Simplify The Expression:${ (-5) \cdot 7 - 9(-4) }$
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Introduction
In mathematics, simplifying expressions is a crucial skill that helps us evaluate complex mathematical problems. It involves breaking down the expression into smaller parts, applying the order of operations, and simplifying the result. In this article, we will focus on simplifying the expression using the order of operations and basic arithmetic operations.
Understanding the Order of Operations
The order of operations is a set of rules that helps us evaluate mathematical expressions by following a specific order. 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
Now that we have a good understanding of the order of operations, let's apply it to simplify the expression .
Step 1: Multiply -5 and 7
The first step is to multiply -5 and 7. We can do this by multiplying the absolute value of 5 (which is 5) and 7, and then applying the negative sign to the result.
Step 2: Multiply 9 and -4
The next step is to multiply 9 and -4. We can do this by multiplying the absolute value of 9 (which is 9) and 4, and then applying the negative sign to the result.
Step 3: Subtract -36 from -35
Now that we have the results of the multiplication operations, we can subtract -36 from -35.
Conclusion
In this article, we simplified the expression using the order of operations and basic arithmetic operations. We broke down the expression into smaller parts, applied the order of operations, and simplified the result. By following the order of operations, we can evaluate complex mathematical expressions and arrive at the correct solution.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that helps us evaluate mathematical expressions by following a specific order. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I simplify a mathematical expression?
A: To simplify a mathematical expression, you need to follow the order of operations. This involves breaking down the expression into smaller parts, applying the order of operations, and simplifying the result.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both arithmetic operations that involve combining numbers. However, multiplication involves combining numbers by adding a number a certain number of times, while division involves sharing a number into equal parts.
Final Thoughts
Simplifying expressions is a crucial skill in mathematics that helps us evaluate complex mathematical problems. By following the order of operations and applying basic arithmetic operations, we can simplify expressions and arrive at the correct solution. In this article, we simplified the expression using the order of operations and basic arithmetic operations. We hope that this article has provided you with a better understanding of how to simplify mathematical expressions and has helped you to develop your mathematical skills.
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Introduction
In our previous article, we simplified the expression using the order of operations and basic arithmetic operations. In this article, we will provide a Q&A guide to help you understand how to simplify mathematical expressions and answer common questions related to this topic.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that helps us evaluate mathematical expressions by following a specific order. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I simplify a mathematical expression?
A: To simplify a mathematical expression, you need to follow the order of operations. This involves breaking down the expression into smaller parts, applying the order of operations, and simplifying the result.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both arithmetic operations that involve combining numbers. However, multiplication involves combining numbers by adding a number a certain number of times, while division involves sharing a number into equal parts.
Q: What is the order of operations for fractions?
A: When working with fractions, the order of operations is the same as for whole numbers. However, you need to be careful when simplifying fractions to ensure that you are not multiplying or dividing by zero.
Q: How do I simplify an expression with parentheses?
A: When simplifying an expression with parentheses, you need to evaluate the expression inside the parentheses first. This means that you need to follow the order of operations within the parentheses before moving on to the rest of the expression.
Q: What is the difference between a variable and a constant?
A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that does not change. When simplifying expressions, you need to be careful to distinguish between variables and constants.
Q: How do I simplify an expression with exponents?
A: When simplifying an expression with exponents, you need to follow the order of operations. This means that you need to evaluate any exponential expressions before moving on to the rest of the expression.
Q: What is the order of operations for decimals?
A: When working with decimals, the order of operations is the same as for whole numbers. However, you need to be careful when simplifying decimals to ensure that you are not multiplying or dividing by zero.
Advanced Questions
Q: How do I simplify an expression with multiple variables?
A: When simplifying an expression with multiple variables, you need to follow the order of operations. This means that you need to evaluate any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.
Q: What is the difference between a linear expression and a quadratic expression?
A: A linear expression is an expression that can be written in the form ax + b, where a and b are constants, while a quadratic expression is an expression that can be written in the form ax^2 + bx + c, where a, b, and c are constants.
Q: How do I simplify an expression with absolute values?
A: When simplifying an expression with absolute values, you need to follow the order of operations. This means that you need to evaluate any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.
Q: What is the order of operations for complex numbers?
A: When working with complex numbers, the order of operations is the same as for whole numbers. However, you need to be careful when simplifying complex numbers to ensure that you are not multiplying or dividing by zero.
Conclusion
In this article, we provided a Q&A guide to help you understand how to simplify mathematical expressions and answer common questions related to this topic. We hope that this article has provided you with a better understanding of how to simplify mathematical expressions and has helped you to develop your mathematical skills.
Final Thoughts
Simplifying expressions is a crucial skill in mathematics that helps us evaluate complex mathematical problems. By following the order of operations and applying basic arithmetic operations, we can simplify expressions and arrive at the correct solution. In this article, we provided a Q&A guide to help you understand how to simplify mathematical expressions and answer common questions related to this topic. We hope that this article has provided you with a better understanding of how to simplify mathematical expressions and has helped you to develop your mathematical skills.