https://file.aiquickdraw.com/mathbot/file/1726783964754lqriap5t.jpg

The mathematical expression in the image is:

\[
\frac{3}{10} \div 6 - \frac{4}{5} + \frac{1}{8}
\]

Let's go through the steps to solve it.

### Step 1: Handle the division
\[
\frac{3}{10} \div 6 = \frac{3}{10} \times \frac{1}{6} = \frac{3}{60} = \frac{1}{20}
\]

### Step 2: Rewrite the expression
Now the expression becomes:
\[
\frac{1}{20} - \frac{4}{5} + \frac{1}{8}
\]

### Step 3: Find a common denominator
The least common denominator (LCD) of 20, 5, and 8 is 40. So, we need to rewrite each fraction with 40 as the denominator.

\[
\frac{1}{20} = \frac{2}{40}, \quad \frac{4}{5} = \frac{32}{40}, \quad \frac{1}{8} = \frac{5}{40}
\]

### Step 4: Substitute the new fractions
Now, the expression becomes:
\[
\frac{2}{40} - \frac{32}{40} + \frac{5}{40}
\]

### Step 5: Perform the operations
\[
\frac{2}{40} - \frac{32}{40} = \frac{-30}{40}, \quad \frac{-30}{40} + \frac{5}{40} = \frac{-25}{40}
\]

### Step 6: Simplify the result
\[
\frac{-25}{40} = \frac{-5}{8}
\]

Thus, the final result of the expression is:

\[
\boxed{-\frac{5}{8}}
\]

Would you like more details on any step, or have any other questions?

Here are some related questions to explore:
1. How do you determine the least common denominator (LCD)?
2. What are the properties of fraction division?
3. How do you convert a mixed fraction into an improper fraction?
4. Why is simplifying fractions important in problem-solving?
5. How do you solve complex fractional equations with multiple operations?

**Tip:** Always perform operations like division and multiplication before addition and subtraction, as per the order of operations (PEMDAS).

Solve the expression (3/10) ÷ 6 - (4/5) + (1/8)

Learn how to solve the fractional expression (3/10) ÷ 6 - (4/5) + (1/8) by following a detailed step-by-step process. This problem covers key concepts like division and subtraction of fractions, finding the least common denominator, and applying the order of operations. Suitable for students in Grades 6-8.

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