**Converting Improper Fractions to Mixed Numbers: 1 3/4 x 2 1/2**

In this article, we will explore how to multiply two mixed numbers, specifically 1 3/4 and 2 1/2. Before we dive into the multiplication process, let's first understand what mixed numbers are and how to convert improper fractions to mixed numbers.

### What are Mixed Numbers?

A mixed number is a combination of a whole number and a proper fraction. It is used to represent a value that is greater than one whole unit. For example, 1 1/2, 2 3/4, and 3 2/3 are all mixed numbers.

### Converting Improper Fractions to Mixed Numbers

An improper fraction is a fraction where the numerator is greater than the denominator. To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator and find the quotient and remainder.

For example, let's convert the improper fraction 7/4 to a mixed number:

- Divide the numerator (7) by the denominator (4): 7 ÷ 4 = 1 with a remainder of 3
- The quotient (1) becomes the whole number part, and the remainder (3) becomes the numerator of the fraction part
- So, the mixed number equivalent of 7/4 is 1 3/4

### Multiplying Mixed Numbers: 1 3/4 x 2 1/2

Now that we understand mixed numbers and how to convert improper fractions to mixed numbers, let's multiply 1 3/4 and 2 1/2.

**Step 1: Convert Mixed Numbers to Improper Fractions**

To multiply mixed numbers, we need to convert them to improper fractions first.

- 1 3/4 = 7/4 (conversion: 1 x 4 = 4 + 3 = 7)
- 2 1/2 = 5/2 (conversion: 2 x 2 = 4 + 1 = 5)

**Step 2: Multiply the Improper Fractions**

Now, we can multiply the two improper fractions:

- 7/4 x 5/2 = ?

To multiply fractions, we multiply the numerators and multiply the denominators:

- 7 x 5 = 35 (numerator)
- 4 x 2 = 8 (denominator)

So, the product of the two improper fractions is 35/8.

**Step 3: Convert the Product to a Mixed Number (if necessary)**

In this case, the product 35/8 is an improper fraction. To convert it to a mixed number, we divide the numerator by the denominator:

- 35 ÷ 8 = 4 with a remainder of 3

So, the mixed number equivalent of 35/8 is **4 3/8**.

Therefore, the product of 1 3/4 and 2 1/2 is **4 3/8**.