3/2 divided by 5/8
Understand the Problem
The question is asking to divide the fraction 3/2 by the fraction 5/8. To solve this, we will use the rule that dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, we will multiply 3/2 by the reciprocal of 5/8, which is 8/5.
Answer
The answer is $ \frac{12}{5} $.
Answer for screen readers
The final answer is $ \frac{12}{5} $.
Steps to Solve
- Identify the reciprocal of the second fraction
To divide by a fraction, you multiply by its reciprocal. The reciprocal of $ \frac{5}{8} $ is $ \frac{8}{5} $.
- Set up the multiplication
Now, we can set up the multiplication of the first fraction by the reciprocal of the second fraction: $$ \frac{3}{2} \times \frac{8}{5} $$
- Multiply the numerators and denominators
Multiply the numerators together and the denominators together: $$ \frac{3 \times 8}{2 \times 5} $$
- Calculate the multiplication
This results in: $$ \frac{24}{10} $$
- Simplify the fraction
Now, we simplify $ \frac{24}{10} $ by finding the greatest common divisor (GCD), which is 2: $$ \frac{24 \div 2}{10 \div 2} = \frac{12}{5} $$
The final answer is $ \frac{12}{5} $.
More Information
The result $ \frac{12}{5} $ can also be expressed as a mixed number, which is $ 2 \frac{2}{5} $. This shows that 12 is greater than 5, meaning there are two whole parts and two-fifths leftover.
Tips
- Forgetting to take the reciprocal: Carefully remember that dividing by a fraction means you must flip it to multiply.
- Not simplifying the final fraction: Always check if you can simplify the result.
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