## Simplifying Mixed Numbers: 1 1/6 + 3/4

This article will guide you through the process of adding the mixed number **1 1/6** and the fraction **3/4**.

### Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction, like **1 1/6**. It represents a value greater than one.

### Converting Mixed Numbers to Fractions

To add mixed numbers and fractions, we need to convert them all into fractions. Here's how we convert **1 1/6** into a fraction:

**Multiply the whole number by the denominator:**1 * 6 = 6**Add the numerator:**6 + 1 = 7**Keep the original denominator:**7/6

Therefore, **1 1/6** is equivalent to **7/6**.

### Finding a Common Denominator

Before adding fractions, they need to have the same denominator. The least common denominator for 6 and 4 is 12.

**7/6:**Multiply numerator and denominator by 2: (7 * 2) / (6 * 2) =**14/12****3/4:**Multiply numerator and denominator by 3: (3 * 3) / (4 * 3) =**9/12**

### Adding the Fractions

Now we can add the fractions:

14/12 + 9/12 = 23/12

### Simplifying the Result

The fraction 23/12 is an improper fraction (the numerator is greater than the denominator). To express it as a mixed number:

**Divide the numerator by the denominator:**23 / 12 = 1 remainder 11**The quotient (1) becomes the whole number part:**1**The remainder (11) becomes the numerator of the fraction:**11**The denominator stays the same:**12

Therefore, 23/12 is equivalent to **1 11/12**.

### Conclusion

The sum of 1 1/6 and 3/4 is **1 11/12**. By converting the mixed number to a fraction, finding a common denominator, and adding the fractions, we successfully simplified the expression.