**Subtracting Mixed Numbers: 7 1/6 - 3 5/8 as a Fraction**

In this article, we will learn how to subtract mixed numbers, specifically **7 1/6 - 3 5/8** as a fraction.

**Understanding Mixed Numbers**

A mixed number is a combination of a whole number and a fraction. For example, **7 1/6** is a mixed number, where **7** is the whole number and **1/6** is the fraction.

**Converting Mixed Numbers to Improper Fractions**

To subtract mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.

Let's convert **7 1/6** and **3 5/8** to improper fractions:

**7 1/6 = (7 × 6) + 1 / 6 = 43/6**

**3 5/8 = (3 × 8) + 5 / 8 = 29/8**

**Subtracting the Fractions**

Now that we have converted the mixed numbers to improper fractions, we can subtract them:

**43/6 - 29/8**

To subtract these fractions, we need to find a common denominator. The least common multiple (LCM) of **6** and **8** is **24**. So, we can convert both fractions to have a denominator of **24**:

**43/6 = (43 × 4) / (6 × 4) = 172/24**

**29/8 = (29 × 3) / (8 × 3) = 87/24**

Now, we can subtract:

**172/24 - 87/24 = 85/24**

**Simplifying the Fraction**

We can simplify the fraction **85/24** by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is **1**. Therefore, the simplified fraction is:

**85/24**

**Conclusion**

In this article, we learned how to subtract mixed numbers **7 1/6 - 3 5/8** as a fraction. We converted the mixed numbers to improper fractions, found a common denominator, subtracted the fractions, and simplified the result to get **85/24**.