Question

Solve $2-\dfrac{3}{5}$.

Answer 1

Hint: In this question, we need to solve $2-\dfrac{3}{5}$. Since the number 2 and $\dfrac{3}{5}$ are unlikely so we will convert them into like fraction by first taking LCM of the denominator. Then we will convert the fraction into an equivalent fraction having its denominator equal to the least common multiple. It will give us fractions which can be solved easily.

Complete step-by-step answer:
Here, we are given the expression as $2-\dfrac{3}{5}$. The terms are 2 and $\dfrac{3}{5}$.
Now 2 can be written as $\dfrac{2}{1}$.
As we can see, both the fractions have different denominators, so they are unlike fractions.
Let us first convert them into like fractions by changing their denominator.
Let us take the least common multiple of both their denominators.
Least common multiple of 5 and 1 will be equal to 5.
Now let us convert both fractions to equivalent fractions having denominator 5.
Since $\dfrac{3}{5}$ has already 5 as its denominator, so we will write it as it is.
Now multiplying both the numerator and denominator of $\dfrac{2}{1}$ by 5 we get:
$\dfrac{2\times 5}{1\times 5}=\dfrac{10}{5}$.
So our fraction becomes $\dfrac{10}{5}$.
Hence our expression becomes $\dfrac{10}{5}-\dfrac{3}{5}$.
Since both are like terms, we can just subtract their numerator and write the denominator as it is. Hence we get $\dfrac{10}{5}-\dfrac{3}{5}=\dfrac{10-3}{5}=\dfrac{7}{5}$.
So $\dfrac{7}{5}$ is our required answer.

Note: Students should note that, we can add or subtract like fractions only. For unlike fractions, we have to convert them into like fractions first. Above expression can be solved by following method also:
$\begin{align}
  & \Rightarrow 2-\dfrac{3}{5} \\
 & \Rightarrow \dfrac{\left( 2\times 5 \right)-3}{5}=\dfrac{10-3}{5}=\dfrac{7}{5} \\
\end{align}$
But this is a shortcut method and students can make mistakes. While multiplying or dividing fraction, unlike fractions need not be changed into like fraction.