Simplify: $12(2+7+1)=$

**Simplify: $12(2+7+1)=?$**

Understanding the Problem

When we encounter a mathematical expression like $12(2+7+1)$, our goal is to simplify it and find its value. This involves following the order of operations, which is a set of rules that dictate the order in which we perform mathematical operations.

Order of Operations

The order of operations is a crucial concept in mathematics that helps us evaluate expressions with multiple operations. It is often remembered using the acronym PEMDAS, which stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Simplifying the Expression

Now that we understand the order of operations, let's apply it to the given expression: $12(2+7+1)$.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is $2+7+1$. To evaluate this, we simply add the numbers together:

$2+7+1 = 10$

Step 2: Multiply 12 by the Result

Now that we have the result of the expression inside the parentheses, we can multiply it by 12:

$12 \times 10 = 120$

The Final Answer

Therefore, the simplified value of the expression $12(2+7+1)$ is $120$.

Q&A

Q: What is the order of operations? A: The order of operations is a set of rules that dictate the order in which we perform mathematical operations. It is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an expression with multiple operations? A: To evaluate an expression with multiple operations, follow the order of operations. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the value of the expression $12(2+7+1)$? A: The value of the expression $12(2+7+1)$ is $120$.

Q: Why is it important to follow the order of operations? A: Following the order of operations is crucial in mathematics because it ensures that we evaluate expressions correctly and consistently. It helps us avoid errors and ensures that mathematical expressions are evaluated in a predictable and reliable way.

Q: Can you provide more examples of expressions that require the order of operations? A: Yes, here are a few examples:

• $3(2+5) = ?$
• $12 \div 4 + 3 = ?$
• $2^3 + 5 = ?$

A:

• $3(2+5) = 3 \times 7 = 21$
• $12 \div 4 + 3 = 3 + 3 = 6$
• $2^3 + 5 = 8 + 5 = 13$

Conclusion

In conclusion, simplifying mathematical expressions requires following the order of operations. By understanding the order of operations and applying it to expressions, we can evaluate them correctly and consistently. Remember to always follow the acronym PEMDAS to ensure that you are evaluating expressions in the correct order.