Question

How can you make a mixed fraction for $$80/5$$?

Answer 1

Hint:
In the given question, we have been given a fraction. Clearly, since the fraction has a numerator greater than its denominator, we can say that it is an improper fraction. Now, we have been asked to convert the given improper fraction into mixed fraction. For this, we need to first divide the numerator by the denominator. Then we need to find the quotient and remainder. Then, we just make the given representation of the divisor $$\left(d\right)$$, quotient $$\left(q\right)$$ and remainder $$\left(r\right)$$ – $$q{\displaystyle \frac{r}{d}}$$, and this is the required mixed fraction.

Complete step by step solution:
The given improper fraction is $$f={\displaystyle \frac{12}{5}}$$.
First, we divide the fraction. Then we need to find the quotient and remainder. Then, we just make the given representation of the divisor $$\left(d\right)$$, quotient $$\left(q\right)$$ and remainder $$\left(r\right)$$ – $$q{\displaystyle \frac{r}{d}}$$, and this is the required mixed fraction.
$$5\stackrel{{\displaystyle 16}}{)\phantom{1\begin{array}{l}80\\ {\displaystyle \frac{-5}{\begin{array}{c}30\\ {\displaystyle \frac{-30}{0}}\end{array}}}\end{array}}\stackrel{―}{\phantom{1}\begin{array}{l}80\\ {\displaystyle \frac{-5}{\begin{array}{c}30\\ {\displaystyle \frac{-30}{0}}\end{array}}}\end{array}}}$$
So, this number is perfectly divisible, hence, in the conventional form, it is written as a natural number, but, if we have to write it as a mixed fraction, we get it as,
$${\displaystyle \frac{80}{5}}=16{\displaystyle \frac{0}{5}}$$

Hence, $${\displaystyle \frac{80}{5}}=16=16{\displaystyle \frac{0}{5}}$$.

Additional Information:
The given mixed fraction can also be represented as:
$$f=16+{\displaystyle \frac{0}{5}}$$
Hence, if $$f=a{\displaystyle \frac{b}{c}}$$, then it is same and can be represented as
$$f=a+{\displaystyle \frac{b}{c}}$$

Note:
So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we write the formula which connects the two things. Then we very carefully put in the values into the formula required to solve the expression. The mixed fractions are represented in two ways in which both are equal: $$a{\displaystyle \frac{b}{c}}$$ or $$a+{\displaystyle \frac{b}{c}}$$. Both of these mean the same thing, just a little different way to show it.