Download The Commutative, Associative, and Distributive Laws

Mat 0024 Section 1.2
(When a letter is used to represent a variety of numbers, it is called a VARIABLE.)
Commutative Laws – You can change the order when adding or multiplying
without affecting the answer,
________________ 1. 4 + 5 =
________________ 2. 3 + 6 =
________________ 3. 8  b =
________________4. xy
________________ 5. 5 + ab
________________ 6. 2(x + 3)
Associative Law – Numbers can be grouped in any manner for addition or
multiplication. (Order of numbers remains the same; grouping
symbols—such as parentheses or brackets--change.)
_______________ 7. ( a + 2 ) + 6
_______________ 8. 3(xy)
_______________ 9. (5a)b
_______________ 10. s + ( r + t)
_______________ 11. (3 + w) + k
Distributive Law (Of Multiplication Over Addition)– The product of a number and a
sum can be written as the sum of two products.
______________12. 5 ( a+ b)
______________13. 3(2x + y)
_____________ 14. (a + b)4
______________15. 4 (2x + y + z)
______________16. ( a + 3b + c)4
Factor (write as a product—two expressions multiplied) using the Distributive Property.
______________17. 9x + 9y
______________18. 4 + 4x
______________19. 15x + 5
______________20. 9w + 6
______________21. 8m + 16y + 12
______________22. 6m + 6
Use the commutative and/or associative laws to rewrite these problems to make them
easier to work. Indicate which law you used for each step.
23. (237 + 46) + 4
26.
3
1 1
 (5  )
4
3 4
29. 25(13  4)
24. (75 + 97) + 25
1
2
2
5
27. (  8 ) 
30.
1
2
1
(4  33)
2
25. (38 + 55) +45
28. (7  2)  50
31.
1
(27  20)
2
32. Write a series of steps with labels indicating
which law you used to show that: (2a)4 = 8a
Homework: Page 16: odds 1-33, odds 37-51, odds 57-67
(021)