¶ … real number is assigned to each statement written in a language, within a range from 0 to 1, where 1 means that the statement is completely true, and 0 means that the statement is completely false, while values less than 1 but greater than 0 represent that the statements are partly true, to a given, quantifiable extent. This makes it possible to analyze a distribution of statements for their truth-content, identify data patterns, make inferences and predictions, and model how processes operate. 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)

3(w -- 4) -- 5(w -- 6)

(0.3m + 35n) -- 0.8(-0.09n -- 22m)

Problem #1

2a (a-5) +4(a-5) I multiply 2a by each term inside the parentheses

2a^-10a+4(a-5) then I multiply 4 by each term inside the parentheses, and the distribution

Property removes parentheses

2a^-10a+4a-20 Now since -10a and 4a are like terms I subtract 4a from -10a to get -6a

2a^-6a-20 the expression fully simplify

Problem # 2

2w-3+3(w-4)-5(w-6) here I multiply 3 by each term inside the parentheses

2w-3+3w-12-5(w-6)...

I added the like terms 0.015m and 17.6m, 1.75n and 0.072n
17.615m+1.75n+0.072n = the expression is now fully simplify

17.615m+1.822n

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 properties of real numbers are very important to know when working with algebra because a variable is simply a letter that represents a real number. Before evaluating an algebraic expression it needed to be simplifying to make all calculation much easier. Like for instance, to simplify the problem given above,…