You can only multiply two numbers at a time. Those two numbers have either like signs or unlike signs. From this information, we can develop our rules for multiplication.
Rules for Multiplication
 Like signs, positive
 Unlike signs, negative
Examples

Reasoning

5(5) = 25
5(5) = 25 
In both examples, the numbers have like signs. Both are either positive or negative. So the sign of the answer is positive. 

Reasoning

3(5) = 15
3(5) = 15 
In both examples, the numbers have unlike signs. One is positive and the other is negative, so the sign of the answer is negative. 
Remember: use your rules to find the sign of your answer first. Then do the indicated operation.
There is another situation that we need to address when multiplying. You can only multiply two numbers at a time, but we can multiply any number of numbers together by multiplying our first answer by the next number and so on, until we have multiplied all of the numbers together. Since the associative property says that we can multiply the numbers in any order, we can develop rules to first find the sign of our answer.
Multiplying more than two numbers
Count the number of minus signs in the problem
 Even: positive
 Odd: negative
Examples

Reasoning

2(8)(4)
64 
Count the minus signs. There are three, which is odd. The answer is negative. Then multiply the numbers 2(8) = 16
and 16(4) = 64. 

Reasoning

2(4)(5)
40 
Count the minus signs. There are two, which is even. The answer is positive. Then multiply the numbers 2(5) = 10
and 10(4) = 40. 

Reasoning

2/3(5)(6)(4/5)
2/3(5/1)(6/1)(4/5)
2/3(5/1)(26/1)(4/5)
2(1)(2)(4)
16 
I suggest that when you are working with fractions, change the integers into fractions by putting them over one. Then count the minus signs. There are three, which is odd, so your answer is negative. Then reduce where you can. Three goes into six twice and the fives cancel. Finally multiply
2(1) = 2, 2(2) = 4, 4(4) = 16 
Multiplying expressions containing variables
You can also multiply expressions containing variables.
Examples:

Reasoning 
5a(6b)
30ab 
Unlike signs, so your answer is negative. Multiply 5(6) = 30 and multiply a(b) = ab. 

Reasoning 
3x(4y)  2x(5y)
12xy  10xy
2xy 
Remember: Order of operations tells us to multiply before we add.
Multiply 3x(4y), like signs; positive,
3x(4y) = 12xy
Multiply 2x(5y), Unlike signs; negative,
2x(5y) = 10xy
Add 12xy  10xy = 2xy, Unlike signs; subtract and put the sign of the biggest number. 
In this example, remember that we can combine (add) like terms.
Like terms
Same variable(s)
Same exponent(s) on those variable(s) 

Reasoning

4a(3b)  2a(7b)
12ab  14ab
2ab 
Multiply 4a(3b) = 12ab, like signs; positive
Multiply 2a(7b) = 14ab, Unlike signs; negative
Add 12ab  14ab = 2ab, Unlike signs; subtract and put the sign of the biggest number. 
Just as a minus sign in front of parenthesis changes the sign of the number(s) inside the parenthesis so does multiplying by a negative one.
Examples

Reasoning

1(5) = 5 
Unlike signs; negative 
1(5) = 5 
Like signs; positive 
This is called the Multiplication Property of 1.
The product of any number and 1 changes the sign of the number
(is its additive inverse).
1(a) = a, a(1) = a 

Multiplying Decimals
Now letâ€™s review the process of multiplying decimals. Remember: your answer must have the same number of decimal places as your factors.
Process for multiplying decimals
 Multiply the numbers
 Count the number of decimal places in your factors. That is, count how many numbers are to the right of the decimals.
 In your answer, starting at the right count back that number of places and put your decimal there.
 If there are not enough numbers, you must add zeros to the left of your number.
Examples

Reasoning

.2(.7)
.14 
Unlike signs; negative
Multiply: 2(7) = 14
There are two decimal places so starting at the right of the four, we move two places to the left, .14 

Reasoning

.4(.1)
.04 
Like signs; positive
Multiply 4(1) = 4
There are two decimal places, so starting at the right of the four, we move two places to the left. But since there is only one number in our answer, we must add a zero to get .04 
Try these exercises
Multiply
 3(4)
 5(7)
 6(9)
 7(8)
 2/3(9/8)
 4/5(15/7)
 3(2)(5)(8)
 1/4(8)(1/3)(6)
 .15(3)
 .05(.07)
Simplify
 2x(3y)  4x(5y)
 3(2x  6)  4(3x  4)
Hint: Use the distributive property.
 4(8)  3(5)
 2/3(6x  9) + 3/4(8x 12)
Hint: Divide by the 3 or 4 then multiply by the 2 or 3.
 1.1(2.3)  .25(.3)
Answers to Practice Problems
 3(4) = 12
 5(7) = 35
 6(9) = 54
 7(8) = 56
 (2/3)(39/48) = 3/4
 4/5(315/7) = 12/7
 (3(2)(5)(8) = 240
 (1/4)(28/1)(1/3)(26/1) = 4
 .15(3) = .45
 .05(.07) = .0035
 2x(3y)  4x(5y)
6xy  20xy
26xy
 (2x  6)  4(3x  4)
6x  12  12x + 16
6x + 4
 4(8)  3(5)
32 + 15
17
 1/3(6x  9) + 3/4(8x  12)
4x  6 + 6x  9
10x  15
 1.1(2.3)  .25(.3)
2.53  .075
2.605