Solve: Adding Fractions 3/5 + 2/7 Step by Step

To solve the given problem, we will follow these steps:

• Step 1: Determine a common denominator for the fractions.
• Step 2: Convert each fraction to have the common denominator.
• Step 3: Add the numerators and keep the common denominator.
• Step 4: Simplify the resulting fraction if possible.

Let's proceed with each step:

Step 1: Determine a common denominator.
The denominators of the fractions are 5 and 7. The least common multiple (LCM) of 5 and 7 is 35. Thus, the common denominator is 35.

Step 2: Convert each fraction to have the common denominator of 35.
Convert $\frac{3}{5}$ to a fraction with a denominator of 35: $\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}$.
Convert $\frac{2}{7}$ to a fraction with a denominator of 35: $\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}$.

Step 3: Add the numerators and use the common denominator.
Now add the fractions: $\frac{21}{35} + \frac{10}{35} = \frac{21+10}{35} = \frac{31}{35}$.

Step 4: Simplify the result.
The fraction $\frac{31}{35}$ is already in its simplest form since 31 and 35 have no common factors other than 1.

Therefore, the solution to the problem is $\frac{31}{35}$.