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To solve the problems by placing parentheses to make each equation true, I'll evaluate the given expressions. Let's go through them one by one:

1. **\(16 - 7 + 8 = 1\)**
   - To make this equation true, place parentheses around \(16 - (7 + 8)\):
     \[
     16 - (7 + 8) = 16 - 15 = 1
     \]
   - True statement: \(16 - (7 + 8) = 1\).

2. **\(3 \times 5 - 4 = 3\)**
   - To make this equation true, place parentheses around \((3 \times 5) - 4\):
     \[
     (3 \times 5) - 4 = 15 - 4 = 11
     \]
   - This does not give 3, so we need a different placement.
   - Try this: \(3 \times (5 - 4) = 3 \times 1 = 3\).
   - True statement: \(3 \times (5 - 4) = 3\).

3. **\(20 - 8 \div 2 + 3 = 19\)**
   - To make this equation true, place parentheses around \(20 - (8 \div 2) + 3\):
     \[
     20 - (8 \div 2) + 3 = 20 - 4 + 3 = 19
     \]
   - True statement: \(20 - (8 \div 2) + 3 = 19\).

4. **\(18 - 2 + 3 + 6 - 6 \times 3 = 1\)**
   - To make this equation true, place parentheses around \(18 - 2 + 3 + (6 - 6 \times 3)\):
     \[
     18 - 2 + 3 + (6 - 18) = 18 - 2 + 3 - 12 = 19 - 12 = 7 \quad (\text{Not } 1)
     \]
   - Try: \((18 - 2 + 3 + 6) - (6 \times 3)\):
     \[
     (18 - 2 + 3 + 6) - (6 \times 3) = 25 - 18 = 7 \quad (\text{Not } 1)
     \]
   - Try: \((18 - (2 + 3)) + 6 - (6 \times 3)\):
     \[
     (18 - 5) + 6 - 18 = 13 + 6 - 18 = 19 - 18 = 1
     \]
   - True statement: \((18 - (2 + 3)) + 6 - 6 \times 3 = 1\).

5. **\(27 \div 2 + 1 - 5 - 36 \div 9 = 0\)**
   - To make this equation true, place parentheses around \(27 \div (2 + 1 - 5) - (36 \div 9)\):
     \[
     27 \div (-2) - 4 = \text{Does not make sense (Negative division).}
     \]
   - Try: \((27 \div 2) + 1 - (5 - 36 \div 9)\):
     \[
     (27 \div 2) + 1 - (5 - 4) = 13.5 + 1 - 1 = 13.5 \quad (\text{Not } 0)
     \]
   - Try: \(27 \div (2 + 1) - 5 - (36 \div 9)\):
     \[
     27 \div 3 - 5 - 4 = 9 - 5 - 4 = 0
     \]
   - True statement: \(27 \div (2 + 1) - 5 - 36 \div 9 = 0\).

### Summary of Solutions:
1. \(16 - (7 + 8) = 1\)
2. \(3 \times (5 - 4) = 3\)
3. \(20 - (8 \div 2) + 3 = 19\)
4. \((18 - (2 + 3)) + 6 - 6 \times 3 = 1\)
5. \(27 \div (2 + 1) - 5 - 36 \div 9 = 0\)

Would you like more details on any specific step or have any further questions? 

Here are 5 related questions to explore:
1. How do the order of operations (PEMDAS) influence the placement of parentheses?
2. Can different parenthesis placements lead to multiple valid solutions?
3. How does division by zero affect the validity of an equation?
4. How do nested parentheses alter the evaluation of expressions?
5. What are some common pitfalls when solving equations with multiple operations?

**Tip:** When solving complex expressions, always start by simplifying the innermost parentheses to avoid mistakes.

Place parentheses in the number sentences to make each a true statement: 1. 16 - 7 + 8 = 1 2. 3 x 5 - 4 = 3 3. 20 - 8 ÷ 2 + 3 = 19 4. 18 - 2 + 3 + 6 - 6 x 3 = 1 5. 27 ÷ 2 + 1 - 5 - 36 ÷ 9 = 0

Learn how to use parentheses to solve arithmetic equations correctly by following the order of operations (PEMDAS). This problem set includes five different equations that require placing parentheses to make each statement true. Suitable for students in Grades 5-7.

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