Question

How do you simplify \[\dfrac{2}{3} + \dfrac{2}{9}\] ?

Answer 1

Hint: To add or subtract the two or more fractions we can do it easily by making their denominator similar. The denominators given are 3 and 9 in which 3 is less than 9 so we should multiply a number in both numerator and denominator both to make 3 equal to 9.

Complete Step by Step Solution:
We have been given with the two fractions $\dfrac{2}{3}$ and $\dfrac{2}{9}$. The easy method to add or subtract the two fractions is to make the denominator of the fractions the same.
Hence, by seeing the above two fractions we can see that the denominators are 3 and 9. If we can, however, make the denominators similar then, we can directly add both the fractions and get the required addition or answer. The denominators given are 3 and 9 in which 3 is less than 9. So, to make 3 equal to 9 we have to multiply 3 with 3, so it will become 9. But we can not multiply 3 only with a denominator; we have to also multiply it with a numerator. Therefore, we can say that 3 should be multiplied with both numerator and denominator –
$ \Rightarrow \dfrac{2}{3} \times \dfrac{3}{3}$
After solving the above, we get –
$ \Rightarrow \dfrac{6}{9}$
Hence, now simply adding the two fractions, we get –
$ \Rightarrow \dfrac{6}{9} + \dfrac{2}{9}$
Taking the denominator common, we can directly add their numerators and get the simplification –
$ \Rightarrow \dfrac{8}{9}$

Hence, the above fraction is the simplification of $\dfrac{8}{9}$ which is the required fraction.

Note: We can also solve this by taking LCM of 3 and 9 which will be 9. Then, divide the denominator with 3 in the fraction $\dfrac{2}{3}$ and multiply it with 2 and repeat the same procedure in the other fraction. We will get the required answer.