Read the following instructions in order to complete this assignment and review the example of how to complete the math required for this assignment:
Use the properties of real numbers to simplify the following expressions:
2a(a – 5) + 4(a – 5)
2w – 3 + 3(w – 4) – 5(w – 6)
0.05(0.3m + 35n) – 0.8(-0.09n – 22m)
Write a two- to three-page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, do the following:
Demonstrate your solution to the above problems, making sure to include all mathematical work. Show every step of the process of simplifying and identify which property of real numbers was used in each step of your work. Please include your math work on the left and the properties used on the right.
Explain why the properties of real numbers are important to know when working with algebra. In what ways are they useful for simplifying algebraic expressions?
Incorporate the following five math vocabulary words into the text of your paper. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work):
Simplify
Like terms
Coefficient
Distributive
Removing parentheses
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Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
How would you like us to help you with this assignment?
I don't know what am doing could you show me how to slove the problem?
2a(a – 5) + 4(a – 5)
2a^2 - 10 + 4a - 20
2a^2 + 4a - 30
How did you get that answer? and can you show me how I used the expression.I'm so lost...
Please use the same names for your posts.
If you don't understand my work above, then I urge you to go back and study your book again. I can't simplify that any more.
So, how did you get - 30?
-10 + -20 = -30
I have to use mybay correct to get the answer.
To simplify the given expressions, we will use the properties of real numbers and follow the steps indicated in the instructions.
Let's start with the first expression:
2a(a – 5) + 4(a – 5)
Step 1: Apply the distributive property by multiplying each term inside the parentheses by the coefficient outside the parentheses:
2a^2 - 10a + 4a - 20
Step 2: Combine like terms. Like terms have the same variable and exponent:
2a^2 - 6a - 20
In this step, the properties of real numbers used were the distributive property and the combining like terms property.
Moving on to the second expression:
2w – 3 + 3(w – 4) – 5(w – 6)
Step 1: Apply the distributive property by multiplying each term inside the parentheses by the coefficient outside the parentheses:
2w - 3 + 3w - 12 - 5w + 30
Step 2: Combine like terms:
(2w + 3w - 5w) + (-3 - 12 + 30)
Step 3: Perform the operations within the parentheses:
(2w + 3w - 5w) + (15)
Step 4: Combine like terms:
0w + 15
Step 5: Simplify further:
15
In this example, the properties of real numbers used were the distributive property, combining like terms property, and the additive identity property.
Finally, let's simplify the third expression:
0.05(0.3m + 35n) – 0.8(-0.09n – 22m)
Step 1: Apply the distributive property by multiplying each term inside the parentheses by the coefficient outside the parentheses:
0.05 * 0.3m + 0.05 * 35n - 0.8 * (-0.09n) - 0.8 * (-22m)
Step 2: Simplify the terms:
0.015m + 1.75n + 0.072n + 17.6m
Step 3: Combine like terms:
(0.015m + 17.6m) + (1.75n + 0.072n)
Step 4: Simplify further:
17.615m + 1.822n
In this case, the properties of real numbers used were the distributive property and combining like terms property.
Now, let's answer the question regarding the importance of knowing the properties of real numbers when working with algebra.
The properties of real numbers provide a set of rules and principles that allow us to manipulate algebraic expressions and equations in a systematic and consistent manner. By understanding these properties, we can simplify expressions, solve equations, and perform various algebraic operations more efficiently.
For example, the distributive property is crucial when simplifying expressions because it allows us to multiply a single term by each term inside the parentheses. This property helps us combine like terms and reduce the complexity of an expression.
The concept of like terms is also essential as it allows us to combine terms with the same variables and exponents. By recognizing like terms, we can simplify expressions by combining them and reduce them to their simplest form.
Another property that is frequently used is the additive identity property, which states that adding zero to any number does not change its value. This property is often employed when simplifying expressions or performing addition/subtraction operations.
Knowing the properties of real numbers helps in developing a deeper understanding of algebraic concepts and allows for consistent and accurate mathematical reasoning. It allows us to simplify expressions, solve equations, and make connections between different mathematical ideas.
In the context of this assignment, knowing the properties of real numbers is crucial for simplifying the given expressions and demonstrating the steps clearly. It helps in organizing and explaining the mathematical work concisely, and it ensures that the solution is accurate and aligned with mathematical principles.
Incorporating the math vocabulary words provided:
- Simplify: We simplified the given expressions by reducing them to their simplest form.
- Like terms: Like terms are terms that have the same variables and exponents.
- Coefficient: A coefficient is the numerical factor in front of a variable.
- Distributive: The distributive property is used to multiply each term inside the parentheses by a factor outside the parentheses.
- Removing parentheses: The distributive property involves removing parentheses by distributing the multiplication.
By incorporating these vocabulary words into your paper appropriately, you will demonstrate your understanding of these mathematical terms and their application in solving algebraic problems.