Question

How do we write the simplest form given $\dfrac{2}{3}+\dfrac{1}{3}$ ?

Answer 1

Hint: We add 2 fractions by making their denominator same , we do that by taking the LCM of the 2 fractions . After making their denominator the same we can just add the 2 numerators keeping the denominator unchanged.

Complete step-by-step answer:
We have to add $\dfrac{2}{3}+\dfrac{1}{3}$
We can see that the 2 fractions have same denominator, now we just can add the 2 numerator keeping the denominator unchanged
 So we can write $\dfrac{2}{3}+\dfrac{1}{3}$ is equal to $\dfrac{3}{3}$ which is equal to 1.
The simplest form of $\dfrac{2}{3}+\dfrac{1}{3}$ is equal to 1.

Note: When we add 2 or more fractions which do not have same denominator, we just take the LCM of the denominators and convert all denominators to the LCM for example we have $\dfrac{3}{4}+\dfrac{5}{6}$ we can calculate the LCM of 4 and 6 that is 12. We can write $\dfrac{3}{4}$ as $\dfrac{9}{12}$ by multiplying 3 to both denominator and numerator. We can write $\dfrac{5}{6}$ as $\dfrac{10}{12}$ by multiplying 2 to both numerator and denominator. Now we can add the numerators so $\dfrac{3}{4}+\dfrac{5}{6}$ is equal to $\dfrac{19}{12}$ . It is not necessary to change the denominator to LCM, we can convert it to any number. Just keep in mind that we have to multiply the same number to denominator and numerator. Always remember when we multiply the same number to denominator and numerator the value of the fraction will not change, it remains the same except 0. We can not multiply 0 to numerator and denominator, the value of $\dfrac{0}{0}$ does not exist.