**Adding Mixed Numbers: 1 5/6 + 1 3/4**

When working with mixed numbers, it's essential to understand how to add them correctly. In this article, we'll explore the step-by-step process of adding two mixed numbers: 1 5/6 and 1 3/4.

**Step 1: Convert the Mixed Numbers to Improper Fractions**

To add mixed numbers, we need to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than the denominator.

### Convert 1 5/6 to an Improper Fraction

- Multiply the whole number part (1) by the denominator (6): 1 × 6 = 6
- Add the numerator (5) to the product: 6 + 5 = 11
- Write the result as an improper fraction: 11/6

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

- Multiply the whole number part (1) by the denominator (4): 1 × 4 = 4
- Add the numerator (3) to the product: 4 + 3 = 7
- Write the result as an improper fraction: 7/4

**Step 2: Add the Improper Fractions**

Now that we have the improper fractions, we can add them.

### Add 11/6 and 7/4

To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 6 and 4. The LCM of 6 and 4 is 12.

- Convert both fractions to have a denominator of 12:
- 11/6 = (11 × 2) / (6 × 2) = 22/12
- 7/4 = (7 × 3) / (4 × 3) = 21/12

- Add the numerators: 22 + 21 = 43
- Write the result as an improper fraction: 43/12

**Step 3: Convert the Result back to a Mixed Number**

To convert the improper fraction back to a mixed number, we divide the numerator by the denominator.

### Convert 43/12 to a Mixed Number

- Divide the numerator (43) by the denominator (12): 43 ÷ 12 = 3 with a remainder of 7
- Write the result as a mixed number:
**3 7/12**

Therefore, the result of adding 1 5/6 and 1 3/4 is **3 7/12**.