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We're asked to express each of the given
improper fractions as mixed numbers
let's work through the first one
and then see if we can write-upa formal process so what I'm going to do to begin to
understand what is
the fraction that's represented here
I'm going to use long division
and I'm going to divide five into
forty two
that's gonna go eight times
five is forty
I'm going to subtract forty from forty two and i'm gonna get two and I'm going to stop
there because
two is less than five
so that is my remainder
so i'm going to be able then to write
forty-two over five as
eight
whole pieces of five size five
and then remainder
two
over
five so there is my mixed number
i can work backwards and check eight times five is forty plus two is forty-two
over five
so let's see if we can write up a process here that will help us with the
other two problems
so we are looking for steps to convert an improper fraction to a mixed
number
the first thing we did was to divide the numerator
that was our forty-two by the denominator of five using long division
the quotient
which is this number here
becomes the whole number part
once we found the remainder
which was two
we placed it over the denominator to get the fraction part
and then we could add a step four that says
check by converting to an improper fraction just to be sure that you're correct
so let's see how this process would work for the remaining two examples
we are going to convert fifty-three over nine
to a mixed number so I'm going to use long division
with nine
dividing into
fifty-three
nine doesn't go into five but goes into
fifty-three
five the whole times without going over
five times nine is forty five if I subtract
I get eight
eight s less than nine so this is our remainder I'm just going to write that as an R
the whole number part is this five here so fifity-three over nine is the five
whole parts and then
eight
over
nine
once again I can check
five times nine is forty five-plus eight gives me fifty-three over the denominator
nine
we're gonna do one last one eighty four over seven if I follow the steps
I'm going to use long division
denominator dividing into the numerator
eight-four
seven goes into eight one time
giving me
seven when I subtract
I get fourteen
seven goes into fourteen two times
two times seven is fourteen when I subtract i get a remainder of zero so let's see how
that's going to look
eighty-four over seven then the whole number part is twelve
the remainder zero over seven so technically that's how i would write
eighty-four over seven as a mixed number however this will simplify
to just be
twelve