Simplify The Expression: ${ 8 \times 4 + (9 - 2) \div 4 }$
Introduction
In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. It involves breaking down complex expressions into simpler ones, making it easier to understand and work with. In this article, we will focus on simplifying the expression: 8 × 4 + (9 - 2) ÷ 4. We will use the order of operations (PEMDAS) to simplify the expression step by step.
Understanding the Order of Operations
Before we dive into simplifying the expression, it's essential to understand the order of operations, also known as PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It tells us which operations to perform first when we have multiple operations in an expression.
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next (e.g., 2^3).
- 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
Now that we understand the order of operations, let's simplify the expression: 8 × 4 + (9 - 2) ÷ 4.
Step 1: Evaluate the Expression Inside the Parentheses
The first step is to evaluate the expression inside the parentheses: 9 - 2.
9 - 2 = 7
So, the expression becomes: 8 × 4 + 7 ÷ 4.
Step 2: Multiply 8 and 4
Next, we multiply 8 and 4.
8 × 4 = 32
Now, the expression becomes: 32 + 7 ÷ 4.
Step 3: Divide 7 by 4
Now, we divide 7 by 4.
7 ÷ 4 = 1.75
So, the expression becomes: 32 + 1.75.
Step 4: Add 32 and 1.75
Finally, we add 32 and 1.75.
32 + 1.75 = 33.75
Therefore, the simplified expression is: 33.75.
Conclusion
Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations (PEMDAS), we can break down complex expressions into simpler ones, making it easier to understand and work with. In this article, we simplified the expression: 8 × 4 + (9 - 2) ÷ 4, step by step, using the order of operations. We evaluated the expression inside the parentheses, multiplied 8 and 4, divided 7 by 4, and finally added 32 and 1.75. The simplified expression is: 33.75.
Frequently Asked Questions
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 we have multiple operations in an expression. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I simplify an expression using the order of operations?
A: To simplify an expression using the order of operations, follow these steps:
- Evaluate expressions inside parentheses first.
- Evaluate any exponential expressions next.
- Evaluate multiplication and division operations from left to right.
- Finally, evaluate any addition and subtraction operations from left to right.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both arithmetic operations that involve numbers. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.
Tips and Tricks
Tip 1: Use the Order of Operations to Simplify Expressions
When simplifying expressions, use the order of operations to ensure that you perform the operations in the correct order.
Tip 2: Evaluate Expressions Inside Parentheses First
When simplifying expressions, evaluate expressions inside parentheses first, as they take precedence over other operations.
Tip 3: Use Exponents to Simplify Expressions
When simplifying expressions, use exponents to simplify expressions that involve repeated multiplication or division.
Real-World Applications
Application 1: Simplifying Expressions in Algebra
Simplifying expressions is an essential skill in algebra, where we use variables and constants to represent unknown values. By simplifying expressions, we can solve equations and inequalities more efficiently.
Application 2: Simplifying Expressions in Calculus
Simplifying expressions is also essential in calculus, where we use limits, derivatives, and integrals to study functions and their behavior. By simplifying expressions, we can solve problems more efficiently and accurately.
Application 3: Simplifying Expressions in Real-World Scenarios
Simplifying expressions is also essential in real-world scenarios, where we use mathematical models to describe and analyze complex systems. By simplifying expressions, we can make predictions and decisions more efficiently and accurately.
Final Thoughts
Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations (PEMDAS), we can break down complex expressions into simpler ones, making it easier to understand and work with. In this article, we simplified the expression: 8 × 4 + (9 - 2) ÷ 4, step by step, using the order of operations. We evaluated the expression inside the parentheses, multiplied 8 and 4, divided 7 by 4, and finally added 32 and 1.75. The simplified expression is: 33.75.
Introduction
In our previous article, we simplified the expression: 8 × 4 + (9 - 2) ÷ 4, step by step, using the order of operations (PEMDAS). We evaluated the expression inside the parentheses, multiplied 8 and 4, divided 7 by 4, and finally added 32 and 1.75. The simplified expression is: 33.75. In this article, we will answer some frequently asked questions related to simplifying expressions.
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 we have multiple operations in an expression. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: How do I simplify an expression using the order of operations?
A: To simplify an expression using the order of operations, follow these steps:
- Evaluate expressions inside parentheses first.
- Evaluate any exponential expressions next.
- Evaluate multiplication and division operations from left to right.
- Finally, evaluate any addition and subtraction operations from left to right.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both arithmetic operations that involve numbers. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.
Q: Can I simplify an expression with multiple operations?
A: Yes, you can simplify an expression with multiple operations. Just follow the order of operations and perform the operations in the correct order.
Q: How do I handle expressions with negative numbers?
A: When simplifying expressions with negative numbers, remember to follow the order of operations. Evaluate expressions inside parentheses first, then evaluate any exponential expressions, and finally evaluate any multiplication and division operations.
Q: Can I simplify an expression with fractions?
A: Yes, you can simplify an expression with fractions. Just follow the order of operations and perform the operations in the correct order.
Q: How do I handle expressions with decimals?
A: When simplifying expressions with decimals, remember to follow the order of operations. Evaluate expressions inside parentheses first, then evaluate any exponential expressions, and finally evaluate any multiplication and division operations.
Q: Can I simplify an expression with variables?
A: Yes, you can simplify an expression with variables. Just follow the order of operations and perform the operations in the correct order.
Q: How do I handle expressions with exponents?
A: When simplifying expressions with exponents, remember to follow the order of operations. Evaluate expressions inside parentheses first, then evaluate any exponential expressions, and finally evaluate any multiplication and division operations.
Q: Can I simplify an expression with multiple variables?
A: Yes, you can simplify an expression with multiple variables. Just follow the order of operations and perform the operations in the correct order.
Tips and Tricks
Tip 1: Use the Order of Operations to Simplify Expressions
When simplifying expressions, use the order of operations to ensure that you perform the operations in the correct order.
Tip 2: Evaluate Expressions Inside Parentheses First
When simplifying expressions, evaluate expressions inside parentheses first, as they take precedence over other operations.
Tip 3: Use Exponents to Simplify Expressions
When simplifying expressions, use exponents to simplify expressions that involve repeated multiplication or division.
Real-World Applications
Application 1: Simplifying Expressions in Algebra
Simplifying expressions is an essential skill in algebra, where we use variables and constants to represent unknown values. By simplifying expressions, we can solve equations and inequalities more efficiently.
Application 2: Simplifying Expressions in Calculus
Simplifying expressions is also essential in calculus, where we use limits, derivatives, and integrals to study functions and their behavior. By simplifying expressions, we can solve problems more efficiently and accurately.
Application 3: Simplifying Expressions in Real-World Scenarios
Simplifying expressions is also essential in real-world scenarios, where we use mathematical models to describe and analyze complex systems. By simplifying expressions, we can make predictions and decisions more efficiently and accurately.
Final Thoughts
Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations (PEMDAS), we can break down complex expressions into simpler ones, making it easier to understand and work with. In this article, we answered some frequently asked questions related to simplifying expressions. We hope that this article has been helpful in clarifying any doubts you may have had about simplifying expressions.
Additional Resources
Online Resources
- Khan Academy: Simplifying Expressions
- Mathway: Simplifying Expressions
- Wolfram Alpha: Simplifying Expressions
Books
- "Algebra and Trigonometry" by Michael Sullivan
- "Calculus" by Michael Spivak
- "Mathematics for Computer Science" by Eric Lehman
Videos
- "Simplifying Expressions" by Khan Academy
- "Simplifying Expressions" by Mathway
- "Simplifying Expressions" by Wolfram Alpha
Conclusion
Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations (PEMDAS), we can break down complex expressions into simpler ones, making it easier to understand and work with. In this article, we answered some frequently asked questions related to simplifying expressions. We hope that this article has been helpful in clarifying any doubts you may have had about simplifying expressions.