5 5/8 divided by 2
Understand the Problem
The question is asking to divide a mixed number, 5 5/8, by 2. This involves converting the mixed number into an improper fraction and then performing the division.
Answer
2 13/16
Answer for screen readers
The final answer is 2 13/16
Steps to Solve
- Convert the mixed number to an improper fraction
To convert 5 5/8 to an improper fraction, first multiply the whole number part by the denominator and then add the numerator.
$$ 5 rac{5}{8} = rac{(5 imes 8) + 5}{8} = rac{40 + 5}{8} = rac{45}{8} $$
- Rewrite the division as multiplication by the reciprocal
To divide by 2, you can multiply by the reciprocal of 2, which is 1/2.
$$ rac{45}{8} \div 2 = rac{45}{8} \times rac{1}{2} $$
- Multiply the fractions
Multiply the numerators and the denominators:
$$ rac{45}{8} \times rac{1}{2} = rac{45 \times 1}{8 \times 2} = rac{45}{16} $$
- Convert the result back to a mixed number (if necessary)
Since the result is an improper fraction, we can convert it back to a mixed number. Divide 45 by 16 to get the whole number part and the remainder:
$$ 45 \div 16 = 2 \ with \ a \ remainder \ of \ 13 $$
So, $$ rac{45}{16} = 2 \frac{13}{16} $$
The final answer is 2 13/16
More Information
Division of mixed numbers often requires converting between mixed numbers and improper fractions. These concepts lay foundational work for more advanced arithmetic operations.
Tips
A common mistake is forgetting to convert the mixed number to an improper fraction before performing operations, or not correctly converting the final improper fraction back to a mixed number.
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