Question

How do you simplify $\dfrac{1}{5} + \dfrac{1}{{10}}$ ?

Answer 1

Hint:Here two fractions are given. In fraction $\dfrac{1}{5}$, 1 is numerator and 5 is denominator . Similarly in fraction $\dfrac{1}{{10}}$, 1 is numerator and 10 is denominator. To add these two fractions first make the denominators common by taking LCM or ( least common multiple ) of both denominators and start solving.

Complete step by step answer:
First, find the least common multiple or LCM of two denominators.
LCM of 5 and 10 is 10
Make the denominator common of both the fractions, by multiplying both by appropriate factors.
For the first fraction $\dfrac{1}{5}$, to make common denominator 10 multiply the numerator and denominator by 2.
We get, $\dfrac{{1 \times 2}}{{5 \times 2}} = \dfrac{2}{{10}}$
Similarly, for the second fraction $\dfrac{1}{{10}}$, the denominator is already common which is 10.
$ \Rightarrow \dfrac{{1 \times 1}}{{10 \times 1}} = \dfrac{1}{{10}}$
Now, both the fractions have the same denominator 10. You can add them.
$ \Rightarrow \dfrac{2}{{10}} + \dfrac{1}{{10}}$
Combine the numerator of both fractions over the common denominator 10 for addition.
$ \Rightarrow \dfrac{{2 + 1}}{{10}}$
$ \Rightarrow \dfrac{3}{{10}}$

Thus, simplification of $\dfrac{1}{5} + \dfrac{1}{{10}}$ is $\dfrac{3}{{10}}$.

Additional information:
$\dfrac{3}{{10}}$ can also be written in decimal form .
The decimal form of $\dfrac{3}{{10}}$ is 0.3

Note: When simplifying two fractions having two different denominators, take their LCM ( or least common multiple ) of both denominators.
Make sure to multiply both fractions by appropriate factors to make the denominator common and to simplify the question.