**Operating with Mixed Numbers: Understanding 7 1/2 - 3 3/5**

In this article, we will explore the operation of subtracting mixed numbers, specifically focusing on the example of 7 1/2 - 3 3/5. We will break down the process step-by-step, providing a clear and concise explanation to help you understand the concept.

**Understanding Mixed Numbers**

Before we dive into the operation, let's quickly review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, 7 1/2 is a mixed number, where 7 is the whole number and 1/2 is the fraction.

**Converting Mixed Numbers to Improper Fractions**

To operate with mixed numbers, it's often helpful to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator.

### Converting 7 1/2 to an Improper Fraction

- Multiply the whole number (7) by the denominator (2): 7 × 2 = 14
- Add the numerator (1): 14 + 1 = 15
- Write the improper fraction: 15/2

### Converting 3 3/5 to an Improper Fraction

- Multiply the whole number (3) by the denominator (5): 3 × 5 = 15
- Add the numerator (3): 15 + 3 = 18
- Write the improper fraction: 18/5

**Subtracting Improper Fractions**

Now that we have converted both mixed numbers to improper fractions, we can subtract them. To subtract fractions, we need to have the same denominator. In this case, we can find the least common multiple (LCM) of 2 and 5, which is 10.

### Subtracting the Improper Fractions

- Convert both fractions to have a denominator of 10:
- 15/2 = 75/10
- 18/5 = 72/10

- Subtract the fractions: 75/10 - 72/10 = 3/10

**Simplifying the Result**

Our result is an improper fraction, 3/10. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case.

### Simplified Result

- The simplified result is: 3/10

**Conclusion**

In conclusion, we have successfully subtracted the mixed numbers 7 1/2 - 3 3/5 by converting them to improper fractions, finding the least common multiple, subtracting the fractions, and simplifying the result. The final answer is 3/10.