Question

What is the value of $\dfrac{2}{6} + \dfrac{3}{5}$ ?

Answer 1

Hint: Here we are going to add two fraction numbers. For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common denominator. So we can calculate as the least common multiple of both denominators.

Complete step-by-step solution:
Here given addition of two fraction number is $\dfrac{2}{6} + \dfrac{3}{5}$
Now, it is useful to notice that in the first fraction $\dfrac{2}{6}$ both numerator and denominator are even numbers so it can be reduced by common factors of them, we get,
$ \Rightarrow \dfrac{2}{6} = \dfrac{1}{3}$
After the reduction our expression becomes $\dfrac{1}{3} + \dfrac{3}{5}$
To calculate the value of such expressions ,we have to write both fractions as fractions with the same denominator.
Here our denominator is $3$ and $5$ now we are going to calculate the least common multiple of both denominators $LCM\left( {3,5} \right) = 15$.
It is enough to find the common denominator by multiplying the denominators $3 \times 5 = 15$ .
Now,
\[\dfrac{{1 \times 5}}{{3 \times 5}} + \dfrac{{3 \times 3}}{{5 \times 3}} = \dfrac{5}{{15}} + \dfrac{9}{{15}}\]
If both denominators have same number we can add their number numerator and simply write down like this,
$ \Rightarrow \dfrac{{5 + 9}}{{15}}$
On simplifying it, we get,
$ \Rightarrow \dfrac{{14}}{{15}}$
This is the final answer for the fraction addition of the given two numbers.

Note: A fraction is a part of a whole or a collection and it consists of a numerator and denominator. While adding or subtracting that, we need to make sure that the denominators are the same. And also reduce the answer if possible. If the numerator of the is $0$ the answer could be $0$if the denominator is $0$the fraction is indeterminate fraction and we cannot calculate the expression, which is a special kind of undefined expression.