Solve the Fraction Addition: 1/5 + 7/10 Step by Step

To solve the problem of adding the fractions $\frac{1}{5}$ and $\frac{7}{10}$, we follow these steps:

• Step 1: Identify the least common multiple (LCM) of the denominators 5 and 10, which is 10.
• Step 2: Convert $\frac{1}{5}$ to a fraction with a denominator of 10. To do this, multiply both the numerator and denominator by 2: $\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}$
• Step 3: Observe that $\frac{7}{10}$ already has the common denominator of 10.
• Step 4: Add the two fractions with a common denominator: $\frac{2}{10} + \frac{7}{10} = \frac{2 + 7}{10} = \frac{9}{10}$

The sum of $\frac{1}{5}$ and $\frac{7}{10}$ is thus $\mathbf{\frac{9}{10}}$.