1 2/5 / 2/5
Check the final answer first, then review the worked steps.
Problem
1 2/5 / 2/5
Answer
\(\frac{7}{2}\)
Step-by-step solution
- Convert the mixed number to an improper fraction: To divide $1\frac{2}{5}$ by $\frac{2}{5}$, first convert the mixed number $1\frac{2}{5}$ into an improper fraction. Multiply the whole number by the denominator and add the numerator: $1 \times 5 + 2 = 7$. Thus, $1\frac{2}{5} = \frac{7}{5}$.
- Set up the division problem: Now the expression is $\frac{7}{5} \div \frac{2}{5}$.
- Perform the division: To divide by a fraction, multiply by its reciprocal. The reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$. So, the expression becomes: $$\frac{7}{5} \times \frac{5}{2}$$.
- Simplify the expression: Multiply the numerators and the denominators: $$\frac{7 \times 5}{5 \times 2} = \frac{35}{10}$$.
- Reduce to simplest form: Divide both the numerator and the denominator by their greatest common divisor, which is 5: $$\frac{35 \div 5}{10 \div 5} = \frac{7}{2}$$.