https://file.aiquickdraw.com/mathbot/file/1726886244303209ebggb.jpg

Let's go through each of the problems in the image one by one and solve them.

### Problem 51:
\[
\frac{4}{81} \div \frac{1}{9} \cdot \frac{7}{9}
\]

#### Steps:
1. First, solve the division by multiplying by the reciprocal:
   \[
   \frac{4}{81} \div \frac{1}{9} = \frac{4}{81} \cdot \frac{9}{1} = \frac{4 \cdot 9}{81} = \frac{36}{81} = \frac{4}{9}
   \]
2. Now, multiply this result by \(\frac{7}{9}\):
   \[
   \frac{4}{9} \cdot \frac{7}{9} = \frac{4 \cdot 7}{9 \cdot 9} = \frac{28}{81}
   \]

So, the final answer to **Problem 51** is:
\[
\frac{28}{81}
\]

---

### Problem 53:
\[
\frac{1}{2} + \frac{3}{8} \div \left( \frac{9}{12} \right)
\]

#### Steps:
1. First, simplify the division inside the parentheses. \(\frac{9}{12}\) can be simplified to:
   \[
   \frac{9}{12} = \frac{3}{4}
   \]
   So, the division becomes:
   \[
   \frac{3}{8} \div \frac{3}{4} = \frac{3}{8} \cdot \frac{4}{3} = \frac{3 \cdot 4}{8 \cdot 3} = \frac{12}{24} = \frac{1}{2}
   \]
2. Now, add this result to \(\frac{1}{2}\):
   \[
   \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1
   \]

So, the final answer to **Problem 53** is:
\[
1
\]

---

### Problem 55:
\[
\left( -\frac{3}{4} \right)^2 - \frac{1}{8} \div \frac{1}{3} - \frac{3}{16}
\]

#### Steps:
1. First, square \(-\frac{3}{4}\):
   \[
   \left( -\frac{3}{4} \right)^2 = \frac{9}{16}
   \]
2. Now solve the division \(\frac{1}{8} \div \frac{1}{3}\):
   \[
   \frac{1}{8} \div \frac{1}{3} = \frac{1}{8} \cdot \frac{3}{1} = \frac{3}{8}
   \]
3. Subtract \(\frac{3}{16}\) from \(\frac{9}{16}\):
   \[
   \frac{9}{16} - \frac{3}{16} = \frac{6}{16} = \frac{3}{8}
   \]
4. Finally, subtract the result of the division from this:
   \[
   \frac{3}{8} - \frac{3}{8} = 0
   \]

So, the final answer to **Problem 55** is:
\[
0
\]

---

Let me know if you want any further clarification or more detailed steps!

Here are 5 follow-up questions for practice:
1. How do you multiply fractions? 
2. What is the result of dividing two fractions?
3. Can you explain how to simplify fractions?
4. How would you solve \(\frac{2}{3} + \frac{5}{6}\)?
5. What does squaring a fraction do to both the numerator and the denominator?

**Tip**: Always simplify fractions before performing operations like multiplication or division to make calculations easier!

Solve the following fraction problems: 51) 4/81 ÷ 1/9 ⋅ 7/9, 53) 1/2 + 3/8 ÷ (9/12), 55) (-3/4)^2 - 1/8 ÷ 1/3 - 3/16.

This guide provides detailed step-by-step solutions for fraction operations including division, multiplication, and exponentiation. Problems such as 4/81 ÷ 1/9 ⋅ 7/9, 1/2 + 3/8 ÷ (9/12), and (-3/4)^2 - 1/8 ÷ 1/3 - 3/16 are solved, covering key mathematical concepts suitable for students in Grades 7-9.

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