To solve the division $55 \frac{1}{2} \div 0.6$, we first need to convert the mixed number and decimal to fractions for easier calculation.

Step 1: Convert Mixed Number to an Improper Fraction

The mixed number $55 \frac{1}{2}$ can be converted to an improper fraction:

$55 \frac{1}{2} = \frac{55 \times 2 + 1}{2} = \frac{111}{2}$

Step 2: Convert Decimal to Fraction

Next, convert the decimal $0.6$ to a fraction:

$0.6 = \frac{6}{10} = \frac{3}{5}$

Step 3: Division of Fractions

Now, to divide by a fraction, multiply by its reciprocal:

$\frac{111}{2} \div \frac{3}{5} = \frac{111}{2} \times \frac{5}{3}$

Step 4: Perform the Multiplication

Multiply the numerators and denominators:

$= \frac{111 \times 5}{2 \times 3} = \frac{555}{6}$

Step 5: Simplify the Fraction

To simplify, divide the numerator and the denominator by their greatest common divisor (GCD), which is 3:

$\frac{555}{6} = \frac{185}{2}$

Step 6: Convert to Mixed Number

Finally, convert $\frac{185}{2}$ back to a mixed number:

$\frac{185}{2} = 92 \frac{1}{2}$

Final Answer

$55 \frac{1}{2} \div 0.6 = 92 \frac{1}{2}$

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Related Questions:

1. How do you divide fractions and mixed numbers in general?
2. What are some methods to convert decimals to fractions?
3. Can we multiply fractions directly without converting to improper fractions?
4. How do we find the greatest common divisor (GCD) of two numbers?
5. How can we solve similar problems with more complex fractions or decimals?

Tip:

When dividing by a decimal, consider converting all numbers to fractions to simplify the calculation.