Question

Find the sum. $$\frac{2}{3}+\frac{1}{6}$$

Short answer

The sum of the fractions \(\frac{2}{3}\) and \(\frac{1}{6}\) is \(\frac{5}{6}\).

Step-by-step solution

Identify the denominators

The denominators are the bottom numbers of the fractions. Here, we have denominators of 3 and 6. We need to find the least common denominator (LCD) to add these two fractions. The LCD is the least common multiple (LCM) of the two denominators.

Find the least common denominator (LCD)

As 3 and 6 are both multiples of 3, and 6 is the smallest number that both 3 and 6 go into, our LCD is 6.

Convert the fractions

We must rewrite the fractions so that they both have the LCD 6 as the denominator. The first fraction remains the same as its denominator is part of LCD (6). For the second fraction, it is already the same as our LCD, so no changes are needed.

Add the fractions

Now that both fractions have the same denominator, add the numerators together. Here, 4 (from \(\frac{2}{3}\) converted into \(\frac{4}{6}\)) and 1 (from \(\frac{1}{6}\)) make 5. So, the sum of the fractions is \(\frac{5}{6}\).