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
\[
55 \frac{1}{2} \div 0.6 = 92 \frac{1}{2}
\]

Would you like more details, or do you have any questions?

### 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.

Learn how to solve 55 1/2 ÷ 0.6 by converting mixed numbers and decimals into fractions, followed by dividing fractions using reciprocal multiplication. This detailed, step-by-step solution covers key concepts such as improper fractions and greatest common divisor (GCD), suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation