## Multiplying Mixed Numbers: 1 1/6 x 3 1/2

This article will guide you through the process of multiplying the mixed numbers 1 1/6 and 3 1/2.

### Understanding Mixed Numbers

Before diving into the multiplication, let's understand what mixed numbers are. A mixed number combines a whole number with a fraction, like 1 1/6. This represents one whole plus one-sixth.

### Converting to Improper Fractions

The easiest way to multiply mixed numbers is to convert them into improper fractions. To do this:

**Multiply the whole number by the denominator of the fraction:**1 x 6 = 6**Add the numerator of the fraction:**6 + 1 = 7**Keep the same denominator:**7/6

So, 1 1/6 is equivalent to 7/6.

Similarly, for 3 1/2:

**Multiply the whole number by the denominator:**3 x 2 = 6**Add the numerator:**6 + 1 = 7**Keep the same denominator:**7/2

Therefore, 3 1/2 is equivalent to 7/2.

### Multiplication

Now we can multiply the improper fractions:

(7/6) x (7/2)

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

(7 x 7) / (6 x 2) = 49/12

### Converting Back to a Mixed Number

The result, 49/12, is an improper fraction. To convert it back to a mixed number:

**Divide the numerator by the denominator:**49 ÷ 12 = 4 with a remainder of 1**The quotient becomes the whole number:**4**The remainder becomes the numerator of the fraction:**1**The denominator stays the same:**12

Therefore, 49/12 is equivalent to **4 1/12**.

### Conclusion

By converting the mixed numbers to improper fractions, we were able to multiply them easily. The final result of 1 1/6 x 3 1/2 is **4 1/12**.