3/10 divided by 4/5
Understand the Problem
The question is asking to divide the fraction 3/10 by the fraction 4/5. This involves multiplying the first fraction by the reciprocal of the second fraction.
Answer
$\frac{3}{8}$
Answer for screen readers
The final answer is $\frac{3}{8}$.
Steps to Solve
- Identify the reciprocal of the second fraction
To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{4}{5}$ is $\frac{5}{4}$.
- Rewrite the division as multiplication
Now rewrite the division of fractions as a multiplication problem: $$ \frac{3}{10} \div \frac{4}{5} = \frac{3}{10} \times \frac{5}{4} $$
- Multiply the numerators and denominators
Next, multiply the numerators together and the denominators together: $$ \frac{3 \times 5}{10 \times 4} $$
Calculating the products gives: $$ \frac{15}{40} $$
- Simplify the result if possible
Now we need to simplify the fraction $\frac{15}{40}$. The greatest common divisor of 15 and 40 is 5. So we divide both the numerator and denominator by 5: $$ \frac{15 \div 5}{40 \div 5} = \frac{3}{8} $$
The final answer is $\frac{3}{8}$.
More Information
When dividing fractions, remember to always multiply by the reciprocal. In this case, we transformed $\frac{3}{10} \div \frac{4}{5}$ into $\frac{3}{10} \times \frac{5}{4}$, simplifying to get the answer.
Tips
- Forgetting to take the reciprocal: Always remember that to divide by a fraction, you must multiply by its reciprocal.
- Not simplifying the final answer: Always check if your answer can be simplified further before finalizing it.
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