Fractional Multiplication + Division, Percentages
What is the difference between multiplying and dividing fractions?
When multiplying, you multiply the numerators together and then the denominators together. When dividing, you first must find the reciprocal of the divider, then you may multiply the fractions together.
What must you isolate to solve an equation?
You must isolate the variable you are solving for
What symbol do we use in interval notation to denote an open interval? A closed interval?
“(“ and “[“ (parenthesis and brackets) respectively.
True or False: Exponent rules can also be applied to expressions containing radicals.
True, because radicals can be rewritten as powers
True or False: For nonnegative values of a and b,
sqrt(a)*sqrt(b) = sqrt(a*b)
True
Find 4/9 divided by 2/3 in simplest fractional form
2/3
Solve the following equation: 2(y + 3) – 10 = 6(32 – 3y)
y = 49/5 = 9.8
Write in interval notation: -100 ≤ x < 4
[-100,4)
Simplify the expression and leave no negative powers:
x1/5/x1/2
1/(x3/10)
Simplify the expression:
sqrt(75)−sqrt(12)
3*sqrt(3)
Find 45/60 of 36/14 in simplest fractional form
27/14
Solve for each variable in the system of equations:
6x – 5y = 8
0 = –12x + 2y
x = –1/3 y = –2
Solve the following inequality: 3 - 2x > 8 + 3x
x < -1
Simplify the expression:
(18m11n-4)/(27m15n-7)
(2n3)/(3m4)
Simplify the expression:
(2sqrt(6))*(3sqrt(15))
18*sqrt(10)
A population of 600 increases by 20% and then decreases by 5%. What is the final population?
684
An unknown number added to 18 is equal to four times that unknown number. What is the unknown number?
15 – x = 12 → x = 5
Write in interval notation: |2x + 5| < 25
Simplify the expression, leave no negative powers:
(a4b-2/(a-2b2/3))-3/2
b4/a9
Simplify the expression:
3sqrt(24)/(2sqrt(6)) + 4/sqrt(2)
You walk 2/9ths of your way home before stopping. Then, you walk 5/8ths of the remaining distance. How much longer of your total walk is left?
7/24 of your total walk is left
A group of 120 swinhoe’s white-eye birds are dispersed among 2 trees of different sizes. The number of birds on the larger tree is 4 times the number of birds on the smaller tree. How many birds are on the small tree and how many are on the large tree?
24 birds on the small tree
96 birds on the large tree
Mark's Canoes rents canoes for $20 plus $35 per hour. You do not want to spend more than $150. For how many hours can you afford to rent the canoe?
You can spend less than t ≤ 3.7 or 26/7 hours renting the canoe.
If 52m-1=45, what is 5-m?
1/15
A rectangular garden has an area of 18sqrt(3) square meters and a width of 3sqrt(76) meters. Find the length and perimeter of the garden. Simplify all radicals.
L = 3sqrt(2)
P = 6sqrt(2) + 6sqrt(6)