Vocab
Positive numbers starting at 0; no fractions or decimals included
What are Whole Numbers.
-18 = m+12
-30=1m
1m=-30
m=-30
-2x + 4x +(-10x)
-2x +(-10x) + 4x
-12x + 4x
-8x
a(b + c) = ab + ac
(b + c)a = ab + ac
What are the Properties of Distribution?
Jeremy mowed several lawns to earn money for camp. After he paid $17 for gas, he had $75 leftover to pay towards camp. Write and solve an equation to find how much money Jeremy earned mowing lawns.
g = cost of gas ($)
c = cost of camp ($)
t = total cost ($)
t - g = c ; t = g + c
t - 17 = 75 ; t = 17 + 75
t = 92
The answer to a multiplication problem.
What is the Product?
3n+2=-2n-8
3n=-2n-10
5n=-10
n=-2
2(x + 6) + 3x - 12
2x + 12 + 3x -12
2x + 3x +12 + (-12)
5x +0
5x
if a =b then:
a +c = b + c
a - c = b - c
ac = bc
a/c = b/c
What are the Properties of Equality?
Susan’s cell phone plan allows her to use 950 minutes per month with no additional charge. She has 188 minutes left for this month. How many minutes has she already used this month?
t = total minutes (ea.)
r = remaining minutes (ea.)
u = used minutes (ea.)
t - u = r ; t = r +u
950 - u = 188 ; u = 950 - 188
u = 762
A mathematical sentence that includes an equals sign (i.e., it has an answer/solution).
What is an Equation?
7(h+3)=6(h-3)
7h+21=6h-18
7h=6h-39
1h=-39
h=-39
-7(6y + 8) + 2(21y + 28)
-42y - 56 + 42y + 56
-42y + 42y + 56 - 56
0y + 0
0
a + b + c = c + b + a = b + c + a
abc = cba = bca
What are the Commutative Properties (of Addition and Multiplication, respectively).
Chip earns a base salary of $500 per month as a salesman. In addition to the salary, he earns $90 per product that he sells. If his goal is to earn $5000 per month, how many products does he need to sell?
b = base salary ($ per month)
c = commission salary ($ per each product sold)
g = goal salary ($ per month)
p = products sold (each)
b + c*p = g
500 + 90p = 5000
90p = 5000-500
90p = 4500
p = 50
The number by which another number is to be divided, (i.e., the number that is actively dividing the other), otherwise known as the denominator.
What is the Divisor?
-(5a+6)=2(3a+8)
-5a-6=6a+16
-5a=6a+22
-11a=22
1a=-2
a=-2
y(2x - 4) - 4y +6xy
2xy - 4y - 4y + 6xy
2xy + 6xy - 4y - 4y
8xy - 4y - 4y
8xy -8y
a + 0 = a
1a = a
What are the Identity Properties (of addition and multiplication, respectively).
A pizza shop charges $9 for a large cheese pizza. Additional toppings cost $1.25 per topping. Heather paid $15.25 for her large pizza. How many toppings did she order?
L = cost large pizza ($)
A = cost additional toppings ($ per ea.)
T = number of toppings (ea.)
P = cost total ($)
L + A*T = P
9 + 1.25(T) = 15.25
1.25(T) = 15.25 - 9
1.25(T) = 6.25T
T = 5
The terms of a subtraction problem; the vocabulary word used to describe the first term and the second term in a subtraction problem, respectively.
What are the Minuend and Subtrahend?
(-1/2)(14 + m/10 - 2m) = -12 + m
-7 - 1m/20 + 1m = -12 + 1m
-1m/20 +1m = -5 +1m
-1m/20 = -5
1m = 100
m=100
(2/x)(x+2x) + 2x - 4
(2/x)(1x + 2x) + 2x - 4
(2/x)(3x)+ 2x -4
(6x)/x + 2x -4
6 + 2x - 4
2 + 2x
a + (-a) = 0
a/b * b/a = 1
What are the Inverse Properties (of addition and multiplication, respectively).
You are ordering pizzas and sandwiches. You have a budget of $80. How many 5-dollar sandwiches can you buy if you buy: 3 pizzas, 4 pizzas, 6 pizzas, given pizzas are 10 dollars each.
p = number of pizzas (ea.)
s = number of sandwiches (ea.)
b = budget ($)
5*s + 10*p = b
5*s + 10*p = 80
5*s + 10*(3) = 80 ; s = (80 - 30)/5 ; s = 10
5*s + 10*(4) = 80 ; s = (80 - 40)/5 ; s = 8
5*s + 10*(6) = 80 ; s = (80 - 60)/5 ; s =4