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Mathematics for Technology I (Math 1131)

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Study Force Academy
Durham College, Mathematics
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  • 55 lessons
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  • 10 week duration

Numerical Operations

A numerical operation can be described as an action or process used to solved a numerical problem.

Adding and Subtracting Signed Numbers 

If you have two numbers x and y, the following rules apply when these numbers are being added or subtracted.

  • Rule of Signs for Addition:   (xy) is the same as x + (–y)  or  x – (+y) because a negative beside a positive (or vice versa) always make a negative.
  • Rule of Signs for Subtraction:   x + y is the same as x – (–y) because two negatives side-by-side make a positive.

Here are a few examples:

1   7+22   943   6+4

For #1, the answer is clearly 9. But you could also have gotten 9 if you had:   7  (2) because of the rule of signs for subtraction.

For #2, the answer is 5. But you could also have gotten 5 if you had:   9 + (–4) or 9 – (+4) because of the rule of signs for addition.

For #3, the answer is –2.

A summary of these symbols is shown below:

(+)(+) = (+)()() = (+)(+)() = ()()(+) = ()

More examples:

1   8(6)2   7(5)3   (16)7(9)
Answers

#1:   14

#2:  –2

#3:   18

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Multiplying and Dividing Signed Numbers 

  • Rules of Signs for Multiplication:   
    • (+x)(+y) = (–x)(–y) = +xy
    • (+x)(–y) = (–x)(+y) = –xy
  • It’s also important to note that the same rules apply for division too.

Multiplication of two or more factors can be symbolized in 3 main ways:

1   x×y2   x·y3   xy=xy=xy

For division:

1   x÷y2   xy=xy

Here are a few examples:

1   23=62   2(3)(1)2=123   412=412=412134   153=5

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