Question

Divide. Write your answer as a fraction or a mixed number in simplest form.
14 divided by 5 5/6

Answer 1

To divide \( 14 \) by \( 5 \frac{5}{6} \), we first need to convert the mixed number into an improper fraction.

1. Convert \( 5 \frac{5}{6} \) into an improper fraction:
\[
5 \frac{5}{6} = 5 \times 6 + 5 = 30 + 5 = 35 \quad \text{(the numerator)}
\]
So,
\[
5 \frac{5}{6} = \frac{35}{6}
\]

2. Now, we can express the division as:
\[
14 \div 5 \frac{5}{6} = 14 \div \frac{35}{6}
\]

3. Dividing by a fraction is the same as multiplying by its reciprocal:
\[
14 \div \frac{35}{6} = 14 \times \frac{6}{35}
\]

4. Now, we can multiply:
\[
14 \times \frac{6}{35} = \frac{14 \times 6}{35} = \frac{84}{35}
\]

5. Simplify \( \frac{84}{35} \):
- The greatest common divisor (GCD) of 84 and 35 is 7.
- Divide both the numerator and the denominator by 7:
\[
\frac{84 \div 7}{35 \div 7} = \frac{12}{5}
\]

6. Convert \( \frac{12}{5} \) to a mixed number:
\[
12 \div 5 = 2 \quad \text{remainder } 2
\]
So,
\[
\frac{12}{5} = 2 \frac{2}{5}
\]

Therefore, the final answer is:
\[
\frac{12}{5} \text{ or } 2 \frac{2}{5}
\]