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Mathematics & Economics

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# Simplifying (Coursework Sample)

Instructions:

- 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 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, please make sure to include:
- Your solution to the above problem, making sure to include all mathematical work.
o Plan the logic necessary to complete the problem before you begin writing.
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; the properties used on the right.
- A discussion of why the properties of real numbers are important to know when working with algebra. In what ways are they useful for simplifying algebraic expressions?
- The incorporation of 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
- Distribution
- Removing parentheses
source..

Content:

Simplifying

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Commutative properties

The cumulative property of multiplication and addition states that addition and multiplication can be done in any order one wants without changing the answer.

If c and d are real numbers, then

1. c +d=d+c Commutative Property of Addition

2. c x d=dxc Commutative Property of Multiplication

Note that division and subtraction are not commutative (6-8=-2), but if one first rewrites a subtraction problem as an addition problem and a division problem as a multiplication problem, then he can use the appropriate property.

Note that if two numbers are added in either order, the result is the same .This property is termed as the Commutative Property of Addition. On the other hand, note that if two numbers are multiplied in either order, the result is the same. This property is termed as Commutative Property of Multiplication.

Associative properties

This property states that both multiplication and addition can be done with two numbers at the same time.

If b, c and d are numbers, then

1. (b+c)+d=b+(c+d) Associative Property of Addition

2. (bxc)d=b(cxd) Associative Property of Multiplication

Note that division and subtraction are not associative but if one first rewrites a subtraction problem as an addition problem and a division problem as a multiplication problem, then he can use the appropriate property.

Distributive property

This property is used when an expression has both multiplication and addition. It involves multiplication of all the terms inside the parenthesis.

Identity property

This property states that zero added to any number results to the number itself.

This properties help in solving algebra expressions as they guide one on when and how to multiply terms

The above properties have been used to solve the express...

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