**Simplifying Fractions: 1 3/4 x 4 1/2**

In this article, we will explore how to simplify the product of two mixed numbers: 1 3/4 and 4 1/2.

**Converting Mixed Numbers to Improper Fractions**

Before we can multiply these mixed numbers, we need to convert them to 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 = 4 4 + 3 = 7

So, 1 3/4 = **7/4**

### 4 1/2

Similarly, to convert 4 1/2 to an improper fraction, we multiply the whole number part (4) by the denominator (2) and then add the numerator (1).

4 × 2 = 8 8 + 1 = 9

So, 4 1/2 = **9/2**

**Multiplying Improper Fractions**

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

**7/4 × 9/2**

To multiply fractions, we multiply the numerators (7 and 9) and multiply the denominators (4 and 2).

(7 × 9) = **63**
(4 × 2) = **8**

So, **7/4 × 9/2 = 63/8**

**Simplifying the Fraction**

To simplify the fraction **63/8**, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 63 and 8 is **1**, so we cannot simplify the fraction further.

**Final Answer**

Therefore, the product of 1 3/4 and 4 1/2 in its simplest form is **63/8**.