Algebra > Operations and Properties > Alternate Approach to Addition and Subtraction of Real Numbers
Instructions
Shown on this page, Alternate Approach to Addition and Subtraction of Real Numbers, is a three screen snapshots of the content found in our eBook or print copy of HP Prime Guide Algebra Fundamentals.The snapshot will likely be a partial view, with previous content cut off from top and completion of a topic's explanation cut from the bottom. For additional coverage see the Table of Content of the HP Prime Guide to jump to the second Chapter, Explanation 1.2 - Operations and Properties of Real Numbers, Alternate Approach to Addition and Subtraction of Real Numbers, shown below. Print user will need to turn to this page.
This section continues with the steps necessary to draw HP Prime Family Graph of Function F(x) started in the previous section. If just starting, begin by using the previous section Instructions for Content 2.
Carrying on from the previous section Instructions, press the Plot Setup key. We need to change the values of Function Plot Setup screen shown below in Content 1. Key in -5, 10, -2, 7 into the four fields. The first value in the screenshot for Function Plot Setup needs to be a -5 for the plot to be the one shown in Content 1, Press the Plot key and follow the directions shown below figure 4 to draw the graph of the parabola. For a complete explanation of the Function app see the link, HP Prime: The Basics of Graphing (Function App).
Next we turn to the Alternate Approach to Addition and Subtraction of Real Numbers. Described in Content 1 and Content 2 is a physical Gas Air Balloon representation of how a real world example can be used to come up with an Alternate Approach to Addition and Subtraction of Real Numbers.
Remark: In Content 1 we finish our first HP Prime graphing example. In algebra and math classes plotting functions and relations is one of the most useful and frequent task that we will perform. We then turn to using a Gas Air Balloon to introduce an alternate way of quickly calculating sign results for integer addition and subtraction problems. Conent 2 summarize our Gas Air Balloon findings and leads us into Content 3 where we setting up an alternate rule for doing addition and subtraction of integers. This alternate rule will serve us well when we collect like terms and perform future algebraic calculations with expressions and equations. The alternate rule lets us make things simpler rather than more complex.
When you finished with this section move on to another section or topic.
HP Prime Guide Algebra Fundamentals - Content 1
HP Prime Guide Algebra Fundamentals - Content 1
Instructions
Continue reading with Content 2. Content 2 continues the physical Gas Air Balloon discussion of how a real world example can be used to come up with an Alternate Approach to Addition and Subtraction of Real Numbers. The two figures in Content 2 summarize the results. The alternate approach is to use simplest equivalent representation possible. Thus -2-(-5)=3 is equivalent to -2+5=3 and 5-2=3 is equivalent to 5+(-2)=3. The simplest representations have no double signs in the middle. The simplest in figure 5 is the second representation, -2+5=3, and in the last figure is the first representation, 5-2=3.
HP Prime Guide Algebra Fundamentals - Content 2
HP Prime Guide Algebra Fundamentals - Content 2
Instructions
Continue with Content 3. We translate the above Gas Helicopter example into a working model where we think money. Start by looking at the calculator's image shown below. It shows the final form of the five alternate problems we need to work. First, follow the directions below the calculator's image shown in Content 3 and create the screen with your calculator or calculator app. Read the first full paragraph one in Content 3. Continue on with the rest of Content 3’s explanation.
Taking a closer look at the green Alternate Rule - Addition and Subtractio, we have:
Simplify - write equivalent form by eliminating double signs ( paralels multilication / division rules + - becomes a -, and - - becomes a + )
Calculate Results - think money (first number: sign: + have "+ sign understood, not shown", - owe, second number sign: + get, - bill; show the result
3 - -4 = 3 + 4 = 7 tradtional addition; result 7
-2 - -5 = -2 + 5 = 3 owe $2, get $5; net $7
5 + -2 = 5 - 2 = 3 traditional subtraction; result 3
3 + -4 = 3 - 4 = -1 have $3, bill $4; net owe $1
-3 + -4 = -3 - 4 = -7 owe $3, bill $4; net owe $7
HP Prime Guide Algebra Fundamentals - Content 3
HP Prime Guide Algebra Fundamentals - Content 3
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