CHAPTER 7 / ESSENTIAL PRE-ALGEBRA SKILLS 277
Concept Review 2
1.x+12 (commutative law of arithmetic)
2.− 2 x^2 + 6 x(distributive law)- 10m^3 n^4 (commutative law of multiplication and
associative law of multiplication) - 7y+12 (associative law of arithmetic and com-
mutative law of arithmetic) - false: (Find a common denominator, then
add numerators.)- true: distributive law
- false: a^2 + 2 ab+b^2 (Don’t ever distribute a power
over addition. Expand and “FOIL” (First + Out-
side + Inside + Last).) - false: 15c^2 x(Don’t ever distribute multiplication
over multiplication. Use the associative and com-
mutative laws of multiplication.) - false: 3(2)^6 + 35 (You can distribute, but don’t mul-
tiply before doing the powers!)
7
2
x
y- true: distributive law (Remember you can dis-
tribute division over addition!) - 3x^2 (1 + 4 x)
- 12x^3 + 3 x^2
13.x^3 × 12 +x^2 × 3 - 300 (Reorder: (25 +75) +(48 +52) +(60 +40))
- 3,000y^4 (Reorder: (4 ×25)(6 ×5)(y×y×y^2 ))
- 19,000 (Use the distributive law.)
- 10,000x^2 (You can’t “FOIL” here! Reorder: (4 ×25)
(5 ×20)(x)(x) =(100)(100)(x^2 )) - They’re reciprocals. (Their product is 1.)
- They’re the same.
- They’re opposites. (Their sum is 0.)
- multiplication or division over addition or
subtraction - subtraction and division
- yes
Answer Key 2: Laws of Arithmetic
SAT Practice 2
1.D m−n= 4
m+n= 14
2 m = 18
m= 9 n= 59 × 5 = 45
2.B 4 x(x) − 3 xy(2x) =
4 x^2 − 6 x^2 y= 2 x^2 (2 − 3 y)
3.B Don’t solve for x.It’s too hard, and it’s
unnecessary.
15 x^2 + 10 x=5(3x^2 + 2 x) =5(40) = 200
4.C −2(x+2) +x(x+2)
=(− 2 +x)(x+2) Distributive law
=(x−2)(x+2) Commutative law of
addition
=x^2 − 4 Distributive law (“FOILing”)
5.B (x+y) + 1 = 1 −(1 −x)
associate: x+y+ 1 = 1 −(1 −x)
distribute: x+y+ 1 = 1 − 1 +x
simplify: x+y+ 1 =x
subtract x: y+ 1 = 0
subtract 1: y=− 1
6.E 1 −(1 −(1 −x) −1)
distribute: = 1 −(1 − 1 +x−1)
distribute: = 1 − 1 + 1 −x+ 1
commute: = 1 − 1 + 1 + 1 −x
simplify: = 2 −x- A Each number has 100 factors, to make them
simpler to compare:
a=60(99)^99 +30(99)^99 =90(99)^99
b= 99100 = 99(99)^99
c=90(90)^99 =90(90)^99
8.E 5 x(2x×3) − 5 x^2
parentheses: = 5 x(6x) − 5 x^2
multiplication: = 30 x^2 − 5 x^2
subtraction: = 25 x^2
9.C Just remember that only addition and multi-
plication are commutative and associative. If you’re
not convinced, you might plug in 1, 2, and 3 for x,
y,and z,and notice that equation II is not true.
10.E xy yx
x
y
y
x
xy
xy