Question

How do you evaluate $ \dfrac{2}{5} + \dfrac{3}{{10}} $

Answer 1

Hint: Here in this question, we have + symbol which represents the addition and we have to add the two numbers. The numbers are in the form of fraction. by taking the LCM for the denominators and we are going to simplify the given numbers.

Complete step-by-step answer:
Here in this question, we have to add the numbers. As we know + sign indicates the addition. The numbers are in the form of fraction. In fraction we have 3 types. They are proper fraction, improper fraction and mixed fraction.
In the fraction the numerator is less than the denominator then it is a proper fraction. The numerator is greater than denominator then it is improper fraction. The fraction is combination of whole number and fraction then it is mixed fraction.
Here in this question the both numbers are a proper fraction.
Now consider the given data
 $ \dfrac{2}{5} + \dfrac{3}{{10}} $
The values of denominator are not same so we take LCM for the denominator
The LCM of 5 and 10

5	5, 10
2	1, 2
	1, 1

Therefore, the LCM of 5 and 10 we have $ 5 \times 2 = 10 $
Now taking the LCM we have
 $ \Rightarrow \dfrac{{\dfrac{2}{5} \times 10 + \dfrac{3}{{10}} \times 10}}{{10}} $
On the simplification we get
 $ \Rightarrow \dfrac{{2 \times 2 + 3 \times 1}}{{10}} $
Using the multiplication, we get
 $ \Rightarrow \dfrac{{4 + 3}}{{10}} $
On further simplification we get
 $ \Rightarrow \dfrac{7}{{10}} $
This is also a proper fraction, where the numerator is less than the denominator.
We can’t simplify further. Therefore, we have $ \dfrac{2}{5} + \dfrac{3}{{10}} = \dfrac{7}{{10}} $
So, the correct answer is “ $ \dfrac{7}{{10}} $ ”.

Note: While adding the two fractions we need to check the values of the denominator, if both denominators are having the same value then we can add the numerators. Suppose if the fractions have different denominators, we have to take LCM for the denominators and we simplify for further.