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- Let's try to evaluate seven and six-ninths minus three and two-fifths. So like
- always I like to separate out the whole number parts from the fractional parts.
- This is the same thing as
- seven
- plus six-ninths minus three
- minus
- two-fifth.
- And the reason why I'm saying minus three minus two-fifths
- as this is the same thing as minus three plus two-fifths.
- So you distribute the negative sign: subtracting at three and then you're
- subtracting the two-fifths.
- And so now we can worry about the whole number parts: seven
- minus three.
- Well, seven minus three is going to give us
- four. So that's going to give us four. And then we're going to have six-ninths
- minus
- two-fifths.
- So let me think about what six-ninths minus two-fifths are.
- Six-ninths minus two-fifths. Well we're gonna have to find a common denominator. So this is
- going to be the same thing and I think the least common multiple of nine and five is
- going to be forty-five. Literally them multiplied. They have no common
- factors.
- So it's going to be over forty five,
- till from nine to forty-five to multiply by five so I'm gonna have to multiply the numerator by
- five.
- So six times five is thirty.
- And I'm gonna subtract,
- to go from five to forty-five have to multiply by nine,
- so have to multiply the numerator right nine if I don't wanna change the values.
- So two times nine is
- eighteen.
- And thirty over thirty forty-fifth minus eighteen forty-fifths is going to be
- something over forty-five. Thirty minus eighteen is twelve.
- So this is - if I subtract these two fractions right over here -
- I get twelve,
- twelve forty-fifths.
- So it's four plus twelve forty-fifths, or if we want it to write it as a mixed number,
- this is equal to four and twelve
- fourty-fifths.
- But we're not done yet! We can simplify this further: twelve and forty-five have
- common factors.
- They're both divisible by,
- they're both divisible by three!
- So we can say that this is,
- actually they are both divisible by that while we continue to divide more after that.
- So let's see if we divide the numerator by three
- and the denominator
- by three.
- We end up with four and twelve divided by three
- is four.
- And forty-five divided by three,
- forty-five divided by three is fifteen.
- Four and four-fifteen, so actually we're done!
- These two can't be simplified anymore.
- Four and four-fifteenths.