**Adding Mixed Numbers: 1 3/4 + 2 3/8 as a Fraction**

In this article, we will learn how to add two mixed numbers, 1 3/4 and 2 3/8, and express the result as a fraction.

**Understanding Mixed Numbers**

A mixed number is a combination of a whole number and a fraction. For example, 1 3/4 is a mixed number where 1 is the whole number and 3/4 is the fraction.

**Converting Mixed Numbers to Improper Fractions**

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

**Converting 1 3/4 to an Improper Fraction**

To convert 1 3/4 to an improper fraction, we multiply the whole number part (1) by the denominator (4) and then add the numerator (3).

**1 3/4 = (1 × 4) + 3 = 7/4**

**Converting 2 3/8 to an Improper Fraction**

To convert 2 3/8 to an improper fraction, we multiply the whole number part (2) by the denominator (8) and then add the numerator (3).

**2 3/8 = (2 × 8) + 3 = 19/8**

**Adding the Improper Fractions**

Now that we have converted both mixed numbers to improper fractions, we can add them.

**7/4 + 19/8**

To add these fractions, we need to find the least common multiple (LCM) of the denominators, which is 8. We can then rewrite the fractions with the LCM as the denominator.

**7/4 = 14/8**
**19/8 = 19/8**

Now, we can add the numerators and keep the denominator the same.

**14 + 19 = 33**

**33/8**

**Simplifying the Fraction**

The result of the addition is an improper fraction, 33/8. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1.

**33/8 = 33/8**

Therefore, the result of adding 1 3/4 and 2 3/8 is **33/8** as a fraction.