Perform the operation below. Express your answer as a mixed number in simplest form.

minus, 2, start fraction, 3, divided by, 5, end fraction, minus, 3, one half

−253​−321​

Let's break down the operation:

\[
- \frac{2}{5} - 3\frac{1}{2}
\]

### Step 1: Convert the mixed number to an improper fraction.

For \( 3\frac{1}{2} \), convert the whole number and fraction into a single improper fraction:

\[
3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}
\]

Now, the expression becomes:

\[
- \frac{2}{5} - \frac{7}{2}
\]

### Step 2: Find a common denominator.

The denominators are 5 and 2. The least common denominator (LCD) is 10. Rewrite both fractions with denominator 10:

\[
- \frac{2}{5} = - \frac{4}{10}, \quad \frac{7}{2} = \frac{35}{10}
\]

Now the expression is:

\[
- \frac{4}{10} - \frac{35}{10}
\]

### Step 3: Combine the fractions.

Since the denominators are the same, combine the numerators:

\[
- \frac{4 + 35}{10} = - \frac{39}{10}
\]

### Step 4: Convert the improper fraction to a mixed number.

To convert \( - \frac{39}{10} \) into a mixed number:

\[
39 \div 10 = 3 \text{ remainder } 9
\]

Thus:

\[
- \frac{39}{10} = - 3\frac{9}{10}
\]

### Final Answer:
\[
- 3\frac{9}{10}
\]

Let me know if you need further clarification or details!

---

Here are 5 related questions to explore further:

1. How do you convert between improper fractions and mixed numbers?
2. What is the least common denominator (LCD), and how do you find it?
3. How do you simplify a fraction before performing addition or subtraction?
4. What is the process for adding and subtracting fractions with unlike denominators?
5. How do you handle negative signs in fraction operations?

**Tip:** Always convert mixed numbers to improper fractions before performing arithmetic operations like addition or subtraction.

Perform the operation below. Express your answer as a mixed number in simplest form. −2/5−3 1/2

Learn how to subtract fractions, including converting mixed numbers to improper fractions and finding a common denominator. The example problem involves subtracting −2/5 from 3 1/2, and the answer is simplified as a mixed number −3 9/10. Suitable for Grades 5-7.

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