Question

How do you simplify $ \dfrac{5}{9}-\dfrac{2}{5} $ ?

Answer 1

Hint: In this question, we have to subtract two fractions. And the fractions are having different denominators so we need to find LCM first of both the denominators to make their denominators the same. Then, we have to subtract and simplify.

Complete step by step answer:
Now, let’s solve the question.
First of all, write the fraction given in the question.
 $ \Rightarrow \dfrac{5}{9}-\dfrac{2}{5} $
Now, let’s understand what is like fractions and unlike fractions.
Like fractions are those fractions that have the same denominators. Whereas unlike fractions are those fractions whose denominators are different. They can be converted to like fractions.
To convert unlike fractions to like fractions first we have to take LCM of the denominators whether the cases are of subtraction, addition, greater than or lesser than or ascending or descending. Only in multiplication or division, we don’t convert unlike fractions to like fractions.
So, in this question:
 $ \Rightarrow \dfrac{5}{9}-\dfrac{2}{5} $
Now, let’s take LCM of 9 and 5:
 $ \begin{align}
  & 3\left| \!{\underline {\,
  9,5 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3,5 \,}} \right. \\
 & 5\left| \!{\underline {\,
  1,5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,1 \,}} \right. \\
\end{align} $
LCM of 9 and 5 is: $ 3\times 3\times 5 $ = 45
Now we have to divide the original denominators with the LCM i.e. 45 and the resulting number will be multiplied with the numerator. Let’s see how!
 $ \begin{align}
  & \Rightarrow \dfrac{25}{45}-\dfrac{18}{45} \\
 & \therefore \dfrac{7}{45} \\
\end{align} $
So our final answer is:
 $ \Rightarrow \dfrac{5}{9}-\dfrac{2}{5} $ = $ \dfrac{7}{45} $

Note:
 Students can make the mistake while adding unlike fraction: $ \dfrac{5}{9}-\dfrac{2}{5}=\dfrac{3}{4} $ . This is a major mistake. Another mistake which can be done is after taking LCM, numerators are copied from the original as it is: $ \dfrac{5}{45}-\dfrac{2}{45} $ like this. So, these are the areas where chances of mistakes are more.