notes math

numerator

above the line in a fraction, represents how many parts of a whole

denominator

below the line in a fraction, represents how many equal parts of the whole is divided

how to convert fraction, decimal, and percentage

in fraction form you divide the numerator by denominator, then you get decimal, then multiple 100 you get percentage (3/4, 0.75, 75%)

from percentage you divide by 100, getting decimal, then you divide by the place value (30%, 0.3, 3/10)

PEMDAS

parenthesis, exponents, multiplication and division (left to right), addition and subtraction (left to right)

rational numbers

any number that can be expressed as ratio (fraction) of two integers, denominator CAN’T be zero

irrational number

cannot be expressed as a simple ratio of two integers, has no repeating patterns, ex: pi, e, square roots of non-square numbers

greater than and less than signs tip

alligator is hungry and wants to eat the larger

variable

unknown number is usually a letter like x

constant

stands alone without variable

coefficient

integer that a variable

term

single number or variable separated by + or - signs

inverse

opposite

when it comes to fraction = fraction with a variable what do you do?

cross multiply to get an equation then solve

metric length measurements and what is it similar to

1 meter (door knob height), 1 centimeter (paper clip width), 1 millimeter (grain of rice diameter), 1 kilometer (airport runaway in length)

metric weight measurements and what is it similar to

1 gram (paper clip), 1 milligram (pinch of salt), 1 kilogram (bag of rice)

metric capacity measurements and what is it similar to

1 liter (large water bottle), 1 milliliter (medicine dropper), 1 kiloliter (pool water)

standard measurements in length (smallest to largest)

foot, yard, mile

1 foot is how many inches

12

1 yard is how many feet

3

1 mile is how many yards

1,760

bigger to smaller unit conversion

you use multiplication

smaller to bigger unit conversion

you use division

standard measurements in weight

ounces and pounds

how many ounces in 1 pound?

16 ounces

standard measurements for capacity (smallest to largest)

teaspoon, tablespoon, fluid ounce, cup, pint, quart, gallon

how many teaspoons in a tablespoon?

3 teaspoons

how many tablespoons are in a fluid ounce

2 tablespoons

how many fluid ounces are in a cup?

8 fluid ounces

how many cups are a pint?

2 cups

how many pints in a quart?

2 pints

how many quarts in a gallon?

4 quarts

metric conversions saying

King Henry Doesn’t Usually Drink Cold Milk

K: kilo (k)

H: hecto (h)

D: deka (da)

U: unit

D: deci (d)

C: centi (c)

M: milli (m)

divide 10 going up, x10 going down each word

how many pounds in a kilogram?

2.2 pounds

how many centimeters in an inch?

2.54 centimeters

how many feet in a meter?

3.28 feet

how many grams in an ounce?

28.35 grams

how many kilometers in a mile?

1.6 kilometers

4 times a number

4x

4 more than a number

x + 4

4 less than a number

x - 4

4 times the difference of two numbers

4 (x - y)

word problem using percentages equation

is/of x 100, ex: what percent of 12 is 27 so 27/12 × 100 = 225%

rate

comparing two quantities with different units, ex: 36 miles in 4 days

unit rate

a denominator with 1, usually money

inequalities are

the greater than, greater than or equal to, less than and less than or equal to signs

inequalities sign switches when

you divide or multiply by a negative number

direct proportional equation

always increases at the same rate, y = kx, y = x/7, y = 2/3 x

not directly proportional

increase differently, y = mx + b, y = 6/x, y = 9

mean

average number

mode

most frequent

median

middle number, if two median numbers than you find average (add and then divide by 2)

range

difference between the lowest and the highest value

shapes of distribution

symmetry - bimodal (2 peaks) and unimodal (1 peak), mean=median

uniform or rectangular - no mode or roughly the same, mean = median

skewness - left skewed and right skewed (like toes), mode is highest (1 peak) then median closer to it and mean further down the slope

probability equation

number of favorable outcomes/ total number of possible outcomes, if the problem has and then you multiply outcomes and if it has or/either then you add outcomes

dependent and independent variable on the scatter plot goes where

dependent goes on y-axis, independent goes on x-axis

types of tables

cartesian coordinate, scatter plot, line graph, pie/circle graph, bar graph

linear graph

y = mx + b, constant increase or decrease (straight)

exponential graph

y = ab^x, slight curve

quadratic graph

y = ax² + bx + c, U shape

correlation/covariance

relationship between two variables
positive correlation: x increases and so does y

negative correlation: x increases and y decreases
no correlation: random

perimeter

1 dimensional, add all sides, cm

area

2 dimensional, length times width, cm²

volume

3 dimensional, length times width times height, cm³

circumference aka perimeter of circle

C = π times d(diameter)

circles area

A = π times r² (radius)

area of triangle

½ (base times height)

area of a trapezoid

A = (base 1 + base 2) times height / all over 2

area of a semicircle

A = π times r² divided by 2

volume of triangular prism

P= ½ (base times width times height)

volume of cylinder

P= π times r² times h

volume of cone

(π times r² times h) divided by 3

volume rectangular pyramid

length times width times height divided by 3

volume of sphere

4/3 times π times r³