Question

Explain the steps you need to take to add the following fractions: 56
+ 34
.

Answer 1

To add the fractions \( \frac{5}{6} \) and \( \frac{3}{4} \), follow these steps:

1. **Find a common denominator**: To add fractions, you need a common denominator. The denominators here are 6 and 4. The least common multiple (LCM) of 6 and 4 is 12.

2. **Convert each fraction to have the common denominator**:
- For \( \frac{5}{6} \):
\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\]
- For \( \frac{3}{4} \):
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]

3. **Add the numerators**: Now that both fractions have the same denominator, you can add them.
\[
\frac{10}{12} + \frac{9}{12} = \frac{10 + 9}{12} = \frac{19}{12}
\]

4. **Simplify if necessary**: The fraction \( \frac{19}{12} \) is an improper fraction. If desired, you can convert it to a mixed number:
\[
19 \div 12 = 1 \quad \text{remainder } 7
\]
So,
\[
\frac{19}{12} = 1 \frac{7}{12}
\]

5. **Final answer**: The sum of \( \frac{5}{6} + \frac{3}{4} \) is \( \frac{19}{12} \) or \( 1 \frac{7}{12} \) as a mixed number.

Therefore, \( \frac{5}{6} + \frac{3}{4} = \frac{19}{12} \) or \( 1 \frac{7}{12} \).