Question

How do write in the simplest form given $ - \dfrac{4}{5} + \left( { - \dfrac{1}{3}} \right)$ ?

Answer 1

Hint: In this question, we want to write the given expression in the simplest form. In this question, we want to convert the expression in the simplest form by adding two fractions. First, take the LCM of the denominator to make the denominator the same. When the denominator becomes the same, simplify the numerator.
To add fractions there are three simple steps:
1.Make sure that the denominators are the same.
2.Add the numerators; put the answer over the denominator.
3.Simplify the fraction (if needed).

Complete step by step solution:
In this question, the given expression is:
$ - \dfrac{4}{5} + \left( { - \dfrac{1}{3}} \right)$
To add the fraction:
The first step is to make the denominator the same.
In the above expression, we can see that the denominators are different. So, we can’t add the fractions.
Let us take the LCM of the denominator. The denominators have the numbers 3 and 5.
Here, the LCM of the 5 and 3 is 15.
That is equal to,
$ \Rightarrow \dfrac{{ - 12 - 5}}{{15}}$
Let us add the numerator.
The addition of -12 and -5 are -17. So, let us write -17 in the numerator of the above expression.
$ \Rightarrow - \dfrac{{17}}{{15}}$
This can’t be reduced to any simpler fraction. So, this is the simplest form of the given expression.
We can also write the expression in the mixed fraction form.
That is equal to,
$ \Rightarrow - 1\dfrac{2}{{15}}$
Hence, the answer is $ - \dfrac{{17}}{{15}}$.

Note:
When we add or subtract two or more fractions that do not have the same denominator, we need to find the “least common denominator” in order to have equivalent fraction values. Then we need to combine the fractions arithmetically to arrive at a single value.