 9 if u dont actually use it?
    (1 vote)
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  • male robot donald style avatar for user Liam Porter
    24367/6 in lowest tearms
    (3 votes)
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  • blobby green style avatar for user Quinn
    5 Goes equally into both 30 and 45 and is less than 15, so why didn't he use 5?
    (3 votes)
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  • orange juice squid orange style avatar for user Bri
    Do you have to make the denominators the same to find the comparison?
    (2 votes)
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    • blobby green style avatar for user lisa
      Not always. There are several ways to compare fractions. The most general method, that always works for any fractions, is to change to equivalent fractions with a common denominator and then compare the numerators. This works because you are expressing both numbers with a common unit (like halves, thirds, fourths, etc.), and then seeing which has more of that unit.

      If fractions have the same numerator, you can reason about which is bigger:

      3/4 or 3/5?

      A denominator of 5 means a whole has been cut into 5 equal pieces, while 4 means a SAME size whole has been cut into 4 equal pieces. Which piece would be bigger? It makes sense that more pieces means that each piece will be smaller, right? So 1/5 is smaller than 1/4, which means that 3/5 is less than 3/4 - you have the same number of pieces but each piece is smaller.

      Another method is to see if you can compare fractions to 1/2 or to 1.

      For example, which is bigger, 3/5 or 5/12?

      Well, 3/5 is more than 1/2 (if you had to fairly share 5 cookies with your brother, you would each get 1/2 of 5, or 2 and 1/2 cookies), but 5/12 is less than 1/2 (if you were sharing 12 cookies with your brother you would each get 6). So 3/5 is greater than 5/12.

      Another example, which is greater 4/5 or 5/6?

      They are each missing one unit to get to 1. But how close is each to 1?

      4/5 is 1/5 away from 1

      5/6 is 1/6 away from 1.

      But we know that 1/5 is bigger than 1/6, so 4/5 is farther away from one than 5/6.

      Since 5/6 is closer to 1, then it is bigger.
      (3 votes)
  • male robot johnny style avatar for user Judy Odhiambo
    find perimeter and area figure
    (2 votes)
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  • aqualine seed style avatar for user noralavin
    This i one of the best parts about fractions
    (2 votes)
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  • blobby green style avatar for user Evelyn
    this can gt a bit confusing sometimes
    (2 votes)
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  • orange juice squid orange style avatar for user Jimmy
    would you still have to watch the video if you know how to multiply fractions? 😕😕😕
    (1 vote)
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Video transcript

Determine whether 30/45 and 54/81 are equivalent fractions. Well, the easiest way I can think of doing this is to put both of these fractions into lowest possible terms, and then if they're the same fraction, then they're equivalent. So 30/45, what's the largest factor of both 30 and 45? 15 will go into 30. It'll also go into 45. So this is the same thing. 30 is 2 times 15 and 45 is 3 times 15. So we can divide both the numerator and the denominator by 15. So if we divide both the numerator and the denominator by 15, what happens? Well, this 15 divided by 15, they cancel out, this 15 divided by 15 cancel out, and we'll just be left with 2/3. So 30/45 is the same thing as 2/3. It's equivalent to 2/3. 2/3 is in lowest possible terms, or simplified form, however you want to think about it. Now, let's try to do 54/81. Now, let's see. Nothing really jumps out at me. Let's see, 9 is divisible into both of these. We could write 54 as being 6 times 9, and 81 is the same thing as 9 times 9. You can divide the numerator and the denominator by 9. So we could divide both of them by 9. 9 divided by 9 is 1, 9 divided by 9 is 1, so we get this as being equal to 6/9. Now, let's see. 6 is the same thing as 2 times 3. 9 is the same thing as 3 times 3. We could just cancel these 3's out, or you could imagine this is the same thing as dividing both the numerator and the denominator by 3, or multiplying both the numerator and the denominator by 1/3. These are all equivalent. I could write divide by 3 or multiply by 1/3. Actually, let me write divide by 3. Let me write divide by 3 for now. I don't want to assume you know how to multiply fractions, because we're going to learn that in the future. So we're going to divide by 3. 3 divided by 3 is just 1. 3 divided by 3 is 1, and you're left with 2/3. So both of these fractions, when you simplify them, when you put them in simplified form, both end up being 2/3, so they are equivalent fractions.