use all or some of the given numbers "3, 5, 8, 12, 20, 36" to form as many mathematical expression/number phrases as possible to obtain 24 as answer. 

1. you are allowed to use a number only once in the mathematical expression. Use PMDAS

Let's attempt to form mathematical expressions that result in 24, using some or all of the numbers "3, 5, 8, 12, 20, 36" and applying the order of operations (Parentheses, Multiplication and Division, Addition and Subtraction—PMDAS).

### Expressions that equal 24:

1. **\( 36 - 12 = 24 \)**
   - Using 36 and 12.

2. **\( 36 \div 3 + 12 = 24 \)**
   - Using 36, 3, and 12.

3. **\( 36 \div 12 \times 8 = 24 \)**
   - Using 36, 12, and 8.

4. **\( (20 - 12) \times 3 = 24 \)**
   - Using 20, 12, and 3.

5. **\( 8 \times 3 = 24 \)**
   - Using only 8 and 3.

6. **\( 20 + 5 - 36 \div 12 = 24 \)**
   - Using 20, 5, 36, and 12.

These are a few possible expressions using the given numbers.

Do you want more details on any of these expressions, or do you have other questions?

Here are five questions to extend the problem:
1. How can you verify the correctness of each expression using PMDAS?
2. What other combinations of these numbers might lead to different results?
3. How does changing the order of operations affect the results?
4. Can you think of a way to use all six numbers and still get 24?
5. What happens if you introduce additional mathematical operations like exponentiation?

**Tip:** Always apply parentheses first when dealing with multiple operations, especially when expressions involve both multiplication/division and addition/subtraction.

use all or some of the given numbers '3, 5, 8, 12, 20, 36' to form as many mathematical expression/number phrases as possible to obtain 24 as answer. you are allowed to use a number only once in the mathematical expression. Use PMDAS

Explore how to use the numbers '3, 5, 8, 12, 20, 36' to create mathematical expressions that result in 24. This problem utilizes key concepts such as order of operations (PEMDAS) and basic arithmetic, making it suitable for students in Grades 5-7.

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