https://file.aiquickdraw.com/mathbot/file/1727059106047br30aszc.jpg

Let's break down and solve each part of the question from the image.

### (a) \( z \div 17 = 3 \text{ R } 13 \)

This means when \( z \) is divided by 17, the quotient is 3 and the remainder is 13. We can reverse this to solve for \( z \).

\[
z = (17 \times 3) + 13 = 51 + 13 = 64
\]

So, \( z = 64 \).

### (b) \( 34 \div (2x) = 4 \text{ R } 2 \)

This means when 34 is divided by \( 2x \), the quotient is 4 and the remainder is 2. To solve for \( x \), we set up the equation:

\[
34 = (2x \times 4) + 2
\]

Simplifying:

\[
34 = 8x + 2
\]

Subtract 2 from both sides:

\[
32 = 8x
\]

Now divide by 8:

\[
x = 4
\]

### (c) \( (w + 6) \div 7 = 3 \text{ R } 5 \)

This means when \( w + 6 \) is divided by 7, the quotient is 3 and the remainder is 5. To solve for \( w \), we reverse this process:

\[
w + 6 = (7 \times 3) + 5 = 21 + 5 = 26
\]

Now subtract 6 from both sides:

\[
w = 20
\]

### Final answers:
- (a) \( z = 64 \)
- (b) \( x = 4 \)
- (c) \( w = 20 \)

Let me know if you need further details or have any questions. Here are 5 related questions to expand your understanding:

1. How do we generalize division with remainders into algebraic equations?
2. What is the process for solving division problems with unknown variables?
3. Why do we add the remainder after multiplying the quotient by the divisor?
4. Can you think of a way to check the solution for division problems?
5. What role do remainders play in modular arithmetic?

**Tip:** When dividing numbers with remainders, always verify by reversing the calculation through multiplication and addition of the remainder.

Solve for the unknown whole number in the following expressions:
(a) z ÷ 17 = 3 R 13
(b) 34 ÷ (2x) = 4 R 2
(c) (w + 6) ÷ 7 = 3 R 5

This example teaches how to solve division problems with remainders and unknown variables. Learn how to find z, x, and w in equations like z ÷ 17 = 3 R 13 and (w + 6) ÷ 7 = 3 R 5. The solution covers basic algebra and division rules, ideal for students in Grades 5-7.

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