Let's break down and solve the given expression:

\[
\frac{11}{25} \cdot \frac{2}{3} - \frac{1}{6} + \left(-\frac{2}{3} \cdot \frac{4}{25}\right)
\]

### Step 1: Multiply the fractions
\[
\frac{11}{25} \cdot \frac{2}{3} = \frac{11 \times 2}{25 \times 3} = \frac{22}{75}
\]

\[
-\frac{2}{3} \cdot \frac{4}{25} = -\frac{2 \times 4}{3 \times 25} = -\frac{8}{75}
\]

### Step 2: Combine all the terms
Now, the expression becomes:
\[
\frac{22}{75} - \frac{1}{6} - \frac{8}{75}
\]

### Step 3: Simplify by finding a common denominator
The least common denominator between 75 and 6 is 150.

Convert all fractions to have a denominator of 150:
\[
\frac{22}{75} = \frac{44}{150}, \quad \frac{1}{6} = \frac{25}{150}, \quad \frac{8}{75} = \frac{16}{150}
\]

The expression is now:
\[
\frac{44}{150} - \frac{25}{150} - \frac{16}{150}
\]

### Step 4: Perform the subtraction
\[
\frac{44}{150} - \frac{25}{150} = \frac{19}{150}
\]
\[
\frac{19}{150} - \frac{16}{150} = \frac{3}{150}
\]

### Step 5: Simplify the final fraction
\[
\frac{3}{150} = \frac{1}{50}
\]

### Final Answer:
\[
\boxed{\frac{1}{50}}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your knowledge:
1. How do you find the least common denominator (LCD) of multiple fractions?
2. What are the steps to multiply and divide fractions?
3. How can you simplify complex fractions into simpler forms?
4. How do negative signs affect operations with fractions?
5. What are the common methods for adding or subtracting fractions with unlike denominators?

**Tip:** When working with multiple fractions, it's helpful to convert them to a common denominator before performing addition or subtraction.

Learn how to solve arithmetic operations involving fractions step-by-step: 11/25 * 2/3 - 1/6 - (-2/3 * 4/25). This problem covers key concepts like multiplying fractions, finding common denominators, and simplifying complex fractions. 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