Solve the Fraction Addition: 4/15 + 2/5 Step by Step

To solve the problem $\frac{4}{15} + \frac{2}{5}$, we will add these fractions by finding a common denominator.

Step 1: Find the Least Common Denominator (LCD).
The denominators are 15 and 5. The LCM of 15 and 5 is 15, as 15 is already a multiple of 5.

Step 2: Convert each fraction to have the same denominator, 15.
- The fraction $\frac{4}{15}$ already has the denominator 15. - Convert $\frac{2}{5}$ to a fraction with a denominator of 15 by multiplying both the numerator and denominator by 3: $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$.

Step 3: Add the fractions with common denominators.
Now we have: $\frac{4}{15} + \frac{6}{15}$.
Add the numerators: $4 + 6 = 10$.
The new fraction is $\frac{10}{15}$.

Step 4: Simplify the resulting fraction, if possible.
Both 10 and 15 are divisible by 5.
Divide the numerator and the denominator by their greatest common divisor (GCD), which is 5: $\frac{10 \div 5}{15 \div 5} = \frac{2}{3}$.

The solution to the problem is $\frac{2}{3}$.