Question

How do you add a fraction to a decimal?

Answer 1

Hint: We first explain the process of adding a fraction to a decimal. The conversion method in both numbers has to be the same. Either both are decimal or fractions. We explain the process of conversion. Then we take examples to make the process understandable.

Complete step-by-step solution:
We have to explain the process of adding a fraction to a decimal.
The main idea is to convert the numbers into the same form whether it be fraction or decimal.
First, we explain the conversion from decimal to fraction.
In this case we have a decimal point which we need to get rid of. For the given number we move the decimal to the right one position. The decimal goes to the very end of the number following the process. The more we move to the right, the more we multiply with ${{10}^{-1}}$ to compensate for the movement.
Therefore, we get a power form of 10 in the denominator of the fraction. The number of digits after decimal is equal to the power value of 10.
For example: $0.039$ changes to $\dfrac{39}{{{10}^{3}}}=\dfrac{39}{1000}$.
Now we explain the conversion from fraction to decimal. We do this by basic long division method. For example, if we take $\dfrac{3}{25}$, we get
$25\overset{0.12}{\overline{\left){\begin{align}
  & 30 \\
 & \underline{25} \\
 & 50 \\
 & \underline{50} \\
 & 0 \\
\end{align}}\right.}}$
So, the decimal form of $\dfrac{3}{25}$ is $0.12$.
Now we assume we needed the addition of $\dfrac{3}{25}$ to $0.039$.
We add $0.12$ to $0.039$ or $\dfrac{3}{25}$ to $\dfrac{39}{1000}$.
We get $0.12+0.039=0.159$ which his equal to $\dfrac{3}{25}+\dfrac{39}{1000}=\dfrac{120}{1000}+\dfrac{39}{1000}=\dfrac{159}{1000}$.

Note: Addition in mixed form is not possible. The fraction is also required to equal its denominator in both numbers. That helps in addition to the numerators.
We need to convert the mixed fraction which is representation in the form sum of an integer and a proper fraction. We express the process in the form of variables.
Let the mixed fraction be $x\dfrac{c}{b}$. The improper fraction form will look like $x+\dfrac{c}{b}=\dfrac{bx+c}{b}$.