To make the expression \(5 \times 2 + 16 \div 2\) equal to 13, we 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:
\[ 5 \times 2 + 16 \div 2 \]

If you evaluate it using the standard order of operations (PEMDAS/BODMAS), the steps are:
1. Multiplication and division from left to right: \(5 \times 2 = 10\).
2. Then, \(16 \div 2 = 8\).
3. Finally, add the results: \(10 + 8 = 18\).

This gives 18, which is not 13. Therefore, we need to place parentheses to alter the order of operations.

To achieve a result of 13, we can place the grouping symbols as follows:
\[ 5 \times (2 + 16 \div 2) \]

Let's calculate this:
1. First, evaluate inside the parentheses: \(16 \div 2 = 8\).
2. Then, add: \(2 + 8 = 10\).
3. Finally, multiply: \(5 \times 10 = 50\).

This gives 50, which is not the desired result. Let's try another grouping:

\[ (5 \times 2) + (16 \div 2) \]

Now calculate this:
1. First, inside the parentheses: \(5 \times 2 = 10\).
2. Then, divide inside the other parentheses: \(16 \div 2 = 8\).
3. Finally, add the results: \(10 + 8 = 18\).

This still doesn't work. However, consider this grouping:

\[ 5 \times 2 + (16 \div (5 \times 2)) \]

Simplify:
1. Inside the parentheses: \(5 \times 2 = 10\).
2. Divide: \(16 \div 10 = 1.6\).
3. Finally: \(5 \times 2 + 1.6 = 10 + 1.6 = 11.6\).

This still doesn't yield 13, so it’s not possible with this expression as is. However, for \(13\) as the output, you should consider if there might have been a typo or other issue in the initial problem because no simple grouping of operations within the typical interpretation can bring \(13\) from this input.

Would you like to reconsider the problem, or do you have any other queries?

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**Related Questions:**
1. Can you try to solve another similar problem with different numbers?
2. Why is the order of operations so important in mathematics?
3. How do parentheses affect calculations in an expression?
4. What are some common pitfalls when applying the order of operations?
5. Could rounding or decimals affect the outcomes?

**Tip:** Double-check all parts of your problem to ensure there is no error in the numbers given. Even a small change can make a big difference in the outcome!

Explore how to correctly apply the order of operations to the expression 5 x 2 + 16 / 2 to achieve a result of 13. Learn the importance of parentheses in arithmetic calculations. Suitable for students in Grades 5-6.

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