CHAPTER 7 / ESSENTIAL PRE-ALGEBRA SKILLS 275
Concept Review 2: Laws of Arithmetic
Simplifythe following expressions, and indicate what law(s) of arithmetic you use to do it. Write Dfor distrib-
ution, CAfor commutative law of addition, CMfor commutative law of multiplication, AAfor associative law of
addition, and AMfor associative law of multiplication.
- 3 +x+9 _____ 2.− 2 x(x−3) ____
- (5m^2 n)(2mn^3 ) ____ 4. 5 +(7 + 2 y) + 5 y___
Look carefully at the following equations. If the equation is always true,write the law of arithmetic that justi-
fies it (D, CA, CM, AA, or AM). If it is false,rewrite the right side of the equation to make it true.
- 15(67) +15(33) =15(100) 6. _____
- (a+b)^2 =a^2 +b^2 7. _____
- 5c(c× 3 x) = 5 c^2 × 15 cx 8. _____
- 3(2^6 + 34 ) = 66 + 94 9. _____
10. 10. _____
Rewrite the expression 3x^2 + 12 x^3 according to the following laws:
- distributive law: 12. commutative law of addition: 13. commutative law of multiplication:
____________________ _____________________________ ________________________________Do the following calculations mentally(no calculator!) by using the appropriate laws of arithmetic:
- 25 + 48 + 75 + 60 + 52 + 40 =__ 15. (4y)(6y)(25)(y^2 )(5) =__
- 19(550) +19(450) =__ 17. (25 × 5 x)(4x×20) =__
If aand bare not 0:
- What’s the relationship between a÷band b÷a? 18. __
- What’s the relationship between a×band b×a? 19. __
- What’s the relationship between a−band b−a? 20. __
- The distributive law says that only ____ or ____ can be distributed over
grouped __ or __. - Which operations are not commutative? 22. __
- Are powers commutative? That is, is (xm)nalways equal to (xn)m? 23. __
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