Transcript 3.8 The Distributive Property

3.8 The Distributive
Property
Shows how multiplication
affects addition or
subtraction
Example 1
•
•
•
•
•
•
•
3 (5 + 7)
3 (12)
36
3 (5 + 7)
3x5+3x7
15 + 21
36
Distributive Property
• Thinking of groups…
• 3( x + 5) “Three times the quantity of
x plus 5”
• The 3 tells us we have 3 groups that
each have an x and a five in them.
•x 5
x
5
x
5
• Added all together gives 3x + 15
Thinking of a Las Vegas card dealer…
• 3 ( x + 5)
3 is the “dealer”
• 3 (x + 5)
3  x or just
First, deal the 3 out to the x
3x
• 3 (x + 5)
3 5 or
Now, deal the 3 out to the 5
15
• Equals: 3x + 15
3x + 15 is an expression that
can not be simplified or
solved because
• We don’t know the value of x
• The two terms are unlike:
3x is an “x-term”
15 is a “non-x-term” (also called a
“constant”)
Example 2
• Simplify 4 x 29
• I can think of 29 as 30 -1
• 4 ( 30 – 1)
• 120 – 4
• 116