
(9⅓-2⅚+1¼)÷[1⅙+{2⅓+(6+5-4½)}]

To solve the expression \((9 \frac{1}{3} - 2 \frac{5}{6} + 1 \frac{1}{4}) \div \left[1 \frac{1}{6} + \left\{2 \frac{1}{3} + \left(6 + 5 - 4 \frac{1}{2}\right)\right\}\right]\), we'll proceed step by step.

### Step 1: Convert mixed numbers to improper fractions
1. \(9 \frac{1}{3} = \frac{28}{3}\)
2. \(2 \frac{5}{6} = \frac{17}{6}\)
3. \(1 \frac{1}{4} = \frac{5}{4}\)
4. \(1 \frac{1}{6} = \frac{7}{6}\)
5. \(2 \frac{1}{3} = \frac{7}{3}\)
6. \(4 \frac{1}{2} = \frac{9}{2}\)

### Step 2: Simplify the innermost expression inside the braces
\[
6 + 5 - 4 \frac{1}{2} = 11 - \frac{9}{2} = \frac{22}{2} - \frac{9}{2} = \frac{13}{2}
\]

### Step 3: Continue simplifying the expression inside the braces
\[
2 \frac{1}{3} + \frac{13}{2} = \frac{7}{3} + \frac{13}{2} = \frac{14}{6} + \frac{39}{6} = \frac{53}{6}
\]

### Step 4: Simplify the expression inside the brackets
\[
1 \frac{1}{6} + \frac{53}{6} = \frac{7}{6} + \frac{53}{6} = \frac{60}{6} = 10
\]

### Step 5: Simplify the numerator
\[
9 \frac{1}{3} - 2 \frac{5}{6} + 1 \frac{1}{4} = \frac{28}{3} - \frac{17}{6} + \frac{5}{4}
\]
To subtract and add, find a common denominator:
\[
\frac{28}{3} = \frac{56}{6}, \quad \frac{5}{4} = \frac{15}{12} = \frac{30}{24}
\]
Now simplify:
\[
\frac{56}{6} - \frac{17}{6} = \frac{39}{6} = \frac{78}{12}, \quad \frac{78}{12} + \frac{30}{24} = \frac{216}{24} + \frac{30}{24} = \frac{246}{24} = \frac{41}{4}
\]

### Step 6: Perform the division
\[
\frac{41}{4} \div 10 = \frac{41}{4} \times \frac{1}{10} = \frac{41}{40}
\]

### Final Answer:
\[
\frac{41}{40} \text{ or } 1.025
\]

Do you want more details or have any questions?

Here are some related questions:
1. How do you convert a mixed number into an improper fraction?
2. What is the process for finding a common denominator?
3. How do you simplify a complex fraction?
4. What is the distributive property, and how is it applied in expressions like this?
5. How does dividing by a fraction work?

**Tip:** Always simplify expressions inside parentheses, braces, and brackets first, moving from the innermost to the outermost.

Learn how to solve the complex mathematical expression (9⅓ - 2⅚ + 1¼) ÷ [1⅙ + {2⅓ + (6 + 5 - 4½)}] step-by-step with a detailed solution. This problem covers mixed numbers, improper fractions, order of operations, and complex fractions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation