Download operations with signed numbers

OPERATIONS WITH SIGNED NUMBERS
♦ DIVISION
When dividing two real numbers with the same signs (either both positive or both
negative), the quotient (result) will be a positive number.
3 1
−6
Ex.
= (the fraction was reduced by dividing both numbers by 3)
=2
15 5
−3
NOTE: Division by 0 is undefined but 0 divided by a nonzero number is 0.
3
0
Ex.
= undefined
=0
0
5
When dividing two real numbers with different signs, the quotient (result) will be a
negative number.
− 49
Ex.
= −7
7
20
1
=−
− 100
5
(reduce the fraction by dividing both numbers by 20)
♦ MULTIPLICATION
The same rules for division apply to the product (result) of two or more numbers
when they are multiplied.
Ex. –9 • 2= -18 since (-)(+)= (-)
(-2)(-5)(6) = 60 since (-)(-) = (+)
since (+)(+)= (+)
♦ ADDITION
When adding positive real numbers, the sum (result) will be a positive number.
Ex. 500 + 18 = 518
When adding negative numbers, the result will be obtained by adding the numbers
but keeping the negative sign.
Ex. (-8) + (-2) + (-4) = -14
When adding two numbers with opposite signs, the result will be obtained by finding
the difference between the two numbers and keeping the sign of the largest number.
it stays a positive since the largest number is positive)
Ex. –13 + 80 = 67
7 + (-13) = -6
it stays negative since the largest number is a negative)
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♦ SUBTRACTION
If subtracting two numbers and the largest number is the minuend (the first number)
then the difference (result) is obtained by subtracting the numbers and keeping a
positive sign.
Ex. 93 – 41 = 52
If subtracting two numbers and the largest number is the subtrahend (the second
number) then the difference is obtained by subtracting the numbers and keeping a
negative sign.
Ex. 41 – 212 = -171
If subtracting two numbers that both have the negative sign, add the numbers and
keep the negative sign.
Ex. -20 – 15 = -35
ORDER OF OPERATIONS
Just as following a recipe to make a cake, there is also an order when simplifying a
mathematical expression. If the order of operations is not followed, the outcome will be
wrong. The best way to remember the order of operations is by the following sentence:
Please excuse my dear aunt Sally. The operations are in order from the top to the bottom.
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Ex. Simplify:
2
(2 + 3)2 − 7
5
5
−7
5
⇐ First perform the operation inside the parenthesis (addition in this case).
25
−7
5
⇐ The next operation to perform is exponents according to the PEMDAS guideline.
5-7
⇐ Now, do the division since there are no parenthesis, exponents or multiplication in this
expression.
⇐ Finally, subtract the numbers by keeping in mind that you are subtracting a large
number from a smaller number, thus giving us a negative number.
-2
EXERCISES
Simplify the following expressions:
-2 + 4 • 12 –3²
(answer: 37)
[-18 / (2 + 1)²] -[3 • (14 – 20) + 5]
(answer: 11)
-4 • -5 • -3 + 2
(answer: -58)
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