2/5 × (- 3 / 7 ) – 1 / 6 × 3 / 2 + 1 / 14 × 2 / 5

To solve the expression \( \frac{2}{5} \times \left(-\frac{3}{7}\right) - \frac{1}{6} \times \frac{3}{2} + \frac{1}{14} \times \frac{2}{5} \), we will evaluate each term individually and then combine the results.

### Step 1: Evaluate each multiplication

1. \( \frac{2}{5} \times \left(-\frac{3}{7}\right) = \frac{2 \times -3}{5 \times 7} = \frac{-6}{35} \)
2. \( \frac{1}{6} \times \frac{3}{2} = \frac{1 \times 3}{6 \times 2} = \frac{3}{12} = \frac{1}{4} \)
3. \( \frac{1}{14} \times \frac{2}{5} = \frac{1 \times 2}{14 \times 5} = \frac{2}{70} = \frac{1}{35} \)

### Step 2: Combine the results

The expression becomes:
\[
\frac{-6}{35} - \frac{1}{4} + \frac{1}{35}
\]

### Step 3: Simplify the expression

1. Combine the fractions with a common denominator. The common denominator for \( \frac{-6}{35} \) and \( \frac{1}{35} \) is 35:
   \[
   \frac{-6 + 1}{35} = \frac{-5}{35} = \frac{-1}{7}
   \]

2. Now we have:
   \[
   \frac{-1}{7} - \frac{1}{4}
   \]
   To combine these fractions, find the common denominator, which is 28:
   \[
   \frac{-1}{7} = \frac{-4}{28} \quad \text{and} \quad \frac{1}{4} = \frac{7}{28}
   \]
   So, the expression becomes:
   \[
   \frac{-4}{28} - \frac{7}{28} = \frac{-11}{28}
   \]

### Final Answer:
\[
\boxed{\frac{-11}{28}}
\]

Would you like further details or have any questions? 

Here are five related questions:

1. How would you solve an expression with three different fractions with unlike denominators?
2. What is the process of finding a common denominator?
3. Can you explain why multiplying a fraction by a negative number changes the sign?
4. How do you simplify fractions after multiplication?
5. How do you add or subtract fractions with different denominators?

**Tip:** Always simplify fractions at each step to make calculations easier.

Learn how to solve the expression 2/5 × (- 3 / 7 ) – 1 / 6 × 3 / 2 + 1 / 14 × 2 / 5 with a detailed step-by-step solution. This problem covers fractions, multiplication of fractions, and addition and subtraction of 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