Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.

Question

1/5=

2/3=

1/5+2/3=

Answer 1

To add the fractions \( \frac{1}{5} \) and \( \frac{2}{3} \), we first need to find the least common denominator (LCD) of the two fractions.

1. Identify the denominators: The denominators are 5 and 3.

2. Find the LCD: The multiples of 5 are 5, 10, 15, 20, ... and the multiples of 3 are 3, 6, 9, 12, 15, ... The least common multiple of 5 and 3 is 15. So, the LCD is 15.

3. Convert the fractions to equivalent fractions with the LCD:

   • For \( \frac{1}{5} \): \[ \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15} \]

   • For \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]

4. Add the fractions: \[ \frac{1}{5} + \frac{2}{3} = \frac{3}{15} + \frac{10}{15} = \frac{3 + 10}{15} = \frac{13}{15} \]

5. Reduce the final sum: The fraction \( \frac{13}{15} \) is already in its simplest form because 13 is a prime number and does not divide 15.

Thus, the final result is: \[ \frac{1}{5} + \frac{2}{3} = \frac{13}{15} \]