Which Expression Demonstrates The Use Of The Commutative Property Of Addition In The First Step Of Simplifying The Expression { (-1+i)+(21+5i)$}$?A. { (-1+i)+(21+5i)+0$}$B. { -1+(i+21)+5i$}$C.

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The commutative property of addition is a fundamental concept in mathematics that states that the order of the numbers being added does not change the result. In other words, when we add two or more numbers together, we can rearrange them in any order without affecting the final sum. This property is denoted by the equation a + b = b + a, where a and b are any two numbers.

Applying the Commutative Property of Addition in Algebraic Expressions

In algebraic expressions, the commutative property of addition can be used to simplify complex expressions by rearranging the terms. This can make it easier to evaluate the expression and perform calculations. Let's consider the expression {(-1+i)+(21+5i)$}$ and see how we can use the commutative property of addition to simplify it.

Step 1: Identify the Terms in the Expression

The given expression is {(-1+i)+(21+5i)$}$. To simplify this expression, we need to identify the individual terms. In this case, we have two terms: −1+i{-1+i} and 21+5i{21+5i}.

Step 2: Apply the Commutative Property of Addition

Now that we have identified the terms, we can apply the commutative property of addition to rearrange them. According to the commutative property, we can swap the order of the terms without changing the result. Therefore, we can rewrite the expression as (−1+i)+(21+5i)=−1+(i+21)+5i{(-1+i)+(21+5i) = -1 + (i + 21) + 5i}.

Step 3: Simplify the Expression

Now that we have applied the commutative property of addition, we can simplify the expression further. We can combine like terms, which are terms that have the same variable or constant. In this case, we have two like terms: i{i} and 5i{5i}. We can combine these terms by adding their coefficients, which gives us 6i{6i}.

Step 4: Write the Final Simplified Expression

After simplifying the expression, we get −1+(i+21)+5i=−1+21+6i=20+6i{-1 + (i + 21) + 5i = -1 + 21 + 6i = 20 + 6i}.

Conclusion

In conclusion, the commutative property of addition is a powerful tool for simplifying algebraic expressions. By rearranging the terms in an expression, we can make it easier to evaluate and perform calculations. In this example, we used the commutative property of addition to simplify the expression {(-1+i)+(21+5i)$}$ and arrived at the final simplified expression 20+6i{20 + 6i}.

Which Expression Demonstrates the Use of the Commutative Property of Addition?

Now that we have seen how to simplify the expression {(-1+i)+(21+5i)$}$ using the commutative property of addition, let's look at the options provided.

A. {(-1+i)+(21+5i)+0$}$

This expression does not demonstrate the use of the commutative property of addition. The addition of 0 does not change the result, but it does not rearrange the terms.

B. {-1+(i+21)+5i$}$

This expression demonstrates the use of the commutative property of addition. By rearranging the terms, we can simplify the expression and arrive at the final result.

C. {(-1+i)+(21+5i)$}$

This expression is the original expression that we simplified using the commutative property of addition.

Answer

The correct answer is B. {-1+(i+21)+5i$}$. This expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression {(-1+i)+(21+5i)$}$.

Discussion

The commutative property of addition is a fundamental concept in mathematics that can be used to simplify algebraic expressions. By rearranging the terms in an expression, we can make it easier to evaluate and perform calculations. In this example, we used the commutative property of addition to simplify the expression {(-1+i)+(21+5i)$}$ and arrived at the final simplified expression 20+6i{20 + 6i}.

Key Takeaways

  • The commutative property of addition states that the order of the numbers being added does not change the result.
  • By rearranging the terms in an expression, we can simplify it and make it easier to evaluate and perform calculations.
  • The commutative property of addition can be used to combine like terms and simplify algebraic expressions.

