Question

How do you write $ - 5.5$ as a decimal and fraction?

Answer 1

Hint: The given number $ - 5.5$ is already in decimal form, so convert it to fraction now. Whenever they ask us to change a number from a decimal number to a fraction number, first think that decimal number out of $1$. Usually in mathematics out of means division operation. Then multiply both the numerator and the denominator by $10$ and simplify the equation, you get the required answer.

Complete step by step answer:
Here in the question, they have asked to write $ - 5.5$ as a decimal and a fraction number. But the given number $ - 5.5$ is in the decimal form so now we can convert to fraction numbers.
Whenever they ask us to change a number from a decimal number to a fraction number, first think that decimal number out of $1$. Usually in mathematics out of means division operation.
Now, look at the given problem they have asked us to change $ - 5.5$ to fraction. As I said in above, think of $ - 5.5$ out of $1$, which can be written as $\dfrac{{ - 5.5}}{1}$.
In order to make the above form even simpler, we can multiply both numerator and denominator by $10$. Here we are multiplying by $10$ because we have only one digit after the decimal place. Which gives,
$\dfrac{{ - 5.5}}{1} \times \dfrac{{10}}{{10}}$
We can multiply both numerator and denominator by $10$ , only because $\dfrac{{10}}{{10}}$ gives $1$.
On simplifying the above step we get
$ \Rightarrow \dfrac{{ - 5.5}}{1} \times \dfrac{{10}}{{10}} = \dfrac{{ - 55}}{{10}}$
The above equation can be simplified even more to arrive at the answer. Or in other words, we can say that in order to get the lowest terms we need to know common factors for $55$ and $10$. That is both $55$ and $10$ are divisible by $5$.
Therefore, $ \Rightarrow \dfrac{{ - 55}}{{10}} = - \dfrac{{11}}{2}$.
Now, the number $11$ and $2$ have no common factors other than $1$.

Therefore, the simplest fraction form of the decimal number $ - 5.5$ is $ - \dfrac{{11}}{2}$.

Note:
Whenever they give a problem like converting from decimal number to fraction number, first look at the terms after the decimal. If the number of digits after the decimal point is two then you can multiply and divide by $100$ but if you have only one digit then you can divide and multiply by $10$, in order to make it simple.