Question

How do you write -8.875 as a mixed fraction in simplest form?

Answer 1

Hint: We start solving the problem by equating the given decimal to a variable. We then make use of the fact that in order to convert the given decimal of the form \[a.bcd....n places\] can be converted to fraction as \[\dfrac{a.bcd....(n+1)terms}{{{10}^{n}}}\] to proceed through the problem. We use this fact and then factorize the numerator and denominator to proceed further through the problem. We then make the necessary calculations to get the required fraction form of the given decimal.

Complete step by step answer:
According to the problem, we are asked to convert the given decimal -8.875 into a mixed fraction.
Let us assume d = 3.5 ---(1).
We know that in order to convert the given decimal of the form \[a.bcd............n places\] can be converted to fraction as \[\dfrac{abcd.......(n+1)terms}{{{10}^{n}}}\] . Let us use this result to the decimal in equation (1).
So, we have \[d=\dfrac{-8875}{1000}\] ---(2).
Let us factorize the numbers present in the numerator and denominator of equation (2).
So, we get \[-8875=-71\times 125\] , \[1000=8\times 125\] . Let us use these results in equation (2).
\[\Rightarrow d=\dfrac{-71\times 125}{8\times 125}\] ---(3).
Now we will cancel the common factors present in both numerator and denominator in equation (3).
\[\Rightarrow d=\dfrac{-71}{8}\]
So, we have found the simplest fraction form of the given decimal -8.875 as \[\dfrac{-71}{8}\] .
Now finding the mixed fraction for this, we will divide the numerator by denominator and take the quotient as the whole number and the remainder as the numerator whereas no change in the denominator.

Therefore, -8.875 as a mixed fraction in simplest form is \[-8\dfrac{7}{8}\]

Note: We should perform each step carefully in order to avoid confusion and calculation mistakes while solving this problem. We can also solve this problem by multiplying and dividing the given fraction to get the required answer. Do not get confused while converting it from decimal to fraction.