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

When dealing with mixed numbers, it's essential to understand how to add them correctly. In this article, we'll explore the process of adding 1 3/4 and 2 1/2 as a fraction.

**Converting Mixed Numbers to Improper Fractions**

Before we can add these mixed numbers, we need to convert them into improper fractions.

**1 3/4**

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 × 4) + 3 = 7**

So, 1 3/4 becomes **7/4**.

**2 1/2**

Similarly, to convert 2 1/2 to an improper fraction, we multiply the whole number part (2) by the denominator (2) and then add the numerator (1).

**(2 × 2) + 1 = 5**

So, 2 1/2 becomes **5/2**.

**Adding the Improper Fractions**

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

**7/4 + 5/2**

To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 4 and 2. The LCM of 4 and 2 is 4. So, we can rewrite the fractions with the LCM as the denominator.

**7/4 + 10/4**

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

**17/4**

**Simplifying the Fraction**

We can simplify the fraction **17/4** by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1.

**17/4**

So, **1 3/4 + 2 1/2 as a fraction** is equal to **17/4**.