state where to put grouping symbols so that the given expression has the given value. 24 / 2 x 3 + 4; 84

To make the expression \(24 \div 2 \times 3 + 4\) equal to 84, you need to add grouping symbols (parentheses) to change the order of operations. Let's analyze how to do this.

The original expression without any parentheses is:
\[ 24 \div 2 \times 3 + 4 \]

If you evaluate it using the standard order of operations (PEMDAS/BODMAS), the steps are:
1. Division and multiplication from left to right: \(24 \div 2 = 12\).
2. Then, \(12 \times 3 = 36\).
3. Finally, \(36 + 4 = 40\).

This gives 40, which is not 84. Therefore, we need to place parentheses to alter the order of operations.

To achieve a result of 84, we can place the grouping symbols as follows:
\[ 24 \div (2 \times (3 + 4)) \]

Let's calculate this:
1. First, evaluate inside the innermost parentheses: \(3 + 4 = 7\).
2. Next, multiply: \(2 \times 7 = 14\).
3. Finally, divide: \(24 \div 14\).

However, this gives approximately 1.71, which is not the desired result. Let's try another grouping:

\[ (24 \div 2) \times (3 + 4) \]

Now calculate this:
1. First, inside the parentheses: \(24 \div 2 = 12\).
2. Add in the other parentheses: \(3 + 4 = 7\).
3. Multiply the results: \(12 \times 7 = 84\).

So, the correct placement of parentheses to make the expression equal 84 is:
\[ (24 \div 2) \times (3 + 4) \]

Would you like more details, or do you have any questions?

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**Related Questions:**
1. What are the order of operations in mathematics?
2. How would changing the position of parentheses affect an expression's value?
3. Can you explain how division and multiplication are handled with the same precedence?
4. What happens if you add parentheses around the entire expression?
5. How can I simplify complex expressions using the order of operations?

**Tip:** Always remember the order of operations (PEMDAS/BODMAS) to correctly evaluate mathematical expressions!

Explore how to place grouping symbols (parentheses) in the expression 24 / 2 x 3 + 4 to achieve the value of 84. Learn about the order of operations, division, multiplication, and the impact of parentheses in mathematical expressions. Suitable for students in Grades 5-8.

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