## Let's Multiply Mixed Numbers: 1 2/3 x 3 1/2

This article will guide you through multiplying the mixed numbers **1 2/3** and **3 1/2**.

### Understanding Mixed Numbers

Before we start, remember that a mixed number represents a whole number plus a fraction. For example, **1 2/3** is the same as **1 + 2/3**.

### Converting to Improper Fractions

The easiest way to multiply mixed numbers is to convert them into improper fractions. Here's how:

**1 2/3:**Multiply the whole number (1) by the denominator (3), and add the numerator (2). Keep the same denominator. This gives us**(1*3 + 2)/3 = 5/3**.**3 1/2:**Multiply the whole number (3) by the denominator (2), and add the numerator (1). Keep the same denominator. This gives us**(3*2 + 1)/2 = 7/2**.

### Multiplication of Improper Fractions

Now we can multiply our improper fractions:

**5/3 x 7/2**

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

**(5 x 7) / (3 x 2) = 35/6**

### Converting Back to a Mixed Number

Finally, we convert our answer, 35/6, back into a mixed number:

- Divide the numerator (35) by the denominator (6). The quotient is 5 with a remainder of 5.
- Our answer is
**5 5/6**.

### Conclusion

Therefore, **1 2/3 x 3 1/2 = 5 5/6**. By converting mixed numbers to improper fractions, we can easily multiply them.