All numbers and number expressions used in Algebra and higher levels of
mathematics are either positive + or negative -. Because of this, in the
"old days" (when your parents or grandparents were in school) they
were called *signed numbers*.

This is true even for numbers that don't seem to have a sign, for example:

5 is really +5 (positive 5) |
7x - 8 is really +7x - 8 (positive 7x minus 8) |

To do addition, subtraction, multiplication or division with real numbers you need to be aware of the positive and negative signs, even if positive signs are not always written down. If there is no sign, always imagine an invisible +.

In elementary school arithmetic classes you learned how to add and subtract.
In Algebra, we learn that it is all **really** just addition. We use the
concept of opposites to do subtraction.
In Algebra we learn that subtracting is the same as adding the opposite.

For example, **7 - 2** (subtracting 2) is the
same as **7 + (-2)** (adding the opposite of 2).
In either case, the answer is **+5**. For those
too lazy to write down the sign (which is most of us) you can write your answer
as just plain old **5**.

Here are the rules for addition and subtraction when working with two numbers that might be either positive or negative:

Signs of numbers in the problem |
Action |
Sign of the Answer |
Example |

Both positive numbers | Add them | Positive |
5 + 3 = +8
6a + 2a = +8a |

Both negative numbers | Add them | Negative |
- 5 - 3 = -8
-6a - 2a = -8a |

One positive and one negative | Subtract them | Same sign as the biggest number |
+5 - 3 = +2 -5 + 3 = -2 +6a - 2a = +4a |

If you have more than two numbers to add or subtract, take them two at a
time. Use the rules above to get an answer for the first two numbers - then use
the rules to combine that answer with the next number until everything has been
added or subtracted.

Later in elementary school arithmetic classes you learned how to multiply and
divide. In Algebra, we learn that it is all **really** just multiplication.

For example, **8 ÷ 2** (divide
by 2) is the same as **8 • ½** (multiply by
½). In either case, the answer is **+4**.
For those too lazy to write down the sign (which is most of us) you can write
your answer as just plain old **4**.

The rules are slightly different from those for adding and subtracting. In general, signs the same answer is positive, signs different the answer is negative. Also notice that if there is no sign for the number after the multiplication symbol, then the sign is really positive:

5 • 3 = +5 • (+3) = +15 = 15

Here are the rules for multiplication and division when working with two numbers that might be either positive or negative.

Signs of numbers in the problem |
Action |
Sign of the Answer |
Example |

Both positive numbers | Multiply them | Positive |
5 • 3 = +15
6 • 2a = +12a |

Both negative numbers | Multiply them | Positive |
-5 • (- 3) = +15
-6 • (- 2a) = +12a |

One positive and one negative | Multiply them | Negative |
+5 • (- 3) = -15 -5 • 3 = -15 +6 • (-2a) = -12a |

Again, if you have more than two numbers to multiply or divide, take them two at a time. Use the rules above to get an answer for the first two numbers - then use the rules to combine that answer with the next number until everything has been multiplied or divided.

*Comments, questions, or you just need some help? Send an e-mail to
Mrs. Shearer*

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