Positive and negative whole numbers and zero

(… -3, -2, -1, 0,1, 2, 3 …)

Adding and Subtracting Integers

 1)  Change subtracting to adding the opposite.  SMATO 

Subtract

Means

Add

The

Opposite

7 and -7 are opposites

-5 and 5 are opposites

-3 – (-5) becomes -3 + (+5)

7 – 11 becomes 7 + -11

(or think of the subtraction sign being a negative on the 11)

2)  Decide whether the answer will be positive, negative or zero, and write it down!

If the numbers are opposites (4 + -4, -8 + 8, 10 + -10), then the answer is zero.

The larger number’s sign rules.

Positive Answer                                    Negative Answer

-7 + 13                                                 7 + -13

9 + -5                                                  -9 + 5

4 + 4                                                    -4 + -4

8 + 12                                                  -8 + -12

3)  Decide whether to find the sum or difference.

If the signs are the same, find the sum.  Ignore the signs and add the numbers.

-11 + -5= -16              2 + 8= 10                     -13 + -7 + -20

If the signs are different, find the difference.  Ignore the signs and do big minus little.

-5 + 12= 7                   -9 + 5 = -4                   -8 + 13= 5                   6 + -16 = -10

Multiplying and Dividing Integers

1)  Decide whether the answer will be positive, negative, or zero, and write it down.

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Zero

If one of the factors is zero, the whole answer is zero.

(45)(-64)(0)(2)= 0

If you try to divide by zero, there is no solution.

(-82)/0= no solution                  3/0= no solution

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Count the number of negatives.

An even number of negatives gives a positive answer.

(-3)(-2)(-1)(2)(-3)=  + answer  (because there are 4 negatives)

(5)(-2)(-3)= + answer (because there are 2 negatives)

An odd number of negatives gives a negative answer.

(-5)(6)= - answer because there is one negative

(3)(-7)(-1)(-2)= - answer because there are 3 negatives

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2)  Ignore the signs, and multiply and divide the numbers.

(-3)(-2)(-1)(2)(-3)=  36

(-5)(6)= -30

(5)(-2)(-3)=  30

(3)(-7)(-1)(-2)= -42

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