5/6 divided by 2 and 1/5 as a fraction or mixed number in simplest form.
The correct answer and explanation is:
Correct Answer:
56÷215=2566\frac{5}{6} \div 2\frac{1}{5} = \frac{25}{66}
Step-by-Step Explanation (300 words):
To solve 56÷215\frac{5}{6} \div 2\frac{1}{5}, we need to divide a fraction by a mixed number. Follow these steps:
1. Convert the mixed number to an improper fraction.
The mixed number is 2152\frac{1}{5}.
To convert to an improper fraction: 215=2×5+15=1152\frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}
2. Rewrite the division as multiplication by the reciprocal.
When dividing fractions, you multiply the first fraction by the reciprocal (flipped version) of the second: 56÷115=56×511\frac{5}{6} \div \frac{11}{5} = \frac{5}{6} \times \frac{5}{11}
3. Multiply the numerators and denominators.
56×511=5×56×11=2566\frac{5}{6} \times \frac{5}{11} = \frac{5 \times 5}{6 \times 11} = \frac{25}{66}
4. Simplify the result.
Check for any common factors between 25 and 66:
- 25 = 5×55 \times 5
- 66 = 2×3×112 \times 3 \times 11
No common factors, so the fraction is already in simplest form.
Final Answer:
56÷215=2566\frac{5}{6} \div 2\frac{1}{5} = \frac{25}{66}
Summary:
This problem involves converting a mixed number to an improper fraction, then applying the rule for dividing fractions (multiply by the reciprocal), and finally simplifying. Understanding this process is critical in fraction arithmetic and reinforces skills needed in both math and real-world applications such as cooking, measurements, and finance.