Frequently Asked Questions

  • What is the commutative property of addition?
    • The commutative property of addition states that the order of the numbers being added does not change the result.
  • How can the commutative property of addition be used to simplify algebraic expressions?
    • By rearranging the terms in an expression, we can simplify it and make it easier to evaluate and perform calculations.
  • What is the final simplified expression for {(-1+i)+(21+5i)$}$?
    • The final simplified expression is 20+6i{20 + 6i}.
      Q&A: Understanding the Commutative Property of Addition =====================================================

In our previous article, we explored the commutative property of addition and how it can be used to simplify algebraic expressions. In this article, we will answer some frequently asked questions about the commutative property of addition.

Q: What is the commutative property of addition?

A: The commutative property of addition states that the order of the numbers being added does not change the result. In other words, when we add two or more numbers together, we can rearrange them in any order without affecting the final sum.

Q: How can the commutative property of addition be used to simplify algebraic expressions?

A: The commutative property of addition can be used to simplify algebraic expressions by rearranging the terms. By rearranging the terms, we can combine like terms and simplify the expression.

Q: What is the difference between the commutative property of addition and the associative property of addition?

A: The commutative property of addition states that the order of the numbers being added does not change the result. The associative property of addition states that the order in which we add numbers does not change the result. For example, (a + b) + c = a + (b + c).

Q: Can the commutative property of addition be used with other mathematical operations?

A: Yes, the commutative property of addition can be used with other mathematical operations such as multiplication. However, the commutative property of addition is specific to addition and cannot be used with subtraction or other mathematical operations.

Q: How can the commutative property of addition be used in real-life situations?

A: The commutative property of addition can be used in real-life situations such as calculating the total cost of items, calculating the area of a room, or calculating the volume of a container.

Q: What are some common mistakes to avoid when using the commutative property of addition?

A: Some common mistakes to avoid when using the commutative property of addition include:

  • Not rearranging the terms correctly
  • Not combining like terms
  • Not checking the final result for errors

Q: How can the commutative property of addition be used to solve equations?

A: The commutative property of addition can be used to solve equations by rearranging the terms and combining like terms. By rearranging the terms, we can isolate the variable and solve for its value.

Q: Can the commutative property of addition be used with complex numbers?

A: Yes, the commutative property of addition can be used with complex numbers. Complex numbers are numbers that have both a real and imaginary part. The commutative property of addition can be used to simplify complex expressions involving complex numbers.

Q: How can the commutative property of addition be used in calculus?

A: The commutative property of addition can be used in calculus to simplify expressions involving limits, derivatives, and integrals. By rearranging the terms, we can simplify the expression and make it easier to evaluate.

Conclusion

In conclusion, the commutative property of addition is a fundamental concept in mathematics that can be used to simplify algebraic expressions. By rearranging the terms, we can combine like terms and simplify the expression. The commutative property of addition can be used in real-life situations, such as calculating the total cost of items, calculating the area of a room, or calculating the volume of a container. By understanding the commutative property of addition, we can solve equations, simplify complex expressions, and make it easier to evaluate mathematical expressions.

Frequently Asked Questions

  • What is the commutative property of addition?
    • The commutative property of addition states that the order of the numbers being added does not change the result.
  • How can the commutative property of addition be used to simplify algebraic expressions?
    • By rearranging the terms, we can combine like terms and simplify the expression.
  • What is the difference between the commutative property of addition and the associative property of addition?
    • The commutative property of addition states that the order of the numbers being added does not change the result, while the associative property of addition states that the order in which we add numbers does not change the result.
  • Can the commutative property of addition be used with other mathematical operations?
    • Yes, the commutative property of addition can be used with other mathematical operations such as multiplication.
  • How can the commutative property of addition be used in real-life situations?
    • The commutative property of addition can be used in real-life situations such as calculating the total cost of items, calculating the area of a room, or calculating the volume of a container.

Key Takeaways

  • The commutative property of addition states that the order of the numbers being added does not change the result.
  • By rearranging the terms, we can combine like terms and simplify the expression.
  • The commutative property of addition can be used in real-life situations such as calculating the total cost of items, calculating the area of a room, or calculating the volume of a container.
  • The commutative property of addition can be used to solve equations, simplify complex expressions, and make it easier to evaluate mathematical expressions.