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Terms in this set (94)
"base 10" and base system
-any number times 10,100,1000.... you multiply the first digit by that number then add those amount of zeros to the end of the number (ie. 375 x100=37500)
-any number divided by 10,100,1000... you divide the first digit by that number then move the decimal to the left according to the amount of zeroes (ie. 375/1000= .375)
--this is done with any
cardinal numbers
A cardinal number tells "how many." Cardinal numbers are also known as "counting numbers," because they show quantity. (8 puppies..14 friends)
ordinal numbers
Ordinal numbers tell the order of things in a set—first, second, third, etc. Ordinal numbers do not show quantity. They only show rank or position. (3rd fastest...6th in line)
Rational number
Any number that can be written as an integer divided by another integer (fraction)
decimal to fraction and vice versa
-for the amount of numbers in the decimal place that amount of zeros. (.475= 475/1000)
-move the decimal to the left according to the amount of zeros (234/100= 2.34)
turning a decimal into a percent
move the decimal two places to the right (always use the first two numbers then the rest of the numbers are after the decimal.
(ie. .2345= 23.45%)
turning a fraction into a percent
cross multiply so......
375/1237 x ?/100
1237?/1237=37500/1237
?=30.32%
is the square of a number always greater than the number?
no.
(i.e.... 0[squared]= 0........... 1/4 [squared]= 1/8)
expanded notation
The way to write a number that shows the place value of each digit. Example: The expanded form of 456,759 is 400,000 + 50,000 + 6,000 + 700 + 50 + 9
scientific notation
using powers of 10 (i.e 10 ^4) to express large numbers (i.e 43,700 is written in scientific notation as 4.37x10 ^4... or 43.7 x10 ^3)
how to reverse scientific notation
43.7 x 10^3 = 43700
prime numbers
a number that has only 2 factors, one and itself
composite numbers
A positive integer that has factors other than just 1 and the number itself
factor
any whole numbers that when multiplied together form a product.
Example: factors of 12 are 1,2,3,4,6,12
multiples
the result of multiplying any whole number by the counting numbers
Example: multiples of 7 are 7,14,21,28...
are 1 and 2 prime numbers?
1--no 2--yes
is zero and even or odd number
even bc it is in between odd numbers
is the sum of two even numbers always even? what about the sum of two odd numbers?
sum of two even-YES
sum of two odd-NO (1+1=2)
what is the formula for percent increase
new number - old number/old number=x times 100
if a movie ticket was $5 last week and this feel is $6 what was the percent increase
6-5=1/5x100=.20
..... 20% increase
area of a circle
π × r2
Circumference = 2 × π × r
r = radius
how to get the radius
half the Diameter (length from one end to the other)
area of a rectangle
Area = w × h
w = width
h = height
area of a triangle
Area = ½ × b × h
b = base
h = vertical height
circumference of a circle
π x Diameter
how to get the perimeter
sum of all sides
pascals triangle
Each number in the triangle is the sum of the two directly above it.
what is an expression
an equation WITHOUT the = sign
(5-6.......7+9....)
the number of girls is 3 more then the number of boys. if there are 41 students how many girls are there
...
counting numbers
whole numbers except 0--- 1,2,3...
whole numbers
all numbers PLUS 0 -- 0,1,2,3,4,5... (no fractions, decimals...)
exponential notation
543.....
