	3 +   −   − [1 − (2   + 1, 7̅)]   



Let's break down the given expression:

\[
3 + - - [1 - (2 + 1.\overline{7})]
\]

### Step-by-Step Solution:

1. **Simplify the Double Negatives**:
   - The two consecutive negative signs cancel each other out. So, we have:
   \[
   3 + [1 - (2 + 1.\overline{7})]
   \]

2. **Convert the Repeating Decimal**:
   - \(1.\overline{7}\) is a repeating decimal, equivalent to:
   \[
   1.\overline{7} = \frac{17}{9}
   \]

3. **Simplify the Inner Parenthesis**:
   - Now substitute the repeating decimal fraction:
   \[
   3 + [1 - (2 + \frac{17}{9})]
   \]
   Combine the terms inside the parenthesis:
   \[
   2 + \frac{17}{9} = \frac{18}{9} + \frac{17}{9} = \frac{35}{9}
   \]

4. **Simplify the Outer Brackets**:
   - Now simplify the expression inside the brackets:
   \[
   3 + [1 - \frac{35}{9}]
   \]
   Rewrite 1 as a fraction with a denominator of 9:
   \[
   3 + \left[\frac{9}{9} - \frac{35}{9}\right] = 3 + \left[\frac{-26}{9}\right]
   \]

5. **Final Calculation**:
   - Add \(3 + \frac{-26}{9}\):
   Rewrite 3 as a fraction:
   \[
   3 = \frac{27}{9}
   \]
   Now, combine:
   \[
   \frac{27}{9} + \frac{-26}{9} = \frac{1}{9}
   \]

Thus, the final value of the expression is:

\[
\boxed{\frac{1}{9}}
\]

Would you like further details or clarifications on any step?

### Relative Questions:
1. How do you convert repeating decimals to fractions?
2. What is the significance of combining like terms in algebraic expressions?
3. How do you simplify expressions with multiple negatives?
4. Can you explain why fractions are used in some repeating decimals?
5. How do you handle mixed numbers within complex expressions?
6. Why is it important to convert whole numbers to fractions when simplifying?
7. What is the importance of the order of operations in simplifying expressions?
8. How does adding fractions with different numerators work?

**Tip:** When working with repeated decimals, converting them to fractions makes calculations easier and more precise.

Learn how to simplify the expression 3 + - - [1 - (2 + 1.7̅)] step-by-step with detailed explanations. This problem involves arithmetic operations and converting repeating decimals to fractions. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation