A PowerPoint presentation/lesson on the properties of numbers and the distributive property.

2. Mental Math Warm - Up
1. 18 + (2+7) = 27
2. (18+2) + 7 = 27
3. (95)  4 = 180
4. 9 (54) = 180

3. Commutative Properties of
Addition and Multiplication
The order of the values does
NOT change the sum or
product.

4. Commutative Property of Addition
and Multiplication (Cont.)
Arithmetic Algebra
7+3=3+7 a+b=b+a
24=42 ab=ba

5. Example 1

6. Associative Property of
Addition and Multiplication
The grouping of the values
does NOT change the sum or
product.

7. Associative Property of Addition
and Multiplication (Cont.)
Arithmetic Algebra
(2 + 7) + 3 = 2 + (7 + 3) (a + b) + c = a + (b + c)
(9  4)5 = 9(4  5) (ab)c = a(bc)

8. At the Movies…
Tickets Popcorn Candy Drinks
Child - $3 Small - $3 Small - $2 Small - $1
Adult - $5 Medium - $4 Medium - $3 Medium - $2
Senior - $3 Large - $5 Large - $5 Large - $3
At the movies you buy an adult ticket, small
popcorn, and a small drink. What was your
total cost?
$9
What property/properties could you use?
Associative Property
(5 + 3) +1
5 + (3 +1)

9. Example 2
Use mental math and properties to solve the
following problem: 100  3  2
(100  2)  3 Commutative Property
100  (2  3) Associative Property
= 100  6 Multiply within parentheses
= 600 Solve

10. Identity Property of
Addition
The sum of any number and zero
is the original number.
7+0=7
0+x=x

11. Identity Property of
Multiplication
The product of any number and 1
is the original number.
15  1 = 15
1b=b

12. Example 3
Name each property shown.
34=43 Commutative Property of Multiplication
z1=z Identity Property of Multiplication
 +★=★+ Commutative Property of Addition
5(xy) = (5x)y Associative Property of Multiplication

13. Distributive Property
To multiply a sum or difference, multiply each
number within the parentheses by the number
outside the parentheses.
3(2+6) = 3(2) + 3(6) (2-6)3 = 2(3) – 6(3)
a(b+c) = a(b) + a(c) (b-c)a = ba – ca

14. Distributive Property
(cont.)

15. Example 4
Use the Distributive Property to find 20(102) mentally.
20(102) = 20(100 + 2) Think of 102 as 100 + 2
20(100 + 2) = 20(100) + 20(2) Use Distributive Property
= 2000 + 40 Multiply
= 2,040 Add

16. Example 5
You have 3 friends and want to give each friend 6
cupcakes, 5 cookies, and 4 brownies. How many baked
goods will you have all together?
3(6+5+4)
3(6) + 3(5) + 3(4)
18 + 15 + 12
= 45 baked goods

17.  = Cookies  = Brownies  = Cupcakes
Friend 1:   
Friend 2:   
Friend 3:   
Total:

 = 45 baked goods
Example 5 (cont.)
We can also use mathematical models to
demonstrate the distributive property.

18. Practice Problems
1. 3(6+7) = ? 3(6) + 3(7) = 18 + 21 = 39
2. 4(22+3) = ? 4(22) + 4(3) = 88 + 12 = 100
3. 6(b+5) = ? 6(b) + 6(5) = 6b + 30
4. 9(2h-1) = ? 9(2h) – 9(1) = 18h - 9
5. 3(5-3w) = ? 3(5) – 3(3w) = 15 – 9w

19. Practice Problems (Cont.)
6. Suppose your friend wrote 7(2m+t) = 14m + t.
What error did your friend make? What is the
correct answer?
He or she forgot to distribute the 7 to the variable t.
The correct answer should be:
7(2m) + 7(t) = 14m + 7t

20. Picture Citations:
Light Bulb Guy Picture (Slide 2) -
http://www.cascadewellnessclinic.com/articles/2003art/0311art.shtml
Shopping Bag Picture (Slide 5) –
http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscon
tinuum/structure/st275ma.htm
Distributive Arrow picture (Slide 14) - http://www.coolmath.com/reference/math-
dictionary-D.html
Distributive Property Balance (Slide 13) -
http://www.leslienettling.com/6thNewsletters/6thSep8-06.htm

21. Content Citations
Badur, Michalina Central Michigan University student
Davison, David M., Marsha S. Landau, Leah McCracken, and Linda Thompson.
Prentice Hall Pre-algebra: Tools for a Changing World. Upper Saddle
River, NJ: Prentice Hall, 2001. Print.