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We are asked to solve \( 1 \frac{5}{6} + 1 \frac{2}{9} \) and express the answer as a mixed number in its lowest terms.

### Step 1: Convert the mixed numbers to improper fractions.

1. \( 1 \frac{5}{6} \):
   \[
   1 \frac{5}{6} = \frac{6 \times 1 + 5}{6} = \frac{11}{6}
   \]

2. \( 1 \frac{2}{9} \):
   \[
   1 \frac{2}{9} = \frac{9 \times 1 + 2}{9} = \frac{11}{9}
   \]

### Step 2: Find a common denominator.
The denominators are 6 and 9. The least common denominator (LCD) is 18.

Convert the fractions to have the same denominator:

\[
\frac{11}{6} = \frac{11 \times 3}{6 \times 3} = \frac{33}{18}
\]
\[
\frac{11}{9} = \frac{11 \times 2}{9 \times 2} = \frac{22}{18}
\]

### Step 3: Add the fractions.
Now, add the fractions:
\[
\frac{33}{18} + \frac{22}{18} = \frac{33 + 22}{18} = \frac{55}{18}
\]

### Step 4: Convert the improper fraction to a mixed number.
Divide 55 by 18:
\[
55 \div 18 = 3 \text{ remainder } 1
\]

So, \( \frac{55}{18} = 3 \frac{1}{18} \).

Thus, the answer is \( 3 \frac{1}{18} \), already in its lowest terms.

Would you like further details on any part of the solution?

Here are some related questions:
1. How do you find the least common denominator?
2. How do you convert a mixed number to an improper fraction?
3. How do you simplify improper fractions?
4. How do you convert improper fractions to mixed numbers?
5. How can you check if your mixed number is in its lowest terms?

**Tip**: Always ensure that fractions are simplified by finding the greatest common divisor (GCD) of the numerator and denominator.

Work out 1 5/6 + 1 2/9. Give your answer as a mixed number in its lowest terms.

Learn how to add mixed numbers 1 5/6 and 1 2/9 by converting them into improper fractions, finding the least common denominator, and simplifying to the lowest terms. This problem is suitable for students in Grades 5-7.

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