## Let's Explore the World of Mixed Numbers: 1 1/2 x 3 1/2 x 5

In the realm of mathematics, mixed numbers offer a unique way to represent fractions. Today, we'll delve into the multiplication of three mixed numbers: **1 1/2 x 3 1/2 x 5**.

### Understanding Mixed Numbers

Before diving into the multiplication, let's understand what mixed numbers represent. A mixed number combines a whole number with a fraction. For example, **1 1/2** represents one whole unit plus one-half.

### Converting Mixed Numbers to Fractions

To multiply mixed numbers, it's easier to convert them into improper fractions. An improper fraction has a numerator larger than or equal to its denominator.

**1 1/2:**Multiply the whole number (1) by the denominator (2) and add the numerator (1): 1 x 2 + 1 = 3. Keep the same denominator (2). Therefore,**1 1/2 = 3/2**.**3 1/2:**Multiply the whole number (3) by the denominator (2) and add the numerator (1): 3 x 2 + 1 = 7. Keep the same denominator (2). Therefore,**3 1/2 = 7/2**.

### Multiplication of Fractions

Now we have the equation: **3/2 x 7/2 x 5/1**. To multiply fractions, simply multiply the numerators and the denominators:

**Numerator:**3 x 7 x 5 = 105**Denominator:**2 x 2 x 1 = 4

This results in **105/4**.

### Converting Back to a Mixed Number

The final step is to convert the improper fraction back to a mixed number. Divide the numerator (105) by the denominator (4).

- 105 divided by 4 is 26 with a remainder of 1.
- The whole number part of the mixed number is 26.
- The fraction part is the remainder (1) over the original denominator (4): 1/4

Therefore, **1 1/2 x 3 1/2 x 5 = 26 1/4**.

### Conclusion

By converting mixed numbers to fractions and applying the rules of fraction multiplication, we successfully multiplied **1 1/2 x 3 1/2 x 5** and obtained the result **26 1/4**. This journey highlights the power of understanding different mathematical representations and applying appropriate techniques for solving complex problems.