Divide. Write your answer as a fraction or a mixed number in simplest form.

Question

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: $$5\frac{5}{6}=5\times 6+5=30+5=35\text{(the numerator)}$$ So, $$5\frac{5}{6}=\frac{35}{6}$$

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

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

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: $$\frac{84÷7}{35÷7}=\frac{12}{5}$$

6. Convert $\frac{12}{5}$ to a mixed number: $$12÷5=2\text{remainder }2$$ So, $$\frac{12}{5}=2\frac{2}{5}$$

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