(5x10^2) + (4x10^1)+(3x10^0)
binary operation
combines only two numbers at a time to produce a third number
4 ways to model operations
concrete, semiconcrete, semiabstract, abstract
concrete method
use real objects
semiconcrete method
use pictures of real objects
semiabstract method
work with one symbol to represent objects. i.e tally marks
abstract method
use numbers ( 3 rabbits eating 4 carrots a day =3x4)
inverse
operations that undo each other (multi and division are inverse, addict and sub are inverse)
multiplicative identity property of 1
any number multi by 1 is that number
property of reciprocals
...
commutative propety for addit & multiplication
the order of numbers does not change the sum
associative property for addict and multiplication
grouping numbers in a diff way does not change the sum. (3+7)+5 same as 3+(7+5)
array
can help model a multiplication problem. the first number in the problem are the vertical boxes; the 2nd number are the horizontal boxes. i.e 2x3=6
ooo
ooo
adjacent
two angles that share a common vertex
complementary angles
two angles that measure at 90 degrees
supplementary
sum of the measure of two angles is 180 degrees
transversal
a third line intersects two lines
interior angles
the 4 angles that lie between the two lines
consecutive interior angles
the interior angles that lie on the same side of the transversal
alternate interior angles
interior angles that lie on opposite sides of the transversal
corresponding angles
angles in the same place on different lines
congruent
measures of 2 angles that are the same
a triangle measures how many degrees?
180
pythagorean theorem formula
a^2+b^2=c^2
-side c is always the hypotenuse (opposed side of the right angle)
-only use for right triangles
the reciprocal of 3 is...
1/3
do rectangles that have the same perimeter always have the same area
No. Take a square with each side 9 feet long. The perimeter is 9+9+9+9 = 36 ft and the area is 9 x 9 = 81 square feet.
Now squash the square down a bit so that it is a 7 x 11 rectangle. The perimeter is still 36 ft, but the area is now smaller at 77 square feet.
basic properties of a circle
-a line cut down the middle is the diameter
-half of a diameter is the radius
-the perimeter is the circumference
rotation
turn
reflection
flip
translation
a straight shove to a certain distance (slide)
range
measure of variation in the numbers
- subtract smallest number from largest number.
formula for probability
number of ways an event can occur/ total number of possible events
what is the probability of getting 2 green balls out of a hat if it contains 2 green and five yellow balls
2/7
how to determine the odds FOR a situation
the number of ways an event can occur: number of ways it cannot occur
how to determine the odds AGAINST a situation
number of ways it cannot occur: the number of ways an event can occur
sample space
he set of all possible outcomes of that experiment.
combinations
order does not matter
-nCr= n! / r! (n-r)!
permutations
order does matter
-nPr=n! / (n-r)!
inverse relationship
-negative slope
-if the input variable increases, the output variable will decrease. In the equation y=25-4x. if you substitute 4 for x, then y will equal 9. If x increases to 5, then the y value will be 5.
-moving in opposite direction on number line
direct relationship
-positive slope
-if the input variable increases, so will the output variable, and vice versa. For example, in the equation y=3+6x, if x is 2, then y would be 15. If x increased to 3, then y would also increase, to 21.
-moving same direction on number line
"kilo"
thousand (1,000)
"deci"
tenth (0.1)
"centi"
hundredth (0.01)
"milli"
thousandth (0.001)
hypotenuse
the side of a right triangle opposite the right angle--longest side
isosceles triangle
a triangle with two equal sides
volume for general prisms
lxwxh
volume of a cylinder
V = (π x R^2) x H
volume of a cube
lxwxh... since all sides of a cube are the same the formula can also just be L^3
powers of 0 and 1
anything to the 0 power is always 1. anything to the 1 power will always be that number
weighted average
w1 x y1 + w2 x y2 + w3 x y3...
----percent of area=w
----grade of that area=y
how many inches in 1 foot
12
how many feet in 1 yard
3
how many yards in 1 mile
1760
how many pints in 1 quart
2
how many quarts in 1 gallon
4
how many ounces in 1 pound
16
how many pounds are in 1 ton
2000
how many degrees in 1 celsius
33.8
how to convert from 1 unit to another run the metric system
move the decimal however many times whichever way you move
metric units from smallest to largest
milli
centi
deci
meter
deca
hecto
kilo
power of 0
any number raised to the power of 0 is always 1
Integer
Whole numbers plus negative numbers. (Still no fractions or decimals )
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