https://file.aiquickdraw.com/mathbot/file/17302975491779oqacpw4.jpg

Let's go through each question to find the exact values as requested.

---

### Problem 1:
\[
\frac{7}{8} + \frac{1}{6} \div \frac{2}{9}
\]

#### Step 1: Division
The expression contains a division, so let's handle that first:
\[
\frac{1}{6} \div \frac{2}{9} = \frac{1}{6} \times \frac{9}{2} = \frac{9}{12} = \frac{3}{4}
\]

#### Step 2: Addition
Now substitute \(\frac{3}{4}\) back into the expression:
\[
\frac{7}{8} + \frac{3}{4}
\]

Convert \(\frac{3}{4}\) to have a common denominator of 8:
\[
\frac{3}{4} = \frac{6}{8}
\]

Now, add \(\frac{7}{8}\) and \(\frac{6}{8}\):
\[
\frac{7}{8} + \frac{6}{8} = \frac{13}{8} = 1\frac{5}{8}
\]

So, the exact value of Problem 1 is:
\[
1\frac{5}{8} \text{ or } \frac{13}{8}
\]

---

### Problem 2:
\[
\frac{5}{6} + \frac{2}{3} - \frac{12}{35} \times \frac{7}{9}
\]

#### Step 1: Multiplication
First, handle the multiplication:
\[
\frac{12}{35} \times \frac{7}{9} = \frac{12 \times 7}{35 \times 9} = \frac{84}{315}
\]

Simplify \(\frac{84}{315}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 21:
\[
\frac{84}{315} = \frac{4}{15}
\]

#### Step 2: Addition and Subtraction
Now, substitute \(\frac{4}{15}\) back into the expression:
\[
\frac{5}{6} + \frac{2}{3} - \frac{4}{15}
\]

Convert each fraction to have a common denominator of 30:
\[
\frac{5}{6} = \frac{25}{30}, \quad \frac{2}{3} = \frac{20}{30}, \quad \frac{4}{15} = \frac{8}{30}
\]

Now, perform the operations:
\[
\frac{25}{30} + \frac{20}{30} - \frac{8}{30} = \frac{37}{30} = 1\frac{7}{30}
\]

So, the exact value of Problem 2 is:
\[
1\frac{7}{30} \text{ or } \frac{37}{30}
\]

---

Would you like more details on any of these steps or have any questions? 

Here are some related questions for further practice:

1. What is the exact value of \(\frac{3}{4} + \frac{5}{6}\)?
2. How do you simplify the expression \(\frac{4}{9} \div \frac{2}{3} + \frac{1}{2}\)?
3. Find the value of \(\frac{1}{2} + \frac{3}{8} \times \frac{4}{5}\).
4. How do you handle complex expressions with multiple fractions and operations?
5. What is the result of \(\frac{6}{7} - \frac{3}{5} \times \frac{10}{11}\)?

**Tip:** When adding or subtracting fractions, always look for a common denominator to make calculations easier.

1. Find the exact value of 7/8 + 1/6 ÷ 2/9
2. Find the exact value of 5/6 + 2/3 - 12/35 × 7/9

Learn how to solve fraction expressions like 7/8 + 1/6 ÷ 2/9 and 5/6 + 2/3 - 12/35 × 7/9 with step-by-step solutions. This problem covers fraction addition, division, and multiplication, suitable for students in Grades 6-8.

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