https://file.aiquickdraw.com/mathbot/file/1726342839494gc5xh0mh.jpg

The given mathematical expression is:

\[
\frac{2. \overline{3}}{1 - \frac{1}{3}}
\]

Where \( 2.\overline{3} \) represents the repeating decimal \( 2.333\ldots \).

### Step-by-step solution:

1. **Convert repeating decimal to a fraction**:
   \[
   2.\overline{3} = \frac{7}{3}
   \]

2. **Simplify the denominator**:
   \[
   1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}
   \]

3. **Now substitute these into the original expression**:
   \[
   \frac{\frac{7}{3}}{\frac{2}{3}} = \frac{7}{3} \times \frac{3}{2} = \frac{7}{2}
   \]

4. **Final result**:
   \[
   \frac{7}{2} = 3.5
   \]

So, the result of the operation is **3.5**.

Would you like more details on any part of this solution or further clarification?

Here are some related questions:
1. How can you convert any repeating decimal into a fraction?
2. What are the rules for dividing fractions?
3. How would the problem change if the repeating decimal was different, such as \( 2.\overline{6} \)?
4. How do you simplify complex fractions?
5. What is the relationship between mixed numbers and improper fractions?

**Tip**: Always remember that dividing by a fraction is equivalent to multiplying by its reciprocal!

What is the result of the operation 2.3̅ / (1 - 1/3)?

Learn how to simplify the expression 2.3̅ / (1 - 1/3) step-by-step, converting repeating decimals into fractions and simplifying the division of fractions. This problem covers key algebraic concepts 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