①Simplify The Following 121+ (48)-9212
Understanding the Mathematical Expression
When simplifying a mathematical expression, it's essential to follow the order of operations (PEMDAS). This acronym stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. In the given expression, we have parentheses, which indicate that the operations inside the parentheses should be evaluated first.
Breaking Down the Expression
The given expression is: 121 + (48) - 9212
To simplify this expression, we need to follow the order of operations:
- Evaluate the expression inside the parentheses: (48)
- Add 121 to the result of the expression inside the parentheses
- Subtract 9212 from the result of the previous step
Step 1: Evaluate the Expression Inside the Parentheses
The expression inside the parentheses is: (48)
This expression is already simplified, so we can move on to the next step.
Step 2: Add 121 to the Result of the Expression Inside the Parentheses
Now, we need to add 121 to the result of the expression inside the parentheses:
121 + 48 = 169
Step 3: Subtract 9212 from the Result of the Previous Step
Finally, we need to subtract 9212 from the result of the previous step:
169 - 9212 = -9043
Conclusion
Therefore, the simplified expression is: -9043
Why is Following the Order of Operations Important?
Following the order of operations is crucial in mathematics because it ensures that expressions are evaluated consistently and accurately. If we were to evaluate the expression from left to right, we would get a different result:
121 + 48 = 169 169 - 9212 = -9043 ( incorrect)
By following the order of operations, we can avoid errors and ensure that our calculations are accurate.
Common Mistakes to Avoid
When simplifying mathematical expressions, it's essential to avoid common mistakes such as:
- Evaluating expressions from left to right instead of following the order of operations
- Forgetting to evaluate expressions inside parentheses
- Not following the correct order of operations (PEMDAS)
Real-World Applications
Simplifying mathematical expressions is an essential skill in various fields, including:
- Science: Scientists use mathematical expressions to model real-world phenomena and make predictions.
- Engineering: Engineers use mathematical expressions to design and optimize systems.
- Finance: Financial analysts use mathematical expressions to model economic systems and make predictions.
Practice Exercises
To practice simplifying mathematical expressions, try the following exercises:
- Simplify the expression: 2(3 + 4) - 5
- Simplify the expression: 10 - (3 + 2)
- Simplify the expression: 5(2 + 3) + 1
Conclusion
Understanding the Mathematical Expression
When simplifying a mathematical expression, it's essential to follow the order of operations (PEMDAS). This acronym stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. In the given expression, we have parentheses, which indicate that the operations inside the parentheses should be evaluated first.
Breaking Down the Expression
The given expression is: 121 + (48) - 9212
To simplify this expression, we need to follow the order of operations:
- Evaluate the expression inside the parentheses: (48)
- Add 121 to the result of the expression inside the parentheses
- Subtract 9212 from the result of the previous step
Step 1: Evaluate the Expression Inside the Parentheses
The expression inside the parentheses is: (48)
This expression is already simplified, so we can move on to the next step.
Step 2: Add 121 to the Result of the Expression Inside the Parentheses
Now, we need to add 121 to the result of the expression inside the parentheses:
121 + 48 = 169
Step 3: Subtract 9212 from the Result of the Previous Step
Finally, we need to subtract 9212 from the result of the previous step:
169 - 9212 = -9043
Conclusion
Therefore, the simplified expression is: -9043
Why is Following the Order of Operations Important?
Following the order of operations is crucial in mathematics because it ensures that expressions are evaluated consistently and accurately. If we were to evaluate the expression from left to right, we would get a different result:
121 + 48 = 169 169 - 9212 = -9043 ( incorrect)
By following the order of operations, we can avoid errors and ensure that our calculations are accurate.
Common Mistakes to Avoid
When simplifying mathematical expressions, it's essential to avoid common mistakes such as:
- Evaluating expressions from left to right instead of following the order of operations
- Forgetting to evaluate expressions inside parentheses
- Not following the correct order of operations (PEMDAS)
Real-World Applications
Simplifying mathematical expressions is an essential skill in various fields, including:
- Science: Scientists use mathematical expressions to model real-world phenomena and make predictions.
- Engineering: Engineers use mathematical expressions to design and optimize systems.
- Finance: Financial analysts use mathematical expressions to model economic systems and make predictions.
Practice Exercises
To practice simplifying mathematical expressions, try the following exercises:
- Simplify the expression: 2(3 + 4) - 5
- Simplify the expression: 10 - (3 + 2)
- Simplify the expression: 5(2 + 3) + 1
Q&A: Simplifying Mathematical Expressions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: Why is it important to follow the order of operations?
A: Following the order of operations ensures that expressions are evaluated consistently and accurately. If we were to evaluate the expression from left to right, we would get a different result.
Q: What is the difference between evaluating expressions from left to right and following the order of operations?
A: Evaluating expressions from left to right means performing operations in the order they appear from left to right. Following the order of operations means performing operations in the order specified by the acronym PEMDAS.
Q: What are some common mistakes to avoid when simplifying mathematical expressions?
A: Some common mistakes to avoid when simplifying mathematical expressions include:
- Evaluating expressions from left to right instead of following the order of operations
- Forgetting to evaluate expressions inside parentheses
- Not following the correct order of operations (PEMDAS)
Q: How can I practice simplifying mathematical expressions?
A: You can practice simplifying mathematical expressions by trying the following exercises:
- Simplify the expression: 2(3 + 4) - 5
- Simplify the expression: 10 - (3 + 2)
- Simplify the expression: 5(2 + 3) + 1
Q: What are some real-world applications of simplifying mathematical expressions?
A: Simplifying mathematical expressions is an essential skill in various fields, including:
- Science: Scientists use mathematical expressions to model real-world phenomena and make predictions.
- Engineering: Engineers use mathematical expressions to design and optimize systems.
- Finance: Financial analysts use mathematical expressions to model economic systems and make predictions.
Conclusion
In conclusion, simplifying mathematical expressions is an essential skill that requires following the order of operations (PEMDAS). By understanding the importance of following the order of operations and avoiding common mistakes, we can ensure that our calculations are accurate and reliable.