https://file.aiquickdraw.com/mathbot/file/1725931519341rtlaf4cf.jpg

The mathematical expression in the image is:

\[
\left( 3 \frac{1}{2} - 2 \frac{1}{3} \right) \times 1 \frac{4}{5} = ?
\]

Let's break it down and solve step by step:

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

Now the expression becomes:

\[
\left( \frac{7}{2} - \frac{7}{3} \right) \times \frac{9}{5}
\]

### Step 2: Subtract the fractions inside the parentheses.
To subtract \( \frac{7}{2} \) and \( \frac{7}{3} \), we need a common denominator:
- The least common denominator (LCD) of 2 and 3 is 6.
- Convert the fractions:
  \[
  \frac{7}{2} = \frac{21}{6}, \quad \frac{7}{3} = \frac{14}{6}
  \]
- Now subtract:
  \[
  \frac{21}{6} - \frac{14}{6} = \frac{7}{6}
  \]

### Step 3: Multiply by \( \frac{9}{5} \).
Now, we multiply \( \frac{7}{6} \times \frac{9}{5} \):
\[
\frac{7}{6} \times \frac{9}{5} = \frac{7 \times 9}{6 \times 5} = \frac{63}{30}
\]

### Step 4: Simplify the result.
The greatest common divisor (GCD) of 63 and 30 is 3, so we can simplify the fraction:
\[
\frac{63}{30} = \frac{21}{10}
\]

This is an improper fraction, and it can also be written as a mixed number:
\[
\frac{21}{10} = 2 \frac{1}{10}
\]

### Final Answer:
\[
\boxed{2 \frac{1}{10}}
\]

Let me know if you'd like more details or have any questions!

Here are 5 related questions:
1. How do you add and subtract fractions with different denominators?
2. What is the process to convert an improper fraction into a mixed number?
3. How do you multiply mixed numbers without converting them first?
4. Why do we use the least common denominator (LCD) in fraction operations?
5. Can this problem be solved using decimal approximations instead of fractions?

**Tip:** Always simplify fractions as much as possible to make calculations easier and the final answer clearer!

Solve the mathematical expression involving mixed fractions: \( \left( 3 \frac{1}{2} - 2 \frac{1}{3} \right) \times 1 \frac{4}{5} \)

This detailed guide explores how to solve expressions involving mixed fractions, such as \( \left( 3 \frac{1}{2} - 2 \frac{1}{3} \right) \times 1 \frac{4}{5} \). Learn the techniques of converting mixed numbers to improper fractions, finding common denominators, and simplifying results. Ideal for students in Grades 6-8.

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