Question

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

Answer 1

Hint:Here two fractions are given. In fraction ${\displaystyle \frac{1}{5}}$, 1 is numerator and 5 is denominator . Similarly in fraction ${\displaystyle \frac{1}{10}}$, 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 ${\displaystyle \frac{1}{5}}$, to make common denominator 10 multiply the numerator and denominator by 2.
We get, ${\displaystyle \frac{1\times 2}{5\times 2}}={\displaystyle \frac{2}{10}}$
Similarly, for the second fraction ${\displaystyle \frac{1}{10}}$, the denominator is already common which is 10.
$\Rightarrow {\displaystyle \frac{1\times 1}{10\times 1}}={\displaystyle \frac{1}{10}}$
Now, both the fractions have the same denominator 10. You can add them.
$\Rightarrow {\displaystyle \frac{2}{10}}+{\displaystyle \frac{1}{10}}$
Combine the numerator of both fractions over the common denominator 10 for addition.
$\Rightarrow {\displaystyle \frac{2+1}{10}}$
$\Rightarrow {\displaystyle \frac{3}{10}}$

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

Additional information:
${\displaystyle \frac{3}{10}}$ can also be written in decimal form .
The decimal form of ${\displaystyle \frac{3}{10}}$ 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.