Let's solve the equation \( 51 = 45 + \frac{z}{11} \) for \( z \).

### Step-by-Step Solution:

1. **Write down the equation:**
   \[
   51 = 45 + \frac{z}{11}
   \]

2. **Isolate the term with \( z \) by subtracting 45 from both sides:**
   \[
   51 - 45 = \frac{z}{11}
   \]

3. **Simplify the left side:**
   \[
   6 = \frac{z}{11}
   \]

4. **Multiply both sides by 11 to solve for \( z \):**
   \[
   6 \times 11 = z
   \]

5. **Calculate the multiplication:**
   \[
   z = 66
   \]

Thus, the value of \( z \) is \( 66 \).

Would you like more details or have any questions?

Here are some related questions for further practice:

1. Solve for \( x \): \( 40 = 30 + \frac{x}{5} \).
2. Solve for \( y \): \( 25 = 20 + \frac{y}{4} \).
3. Solve the equation: \( 100 = 80 + \frac{z}{10} \).
4. Solve for \( z \): \( 72 = 60 + \frac{z}{12} \).
5. Solve \( 90 = 75 + \frac{w}{3} \) for \( w \).

**Tip:** To isolate a variable in an equation, perform the opposite operations to both sides, step by step.

Learn how to solve the equation 51 = 45 + z/11 with a detailed step-by-step solution. This problem involves basic arithmetic and fractional equations. Suitable for students in Grades 6-8.

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