What is
3
1
divided by
6
5
?
The Correct Answer and Explanation is :
To divide the fraction (\frac{3}{1}) by the fraction (\frac{6}{5}), we follow the rules for dividing fractions. The process involves multiplying the first fraction by the reciprocal of the second fraction.
Steps to Solve:
- Identify the fractions: We have (\frac{3}{1}) and (\frac{6}{5}).
- Reciprocal of the second fraction: The reciprocal of (\frac{6}{5}) is (\frac{5}{6}). The reciprocal is obtained by swapping the numerator and the denominator.
- Multiply the first fraction by the reciprocal:
[
\frac{3}{1} \div \frac{6}{5} = \frac{3}{1} \times \frac{5}{6}
] - Multiply the numerators: Multiply the numerators together:
[
3 \times 5 = 15
] - Multiply the denominators: Multiply the denominators together:
[
1 \times 6 = 6
] - Combine the results: Now, we have:
[
\frac{15}{6}
] - Simplify the fraction: Both 15 and 6 can be divided by their greatest common divisor, which is 3:
[
\frac{15 \div 3}{6 \div 3} = \frac{5}{2}
]
Final Answer:
Thus, (\frac{3}{1}) divided by (\frac{6}{5}) equals (\frac{5}{2}) or 2.5 in decimal form.
Explanation of Fraction Division:
Dividing fractions may initially seem complex, but it fundamentally hinges on the idea of multiplication. When we divide by a fraction, we are essentially asking how many times that fraction fits into another. By converting the division into multiplication with the reciprocal, the operation becomes straightforward. This method emphasizes the relationship between multiplication and division, revealing that division is simply a form of scaling down a quantity, while multiplication increases it. This principle applies universally, whether dealing with whole numbers, fractions, or decimals, making understanding fraction operations crucial in both mathematical theory and practical applications.