Question No. NINE (9) Is Compulsory. Write Short Answers To Any Six Questions: (PART I) Perform The Indicated Operations And Simplify. [1 3 2]+([2 1 0]-[1 3 2])​

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Introduction

In mathematics, simplifying expressions is an essential skill that helps us to solve complex problems and arrive at accurate solutions. In this article, we will focus on simplifying a specific mathematical expression using basic arithmetic operations. We will break down the expression into smaller parts, perform the indicated operations, and simplify the result.

Understanding the Expression

The given expression is: [1 3 2] + ([2 1 0] - [1 3 2])

To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Evaluate the expressions inside the parentheses.
  2. Perform the subtraction operation.
  3. Perform the addition operation.

Step 1: Evaluate the Expressions Inside the Parentheses

Let's evaluate the expressions inside the parentheses:

[2 1 0] - [1 3 2]

To perform the subtraction operation, we need to subtract each element of the second array from the corresponding element of the first array:

[2 1 0] - [1 3 2] = [2-1 1-3 0-2] = [1 -2 -2]

Step 2: Perform the Subtraction Operation

Now that we have evaluated the expression inside the parentheses, we can perform the subtraction operation:

[2 1 0] - [1 3 2] = [1 -2 -2]

Step 3: Perform the Addition Operation

Now that we have the result of the subtraction operation, we can perform the addition operation:

[1 3 2] + [1 -2 -2]

To perform the addition operation, we need to add each element of the second array to the corresponding element of the first array:

[1 3 2] + [1 -2 -2] = [1+1 3-2 2-2] = [2 1 0]

Conclusion

In this article, we simplified a mathematical expression using basic arithmetic operations. We broke down the expression into smaller parts, performed the indicated operations, and simplified the result. By following the order of operations (PEMDAS), we arrived at the final answer: [2 1 0].

Tips and Tricks

  • When simplifying mathematical expressions, always follow the order of operations (PEMDAS).
  • Evaluate expressions inside parentheses first.
  • Perform subtraction and addition operations from left to right.
  • Use parentheses to group numbers and operations to avoid confusion.

Common Mistakes

  • Failing to follow the order of operations (PEMDAS).
  • Not evaluating expressions inside parentheses first.
  • Performing subtraction and addition operations in the wrong order.

Real-World Applications

Simplifying mathematical expressions is an essential skill in various fields, including:

  • Computer programming: Simplifying expressions is crucial in programming languages, where complex expressions are used to perform calculations and operations.
  • Data analysis: Simplifying expressions is necessary in data analysis, where complex expressions are used to perform statistical calculations and operations.
  • Engineering: Simplifying expressions is essential in engineering, where complex expressions are used to perform calculations and operations related to design, construction, and testing of systems.

Conclusion

Introduction

In our previous article, we simplified a mathematical expression using basic arithmetic operations. In this article, we will answer some frequently asked questions related to simplifying mathematical expressions.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying mathematical expressions. The acronym PEMDAS stands for:

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

Q: Why is it important to follow the order of operations (PEMDAS)?

A: Following the order of operations (PEMDAS) is crucial when simplifying mathematical expressions because it ensures that we perform the operations in the correct order. If we don't follow the order of operations, we may arrive at an incorrect solution.

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, we need to follow the order of operations (PEMDAS) within the parentheses. For example, if we have the expression (2 + 3) × 4, we need to evaluate the expression inside the parentheses first: 2 + 3 = 5. Then, we multiply 5 by 4: 5 × 4 = 20.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are two basic arithmetic operations. Addition involves combining two or more numbers to get a total, while subtraction involves finding the difference between two numbers.

Q: How do I simplify complex expressions?

A: To simplify complex expressions, we need to follow the order of operations (PEMDAS) and break down the expression into smaller parts. We can use parentheses to group numbers and operations, and we can use the distributive property to simplify expressions.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that allows us to simplify expressions by distributing a single operation to multiple terms. For example, if we have the expression 2(x + 3), we can use the distributive property to simplify it: 2x + 6.

Q: How do I use the distributive property to simplify expressions?

A: To use the distributive property to simplify expressions, we need to identify the single operation that is being distributed to multiple terms. We can then distribute the operation to each term, and simplify the expression.

Q: What are some common mistakes to avoid when simplifying mathematical expressions?

A: Some common mistakes to avoid when simplifying mathematical expressions include:

  • Failing to follow the order of operations (PEMDAS)
  • Not evaluating expressions inside parentheses first
  • Performing subtraction and addition operations in the wrong order
  • Not using parentheses to group numbers and operations

Conclusion

In conclusion, simplifying mathematical expressions is an essential skill that requires attention to detail and a clear understanding of the order of operations (PEMDAS). By following the order of operations and using the distributive property, we can simplify complex expressions and arrive at accurate solutions.