Question

How do you simplify $\left( \dfrac{2}{5}+\dfrac{1}{5} \right)-\dfrac{3}{10}$ ?
 (a) Using algebraic properties
(b) Using multiplication theorem
(c) Both a and b
(d) None of these

Answer 1

Hint: In the given problem, we are to find the simplified version of $\left( \dfrac{2}{5}+\dfrac{1}{5} \right)-\dfrac{3}{10}$. We will have to start with the terms inside the bracket term to simplify. Then we will proceed with the value and then subtract the value from $\dfrac{3}{10}$ . Thus by further simplification we will get our desired result.

Complete step by step solution:
According to the question, we are to simplify the given problem, $\left( \dfrac{2}{5}+\dfrac{1}{5} \right)-\dfrac{3}{10}$.
So, to start with, we will try to solve the terms inside the first bracket.
Thus, we are getting,
$\dfrac{2}{5}+\dfrac{1}{5}$
We have the denominator of the sum as 5, as the lcm of 5 and 5 will be 5.
$\Rightarrow \dfrac{2+1}{5}=\dfrac{3}{5}$
From the given problem,
 $\left( \dfrac{2}{5}+\dfrac{1}{5} \right)-\dfrac{3}{10}$
Putting the value,
$\Rightarrow \dfrac{3}{5}-\dfrac{3}{10}$
Now, the lcm of 5 and 10 would be, 10.
Then, we get, in the numerator, 3 should be multiplied by $\left( 10\div 5 \right)=2$ and the second 3 should be multiplied by $\left( 5\div 5 \right)=1$.
$\Rightarrow \dfrac{3\times 2-3}{10}$
Simplifying,
$\Rightarrow \dfrac{6-3}{10}=\dfrac{3}{10}$
Hence, the solution is, (a) Using algebraic properties.

Note: This is always to be considered an easy problem to get the solution. But still we have to be cautious about the problem and the calculations given out there. Easier problems can get easily wrong with silly mistakes and give us wrong results. So, taking care of that is quite important.