Mixed numbers and improper fractions
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Proper and Improper Fractions
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Fractions on the number line 2
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Comparing improper fractions and mixed numbers
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Mixed numbers and improper fractions
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Comparing improper fractions and mixed numbers
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Converting Mixed Numbers to Improper Fractions
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Changing a Mixed Number to an Improper Fraction
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Changing an Improper Fraction to a Mixed Number
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Converting mixed numbers and improper fractions
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Ordering improper fractions and mixed numbers
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Ordering improper fractions and mixed numbers
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Fractions cut and copy 2
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Points on a number line
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Fractions on the number line 3
Mixed numbers and improper fractions Converting mixed numbers to improper fractions and improper fractions to mixed numbers
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- We're now going to learn how to go from mixed numbers
- to improper fractions and vice versa.
- So first a little bit of terminology.
- What is a mixed number?
- Well, you've probably seen someone write,
- let's say, two and one half.
- This is a mixed number.
- So you're saying why is it a mixed number?
- Well, because we're including a whole number and a fraction.
- So that's why it's a mixed number.
- It's a whole number mixed with a fraction.
- So two and one half.
- And I think you have a sense of what two and one half is.
- It's some place halfway between two and three.
- And what's an improper fraction?
- Well an improper fraction
- is a fraction where the numerator is larger than the denominator.
- So let's give an example of an improper fraction.
- I'm just going to pick some random numbers.
- Let's say I had twenty-three over five.
- This is an improper fraction.
- Why?
- Because twenty-three is larger than five.
- It's that simple.
- It turns out that you can convert an improper fraction into a mixed number
- or a mixed number into an improper fraction.
- So let's start with the latter.
- Let's learn how to do a mixed number into an improper fraction.
- So first I'll just show you kind of just the basic systematic way of doing it.
- It'll always give you the right answer,
- and then hopefully I'll give you a little intuition for why it works.
- So if I wanted to convert two and one half into an improper fraction,
- or I want to unmix it you could say,
- all I do is I take the denominator in the fraction part, multiply it by the whole number,
- and add the numerator.
- So let's do that.
- I think if we do enough examples,
- you'll get the pattern.
- So two times two is four plus one is five.
- So let's write that.
- It's two times two plus one,
- and that's going to be the new numerator.
- And it's going to be all of that over the old denominator.
- So that equals five halves.
- So two and one half is equal to five halves.
- Let's do another one.
- Let's say I had four and two thirds.
- This is equal to -- so this is going to be all over three.
- We keep the denominator the same.
- And the new numerator is going to be three times four plus two.
- So it's going to be three times four, and then you're going to add two.
- Well that equals three times four--
- order of operations, you always do multiplication first,
- and that's actually the way I taught it-- how to convert this, anyway.
- three times four is twelve plus two is fourteen.
- So that equals fourteen over three.
- Let's do another one.
- Let's say I had six and seventeen eighteenths.
- I gave myself a hard problem.
- Well, we just keep the denominator the same.
- And then new numerator is going to be eighteen times six
- or six times eighteen, plus seventeen.
- Well six times eighteen.
- Let's see, that's sixty plus forty-eight it's one hundred eight,
- so that equals one hundred eight plus seventeen.
- All that over eighteen.
- One hundred eight plus seventeen is equal to one hundred twenty-five over eighteen.
- So, six and seventeen eighteenths is equal to one hundred twenty-five over eighteen.
- Let's do a couple more.
- And in a couple minutes I'm going to teach you how to go the other way,
- how to go from an improper fraction to a mixed number.
- And this one I'm going to try to give you a little bit of intuition for why what I'm teaching you actually works.
- So let's say two and one fourth.
- If we use the-- I guess you'd call it a system that I just showed you--
- that equals four times two plus one over four.
- Well that equals, four times two is eight plus one is nine. Nine over four.
- I want to give you an intuition for why this actually works.
- So two and one fourth, let's actually draw that,
- see what it looks like.
- So let's put this back into kind of the pie analogy.
- So that's equal to one pie.
- Two pies.
- And then let's say, one fourth of a pie. Oh, sorry.
- One fourth is like this. A fourth of a pie, right?
- Two and one fourth, and ignore this, this is nothing.
- It's not a decimal point-- actually, let me erase it
- so it doesn't confuse you even more.
- So go back to the pieces of the pie.
- So there's two and one fourth pieces of pie.
- And we want to rewrite this as just, how many fourths of pie are there total?
- Well if we take each of these pies--
- oh, whoops! I need to change the color--
- if we take each of these pies,
- and we divide it into fourths,
- we can now say how many total fourths of pie do we have?
- Well we have one, two, three, four, five, six, seven, eight, nine fourths.
- Makes sense, right?
- Two and one fourth is the same thing as nine fourths.
- And this will work with any fraction.
- So let's go the other way.
- Let's figure out how to go from an improper fraction
- to a mixed number.
- Let's say I had twenty-three over five.
- So here we go in the opposite direction.
- We actually take the denominator,
- we say how many times does it go into the numerator?
- And then we figure out the remainder.
- So let's say five goes into twenty-three--
- well, five goes into twenty-three four times.
- Four times five is twenty.
- And the remainder is three.
- So twenty-three over five, we can say that's equal to four,
- and in the remainder, three over five.
- So it's four and three fifths.
- Let's review what we just did.
- We just took the denominator
- and divided it into the numerator.
- So five goes into twenty-three four times.
- And what's left over is three.
- So, five goes into twenty-three four and three fifths times.
- Or another way of saying that is twenty-three over five is four and three fifths.
- Let's do another example like that.
- Let's say, seventeen over eight.
- What does that equal as a mixed number?
- You can actually do this in your head,
- but I'll write it out just so you don't get confused.
- Eight goes into seventeen two times.
- Two times eight is sixteen.
- Seventeen minus sixteen is one.
- Remainder, one.
- So, seventeen over eight is equal to two-- that's this two-- and one eighth.
- Right? Because we have one eight left over.
- Let me show you kind of a visual way of representing this too,
- so it actually makes sense how this conversion is working.
- Let's say I had five halves, right?
- So that literally means I have five halves,
- or if we go back to the pizza or the pie analogy,
- let's draw my five halves of pizza.
- So let's say I have one half of pizza here,
- and let's say I have another half of pizza here.
- I just flipped it over.
- So that's two.
- So it's one half, two halves.
- So that's three halves.
- And then I have a fourth half here.
- These are halves of pizza,
- and then I have a fifth half here, right?
- So that's five halves.
- Well, if we look at this, if we combine these two halves,
- this is equal to one piece, I have another piece,
- and then I have half of a piece, right?
- So that is equal to two and one half pizzas.
- Hopefully that doesn't confuse you too much.
- And if we wanted to do this the systematic way,
- we could have said two goes into five--
- well, two goes into five two times,
- and that two is right here.
- And then two times two is four.
- Five minus four is one, so the remainder is one,
- and that's what we use here.
- And of course, we keep the denominator the same.
- So five halves equals two and one half.
- Hopefully that gives you a sense of how to go from a mixed number to an improper fraction,
- and vice versa,
- from an improper fraction to a mixed number.
- If you're still confused let me know,
- and I might make some more modules.
- Have fun with the exercises!
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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