Simplify The Expression: $\[ 36 \div 3^2 \cdot 2 \div 2 \\]
Introduction
In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. When dealing with expressions involving exponents, multiplication, and division, it's essential to follow the correct order of operations to simplify the expression correctly. In this article, we will simplify the expression 36 ÷ 3^2 ⋅ 2 ÷ 2 using the correct order of operations and mathematical properties.
Understanding the Order of Operations
The order of operations is a set of rules that tells us which operations to perform first when simplifying expressions. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Simplifying the Expression
To simplify the expression 36 ÷ 3^2 ⋅ 2 ÷ 2, we need to follow the order of operations.
Step 1: Evaluate the Exponent
The expression contains an exponent, 3^2. To evaluate this, we need to raise 3 to the power of 2.
3^2 = 3 × 3 = 9
So, the expression becomes:
36 ÷ 9 ⋅ 2 ÷ 2
Step 2: Perform Division Operations
Now, we need to perform the division operations from left to right.
36 ÷ 9 = 4
So, the expression becomes:
4 ⋅ 2 ÷ 2
Step 3: Perform Multiplication and Division Operations
Next, we need to perform the multiplication and division operations from left to right.
4 ⋅ 2 = 8
Now, we have:
8 ÷ 2
Step 4: Perform Final Division Operation
Finally, we need to perform the final division operation.
8 ÷ 2 = 4
Conclusion
In this article, we simplified the expression 36 ÷ 3^2 ⋅ 2 ÷ 2 using the correct order of operations and mathematical properties. We evaluated the exponent, performed division operations, and finally performed multiplication and division operations to simplify the expression correctly. By following the order of operations, we can simplify complex expressions and solve problems efficiently and accurately.
Frequently Asked Questions
- What is the order of operations? The order of operations is a set of rules that tells us which operations to perform first when simplifying expressions. The acronym PEMDAS is commonly used to remember the order of operations.
- How do I simplify an expression with an exponent? To simplify an expression with an exponent, you need to raise the base number to the power of the exponent.
- What is the correct order of operations for simplifying expressions? The correct order of operations for simplifying expressions is:
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Simplifying Expressions
- Wolfram Alpha: Order of Operations
Final Thoughts
Simplifying expressions is a crucial skill in mathematics that helps us solve problems efficiently and accurately. By following the correct order of operations and mathematical properties, we can simplify complex expressions and solve problems with confidence. Remember to always follow the order of operations and use mathematical properties to simplify expressions correctly.
Introduction
In our previous article, we simplified the expression 36 ÷ 3^2 ⋅ 2 ÷ 2 using the correct order of operations and mathematical properties. In this article, we will answer some frequently asked questions related to simplifying expressions and provide additional resources for further learning.
Q&A
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when simplifying expressions. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify an expression with an exponent?
A: To simplify an expression with an exponent, you need to raise the base number to the power of the exponent. For example, in the expression 3^2, you need to raise 3 to the power of 2.
Q: What is the correct order of operations for simplifying expressions?
A: The correct order of operations for simplifying expressions is:
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
Q: Can I simplify an expression with multiple operations?
A: Yes, you can simplify an expression with multiple operations by following the correct order of operations. For example, in the expression 2 + 3 × 4, you need to follow the order of operations to simplify the expression correctly.
Q: How do I handle parentheses in an expression?
A: When handling parentheses in an expression, you need to evaluate the expression inside the parentheses first. For example, in the expression (2 + 3) × 4, you need to evaluate the expression inside the parentheses first and then multiply the result by 4.
Q: Can I use a calculator to simplify expressions?
A: Yes, you can use a calculator to simplify expressions, but it's essential to understand the correct order of operations and mathematical properties to ensure that you're simplifying the expression correctly.
Additional Resources
- Khan Academy: Order of Operations
- Mathway: Simplifying Expressions
- Wolfram Alpha: Order of Operations
- Purplemath: Order of Operations
- IXL: Order of Operations
Tips and Tricks
- Always follow the correct order of operations when simplifying expressions.
- Use parentheses to group expressions and make them easier to simplify.
- Understand the properties of exponents, such as the product rule and the power rule.
- Practice simplifying expressions with multiple operations to build your skills and confidence.
Conclusion
Simplifying expressions is a crucial skill in mathematics that helps us solve problems efficiently and accurately. By following the correct order of operations and mathematical properties, we can simplify complex expressions and solve problems with confidence. Remember to always follow the order of operations and use mathematical properties to simplify expressions correctly.