Math Problem Statement

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

Solution

The given mathematical expression is:

2.3113\frac{2. \overline{3}}{1 - \frac{1}{3}}

Where 2.32.\overline{3} represents the repeating decimal 2.3332.333\ldots.

Step-by-step solution:

  1. Convert repeating decimal to a fraction: 2.3=732.\overline{3} = \frac{7}{3}

  2. Simplify the denominator: 113=3313=231 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}

  3. Now substitute these into the original expression: 7323=73×32=72\frac{\frac{7}{3}}{\frac{2}{3}} = \frac{7}{3} \times \frac{3}{2} = \frac{7}{2}

  4. Final result: 72=3.5\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 2.62.\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!

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Math Problem Analysis

Mathematical Concepts

Repeating Decimals
Fractions
Division of Fractions

Formulas

Convert repeating decimal to fraction: 2.3̅ = 7/3
Subtract fractions: 1 - 1/3 = 2/3
Divide by a fraction: a / b = a * (1/b)

Theorems

Division by a fraction is the same as multiplying by its reciprocal

Suitable Grade Level

Grades 6-8