Video and Examples
We know that 5 • 3 = 15, 5 • 2 = 10, and 5 • 1 = 5 because they are the "times tables" we learned in earlier grades. Let's put these multiplication facts into a table and look for patterns.
(+5)(+3) = 15 
In this table we can see that as the second number goes down by one, the product goes down by 5. 

(+5)(+2) = 10 

(+5)(+1) = 5 

(+5)(0) = 0 

(+5)(1) = 5 

(+5)(2) = 10 

(+5)(3) = 15 
Since multiplication is Commutative and (+5)(3) equals 15, then this means (3)(+5) is also equal to 15. This means we can make a new table with (3) as the leading factor. 
(3)(+5) = 15 
In this table we can see that as the second number goes down by one, the product goes up by 3. 

(3)(+4) = 12 

(3)(+3) = 9 

(3)(+2) = 6 

(3)(+1) = 3 

(3)(0) = 0 

(3)(1) = +3 

(3)(2) = +6 

(3)(3) = +9 
These two tables tell us all we need to know about multiplying positive and negative numbers.
When multiplying TWO positives and negatives, you just multiply the absolute values of the numbers. To determine the sign of the product, if both signs match, then the answer is positive and if the two signs are different, then the answer is negative.
How to multiply two numbers. 

Example 1: Begin by multiplying the absolute values of the two numbers, 4 • 7 = 28. Since 4 and +7 have different signs, the product is negative. The product of (4)(+7) is 28. 
Example 3: Both numbers are positive, so the product is positive. (+3)(+9) = +27. 
Example 2: Since both numbers are negative, we automatically know the product will be positive. Multiplying the absolute values, we get 6 • 9 = 54. The product is +54. 
Example 4: Begin by multiplying the absolute values of the two numbers, 8 • 7 = 56. Since +8 and 7 have different signs, the product is negative. The product of (+8)(7) is 56. 
SelfCheck
Question 1 Simplify: 
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Question 2 Simplify: 
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Question 3 Simplify: 
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