Question

What is $\dfrac{2}{3}$ plus $\dfrac{1}{6}?$

Answer 1

Hint: When we add two fractions with distinct denominators, we will do the cross multiplication. We will add the product of the numerator of the first fraction and the denominator of the second fraction and the product of the numerator of the second fraction and the denominator of the first fraction. Then will divide the sum with the product of the denominators.

Complete step by step solution:
Let us consider the given problem.
We know that the word plus means the addition. So, we are asked two fractions with distinct denominators.
We need to find the sum of the fractions $\dfrac{2}{3}$ and $\dfrac{1}{6}.$
Since the denominators of these fractions are distinct, we need to do the cross multiplication. We will first find the product of the numerator of the first fraction and the denominator of the second fraction.
Similarly, we will find the product of the numerator of the second fraction and the denominator of the first fraction.
Then, we will add these products.
Finally, we will divide the sum by the product of the denominators.
So, the first product is $2\times 6=12.$
The second product is $1\times 3=3.$
Now, we will add these products to get $12+3=15.$
Now, the product of the denominators is $6\times 3=18.$
We will divide the above obtained sum by the product of denominators.
We will get $\dfrac{15}{18}.$
When we divide both the numerator and the denominator with $3,$ we will get $\dfrac{15}{18}=\dfrac{5}{6}.$

Hence $\dfrac{2}{3}+\dfrac{1}{6}=\dfrac{15}{18}=\dfrac{5}{6}.$

Note: We know that we will add the numerators directly and leave the denominator as it is when the denominators of the fractions to be added are the same. In that case, we do not need to do the cross multiplication.