Question

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.



1/7=

3/14=

1/7+3/14 =

Answer 1

To add the fractions \( \frac{1}{7} \) and \( \frac{3}{14} \), we first need to find the least common denominator (LCD) of the two fractions.

**Step 1: Find the LCD.**
The denominators are 7 and 14. The least common denominator of 7 and 14 is 14.

**Step 2: Convert \( \frac{1}{7} \) to an equivalent fraction with a denominator of 14.**
To convert \( \frac{1}{7} \) to a fraction with a denominator of 14, we can multiply the numerator and denominator by 2:

\[
\frac{1}{7} = \frac{1 \times 2}{7 \times 2} = \frac{2}{14}
\]

**Step 3: Now we have:**
\[
\frac{1}{7} = \frac{2}{14}
\]
\[
\frac{3}{14} = \frac{3}{14} \text{ (already in the correct form)}
\]

**Step 4: Add the two like fractions.**
Now that both fractions have the same denominator, we can add them:

\[
\frac{2}{14} + \frac{3}{14} = \frac{2 + 3}{14} = \frac{5}{14}
\]

**Final Answer:**
The sum \( \frac{1}{7} + \frac{3}{14} = \frac{5}{14} \).

The fraction \( \frac{5}{14} \) is already in simplest form, so that is the final answer.