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Ms. Gent's Class Notes for Combining How To: |
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Before we can start, we need to remember the following:
Mr. Decarte's contribution to the world of mathematics -- the family of negative numbers -- changed the way we could think about numbers. By expanding the existing number line to the left and recycling the symbol that had been defined as subtract to notate these numbers, he forced us to revisit the meanings of addition and subtraction. So, in short, because he recycled a symbol that the mathematical world was already using (the minus sign) to name the negative numbers, we have to revise the way we use that notation. So here are the ... |
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| Revised Rules for Addition and Subtraction : | |
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1. All
numbers have a sign in front of them. If the sign is invisible,
it's positive.
2. We no longer think of + as add and - as subtract. Now we combine. And now - with that out of the way -- here we go... |
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Combining How To: |
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| 1. |
Circle the bumping signs. Bumping signs are + and - signs that have no number between them. |
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| 2. |
Recode / Rewrite these signs as 1 sign. Use this rule: If the signs are alike, write a + sign. If the signs are different, write a - sign. |
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| 3. | Bring down the rest of the problem (all the stuff that is not inside the circle you made in step #1). |
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| 4. | Identify the two numbers in this step. Circle them if you have to. Remember that all numbers have a sign in front of them. Include this sign in your I.D. |
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| 5. | Ask yourself : Are these numbers on the same side of zero or on opposite sides of zero? |
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| 6. |
If the numbers are on the same side of zero, add them. If they are on opposite sides of zero, subtract them. |
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| 7. | Your final answer will be on the same side of zero as the number with the larger distance from zero (absolute value). |
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