Question

How do you simplify fractions when you have decimals on the numerator?

Answer 1

Hint: Whenever there are decimals in the numerator of the fractions, always convert it into fraction form and then evaluate. A decimal can be converted into fractions by checking the number of decimal places and then putting that number to the power of $10\;$ and writing it in the denominator.

Complete step-by-step solution:
Let us take an example to easily understand this question.
We need to simplify this fraction, $\dfrac{{9.6}}{{504}}$
Firstly, consider the decimal number,$9.6\;$
We can convert this decimal into a fraction, which is $\dfrac{{96}}{{10}}$
The trick for this is that we have to check the number of decimal places after the decimal and then put that number to the power of $10\;$.
Here, the number of decimal places after the decimal is $1$
That’s why the denominator is ${10^1} = 10$.
Now put this back in our main fraction i.e.,
$\Rightarrow \dfrac{{9.6}}{{504}} = \dfrac{{\dfrac{{96}}{{10}}}}{{504}}$
On the RHS side multiply with $10\;$, in the numerator and the denominator.
$\Rightarrow \dfrac{{9.6}}{{504}} = \dfrac{{\dfrac{{96}}{{10}} \times 10}}{{504 \times 10}}$
In the numerator, the $10\;$ gets canceled. We get,
$\Rightarrow \dfrac{{9.6}}{{504}} = \dfrac{{96}}{{504 \times 10}}$
Now we expand the constants in simple numbers.
$\Rightarrow \dfrac{{9.6}}{{504}} = \dfrac{{2 \times 2 \times 2 \times 2 \times 2 \times 3}}{{2 \times 2 \times 2 \times 3 \times 3 \times 7 \times 2 \times 5}}$
Now cancel out the common constants which are in the numerator and the denominator.
After that, we will get,
$\Rightarrow \dfrac{{9.6}}{{504}} = \dfrac{2}{{3 \times 7 \times 5}}$
Multiply all of them together.
$\Rightarrow \dfrac{{9.6}}{{504}} = \dfrac{2}{{105}}$
Now, this fraction can again be written in decimals as
$\Rightarrow \dfrac{{9.6}}{{504}} = 0.0190$
$\therefore$ This is how we simplify the fractions which have decimals in the numerator.

Note: Always check the number of decimal places (number of digits) after the decimal place to convert the decimal into a fraction. The number of digits is then written to the power of $10\;$ and then placed in the denominator and the numerator, the number will be written the same as it is, but without the decimal point.