Category: Algebra

A variable is: A symbol or letter that can be used to represent an unknown value

coffee …$2.00
tea …$3.50
Juice …$1.25

4 coffees and two teas calculate
4c + 2t = $15.00

3x + 2 cannot be determined

evaluate: find a value for an expression by substituting a value in for your variable
when x = -2, 3x + 2 = -4

care order of operation
7 + 3(x-2) when x=4

If you have 1/2 of a candy bar, what percent of the original candy bar do you have left?
50%

cent mean 100 in franch, 100% = 1

$40, sales tax 6.75%, tax is $2.7

the world’s most amazing number!

1) multiplication
2) division

3/3 = π/π = -4/-4 = 1

12 eggs = 1 carton
12 eggs / 1 carton = 1

conversion factor: a number that relates amount of one thing to amount of another.

cartons -> eggs 12eggs = 1carton
yards -> feet 3feet = 1yard
liters -> ounces
dollar -> Euros

1 mile = 5280 feet
1 gallon = 4 quarts
1 gram = 1000 milligrams
1 pound = 16 ounces

1 mile = 1.609 Km
if you run 5 km, 3.1 miles you run

1 mile = 1760 yards
1 yard = 3 feet
1 m = 1.093 yards
1 km = 1000m
1 m = 100cm
1m = 1000mm
1gal = 16cups
1 gal = 3.785liters

Rates: compare two quantities with different units
Ratios: compare two quantities with the same units

ex. “three out of five dentists recommend toothtaste.”

1/2 exact same meaning 1:2

3/5 -> 3:5
8/10 -> 4:5
200/500 -> 2:5
2/9 -> 2:9

learning the ratio and rates is super important

35 MPH(unit)
-> 35 miles per hour

35 miles / 1 hour

example
$12 / 1hour, 4,000,000babies/1year, 260calories/20 ounces of coke

150 miles / 3 hours = 50 miles / 1 hour -> unit rate
50 miles per hour

A unit rate is any rate where the value of the denominator is 1

pretzelicious: $3.50, 15ounces -> $0.23/ounce
pretztastic: $3.6, 18ounce -> 0.20/ounce

US National Deficit: 17 trillion dollars
$17,000,000,000
1.7 * 10^10

10^4 = 10,000

15,000:standard notation
1.5 * 10^4:scientific notation

negative powers
1.5 * 10^-4 = 0.00015
3.2* 10^-5 = 0.000032

2,700,000,000 -> 2.7 * 10^9

convert to scientific notation
34,000,000 -> 3.4 * 10^7

3/5 = 0.6
1/4 = 0.25

repeating decimal
1/3 = 0.333…

0.3-(bar mean forever)
1/7 = 0.14..

1/4 + 0.32 = 0.57

place values
0.627 -> 6tenth, 2hundredths, 7thousandths

2.18 = 109 / 50

1/4 + 0.32 = 0.57 / 100

what is a fraction?
fraction = part / whole

mixed number has whole number and fractions
1+5/8

common denominators!
8/8 – 3/8 = 5/8 keep denominator same

circumference 88, 28.25
diameter 28, 9
circumference/diameter 3.14, 3.14
π = 3.14

radius * 2 = diameter
c = π*d
d = 3, c = 9.42
Area = πr^2

3^2 = 9, base is three exponent
Exponents are powerful!

first power
3^1 = 3

dividing by the base
3^4
3^3
3^2 = 9
3^1 = 3
3^0 = 1
-1 * 4^2 = -4^2 = -16
(-4)^2 = 16

PEMDAS
parentheses, exponents, multiply, divide, add, subtract

more order of operations
6 / [4- (6-8)]+(-2)^3= -7

area of a square
l*l
l^2

Number Lines
– arrows on each end, zero, marks to indicate scale, positive negative direction

arrow, the lines extend on forever
infinity: goes on forever without limit
+ or –
infinity is the largest on positive

the truth about number line

absolute value: distance from zero, cannot be negative, |number|
sum: the result of adding number together
quatient: the result of division
associative property: +, *