The Expression $12x + 15x - 11x$ Can Be Combined Because Of Which Property?A. Commutative Property Of Addition B. Distributive Property C. Additive Inverse Property D. Multiplicative Inverse Property

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Introduction

In mathematics, expressions can be simplified using various properties. The expression $12x + 15x - 11x$ can be combined, but the question is, which property allows us to do so? In this article, we will explore the properties of addition and multiplication to determine the correct answer.

Understanding the Properties

Commutative Property of Addition

The commutative property of addition states that the order of the numbers being added does not change the result. In other words, $a + b = b + a$. This property is useful when rearranging the terms in an expression, but it does not directly apply to the given expression.

Distributive Property

The distributive property states that a single term can be distributed to multiple terms inside parentheses. However, this property is not relevant to the given expression, as there are no parentheses involved.

Additive Inverse Property

The additive inverse property states that for every number, there is a corresponding negative number that, when added together, results in zero. This property is not directly applicable to the given expression.

Multiplicative Inverse Property

The multiplicative inverse property states that for every number, there is a corresponding reciprocal that, when multiplied together, results in one. This property is not relevant to the given expression.

Combining Like Terms

The expression $12x + 15x - 11x$ can be combined because it contains like terms. Like terms are terms that have the same variable raised to the same power. In this case, all three terms have the variable x raised to the power of 1.

To combine like terms, we add or subtract their coefficients. The coefficients are the numbers in front of the variables. In this case, the coefficients are 12, 15, and -11.

# Combining like terms
def combine_like_terms(terms):
    result = 0
    for term in terms:
        result += term
    return result

terms = [12, 15, -11]
result = combine_like_terms(terms)
print(result)  # Output: 16

Conclusion

The expression $12x + 15x - 11x$ can be combined because of the Associative Property of Addition. The associative property of addition states that the order in which we add numbers does not change the result. This property allows us to combine like terms by adding or subtracting their coefficients.

In conclusion, the correct answer is not among the options provided. The expression can be combined because of the associative property of addition, which is not listed as an option.

Final Answer

The final answer is not among the options provided. The correct answer is the associative property of addition.

Additional Information

  • The associative property of addition is a fundamental property of arithmetic that allows us to combine like terms.
  • The associative property of addition is not listed as an option, but it is the correct answer.
  • The expression $12x + 15x - 11x$ can be combined using the associative property of addition.

References

Q&A: The Expression Simplification

Q: What is the correct property that allows us to combine the expression $12x + 15x - 11x$? A: The correct property is the Associative Property of Addition. This property states that the order in which we add numbers does not change the result.

Q: What is the Associative Property of Addition? A: The Associative Property of Addition is a fundamental property of arithmetic that allows us to combine like terms. It states that the order in which we add numbers does not change the result.

Q: How do we combine like terms using the Associative Property of Addition? A: To combine like terms, we add or subtract their coefficients. The coefficients are the numbers in front of the variables. In the expression $12x + 15x - 11x$, the coefficients are 12, 15, and -11.

Q: What is the result of combining the like terms in the expression $12x + 15x - 11x$? A: The result of combining the like terms is $16x$.

Q: Why is the Associative Property of Addition important in mathematics? A: The Associative Property of Addition is important in mathematics because it allows us to simplify expressions and solve equations. It is a fundamental property that is used in many mathematical operations.

Q: What are some other properties of addition that are important in mathematics? A: Some other properties of addition that are important in mathematics include the Commutative Property of Addition, the Distributive Property, and the Additive Inverse Property.

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, $a + b = b + a$.

Q: What is the Distributive Property? A: The Distributive Property states that a single term can be distributed to multiple terms inside parentheses. However, this property is not relevant to the given expression.

Q: What is the Additive Inverse Property? A: The Additive Inverse Property states that for every number, there is a corresponding negative number that, when added together, results in zero. This property is not directly applicable to the given expression.

Q: What is the Multiplicative Inverse Property? A: The Multiplicative Inverse Property states that for every number, there is a corresponding reciprocal that, when multiplied together, results in one. This property is not relevant to the given expression.

Conclusion

The expression $12x + 15x - 11x$ can be combined because of the Associative Property of Addition. This property allows us to combine like terms by adding or subtracting their coefficients. The result of combining the like terms is $16x$. The Associative Property of Addition is an important property in mathematics that allows us to simplify expressions and solve equations.

Final Answer

The final answer is the Associative Property of Addition.

Additional Information

  • The Associative Property of Addition is a fundamental property of arithmetic that allows us to combine like terms.
  • The Associative Property of Addition is not listed as an option, but it is the correct answer.
  • The expression $12x + 15x - 11x$ can be combined using the Associative Property of Addition.

References