**Simplifying Mixed Numbers: 1 3/4 x 2 1/4 x 3/4 as a Fraction**

In this article, we will explore how to simplify the mixed number expression 1 3/4 x 2 1/4 x 3/4 as a fraction.

### Understanding Mixed Numbers

Before we dive into the calculation, let's quickly review what mixed numbers are. 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 Fractions

To simplify the expression 1 3/4 x 2 1/4 x 3/4 as a fraction, we need to convert each mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

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

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

1 × 4 = 4 4 + 3 = 7

So, 1 3/4 is equal to the improper fraction 7/4.

#### Converting 2 1/4 to an Improper Fraction

To convert 2 1/4 to an improper fraction, we multiply the whole number 2 by the denominator 4, and then add the numerator 1:

2 × 4 = 8 8 + 1 = 9

So, 2 1/4 is equal to the improper fraction 9/4.

#### Converting 3/4 to an Improper Fraction

3/4 is already an improper fraction, so we don't need to convert it.

### Multiplying the Improper Fractions

Now that we have converted each mixed number to an improper fraction, we can multiply them together:

(7/4) × (9/4) × (3/4) = ?

To multiply fractions, we multiply the numerators (7, 9, and 3) and the denominators (4, 4, and 4), and then simplify the result:

(7 × 9 × 3) / (4 × 4 × 4) = 189 / 64

So, the result of multiplying the improper fractions is 189/64.

### Simplifying the Result

Finally, we can simplify the fraction 189/64 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 189 and 64 is 1, so the fraction remains the same:

189/64 = 189/64

Therefore, the simplified result of 1 3/4 x 2 1/4 x 3/4 as a fraction is **189/64**.