https://r2.erweima.ai/mathbot/image/1727210615218ighb37l6.jpg

Let's solve the problems in the image step by step.

### Problem 1:
\[
\frac{5}{14} \times \left( -\frac{1}{5} + \frac{3}{5} \right)
\]
First, simplify the expression inside the parentheses:
\[
-\frac{1}{5} + \frac{3}{5} = \frac{2}{5}
\]
Now, multiply:
\[
\frac{5}{14} \times \frac{2}{5} = \frac{5 \times 2}{14 \times 5} = \frac{10}{70} = \frac{1}{7}
\]
So, the answer is:
\[
\frac{1}{7}
\]

### Problem 2:
\[
\left( \frac{2}{7} - \frac{1}{7} \right) \times (-3 + 5)
\]
First, simplify the expression inside the parentheses:
\[
\frac{2}{7} - \frac{1}{7} = \frac{1}{7}
\]
And for the second parentheses:
\[
-3 + 5 = 2
\]
Now, multiply:
\[
\frac{1}{7} \times 2 = \frac{2}{7}
\]
So, the answer is:
\[
\frac{2}{7}
\]

### Problem 3:
\[
-\frac{1}{50} + \frac{1}{10} \times 1
\]
First, simplify the multiplication:
\[
\frac{1}{10} \times 1 = \frac{1}{10}
\]
Now, add the fractions:
\[
-\frac{1}{50} + \frac{1}{10}
\]
We need a common denominator (which is 50):
\[
-\frac{1}{50} + \frac{5}{50} = \frac{-1 + 5}{50} = \frac{4}{50} = \frac{2}{25}
\]
So, the answer is:
\[
\frac{2}{25}
\]

### Problem 4:
\[
\frac{3}{4} + \left( 1 - \frac{13}{6} \right) + \frac{1}{4} \div \frac{6}{7}
\]
First, simplify each part:
\[
1 - \frac{13}{6} = \frac{6}{6} - \frac{13}{6} = -\frac{7}{6}
\]
Now, simplify the division:
\[
\frac{1}{4} \div \frac{6}{7} = \frac{1}{4} \times \frac{7}{6} = \frac{7}{24}
\]
Now, combine everything:
\[
\frac{3}{4} + \left( -\frac{7}{6} \right) + \frac{7}{24}
\]
We need a common denominator (24):
\[
\frac{3}{4} = \frac{18}{24}, \quad -\frac{7}{6} = -\frac{28}{24}, \quad \frac{7}{24} = \frac{7}{24}
\]
Now, add:
\[
\frac{18}{24} - \frac{28}{24} + \frac{7}{24} = \frac{18 - 28 + 7}{24} = \frac{-3}{24} = -\frac{1}{8}
\]
So, the answer is:
\[
-\frac{1}{8}
\]

### Summary of Answers:
1. \(\frac{1}{7}\)
2. \(\frac{2}{7}\)
3. \(\frac{2}{25}\)
4. \(-\frac{1}{8}\)

Do you need further clarification on any of these steps?  
Here are five questions to deepen your understanding:
1. How do you determine the least common denominator when adding or subtracting fractions?
2. What are the rules for multiplying and dividing fractions?
3. How does simplifying expressions inside parentheses help in solving equations?
4. Why is it important to check for common factors when simplifying fractions?
5. How do you handle negative signs when dealing with fractions?

**Tip**: When working with complex fractions, break the problem into smaller, more manageable steps like simplifying parentheses first and then performing multiplications or additions.

Perform operations and simplify the following fraction problems as shown in the image.

Learn how to perform arithmetic operations and simplify fractions, including addition, subtraction, multiplication, and division, with detailed solutions to real examples. Suitable for Grades 5-7.

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