khan academy pre algebra

find greatest common divisor ejemplo

find greatest common divisor of 105 and 75 1) prime factors of 105: 5*7*3 prime factors of 75: 5*3*5 2) 5*3=15 greatest common divisor of 105 and 75 is 15

least common multiple ejemplo

find the lcm of 12 and 20 1) prime factors of 12: 2*2*3 prime factors of 20: 5*2*2 2) 5*2*2*3 3)5*2*2*3=60 least common multiple of 12 and 20 is 60

divisibility of numbers using 5

if final digit is zero or 5 it is divisible by 5

Divisibility of numbers with 8

if las 3 digits are divisible by 8 then the number is divisible by 8

divisibility of numbers with 10

if last digit is zero

divisibility of numbers with 6

if number is divisible by 2 and 3 then it is divisible by 6 1) use divisibility rule for 2 2) use divisibility rule for 3

divisibility of numbers using 2

if ones place is even or 0 it is divisible by 2 i.e. 100, 102, 26, 84

divisibility of numbers using 4

if the last two digits are divisible by 4 then it is divisible by 4

divisibility of 7 ejemplo

is 12390 divisible by 7? 12390 1239-0(2)=1239 123-9(2)=105 10-5(2)=0 YES

ejemplo of divisibility by 8

is 12800 divisible by 8 1)800/8=100 yes

divisibility of 6 ejemplo

is 30 divisible by 6? 1) 30 is even so yes 2) 3+0=3/3=1 yes it meets both rules so yes

Divisibility of 3 ejemplo

is 384 divisble by 3? 384= 3(1+99)+8(1+9)+4 3+8+4=15 15/3=5 yes * note how 99 and 9 are already divisible by 3 so 8*9 is divisible by 3 already. so we just need to now the 8*1 plus all other numbers added

example of divisibility by 4

is 388 divisible by 4 1) 88/4 2)88/4= 22 yes

days of week multiples ejemplo

its monday what day will 250 be? 1) 250/7=35r5 2) day 1 is monday 3)monday, tuesday, wednesday, thursday, friday (r5) it will be friday in 250 days

area of a rectangle equals what

length*width

square unit

a unit that is square i.e. 2 units squared or 2 square units is 2 is a square with perimeter of 2

distributive law of multiplication over addition

the product of a sum is equal to the sum of the products i.e. 3(2+6)=3(2)+3(6)

inverse operation of addition

subtraction i.e. inverse of 5 is -5

divisibility of numbers with 9

sum of all digits if divisible by 9 then yes

divisibility of numbers with 7

take last digit and then subtract it from truncated number. if end result is 0 or 7 the number is divisible by 7

finding all factors with a factor tree (3)

1)find all pf of number 2) put all PF and their factor pairs 3) do all combinations of pf

how to compare fractions with different denominators (3)

1)find least common multiple of each fraction 2) multiply numerator by number required to get equivalent denominator and use new denominator 3) compare

Frequency table

A table for organizing a set of data that shows the number of times each item or number appears.

expanded form

A way to write numbers that shows the place value of each digit. i.e. 536= 500+ 30 + 6

prime number

A whole number greater than 0 that has exactly two different factors, 1 and itself.

composite number

A whole number greater than 1 that has more than two factors.

integer

All whole numbers (both positive and negative) and zero. i.e. -2, -1,0, 1, 2

array

An arrangement of objects in equal rows. i.e. 000 000 000

different ways to decompose fractions (4)

1) 5/9=2/9+3/9 2)5/9= 2+3/9 3) 5/9=1/9+2/9+2/9 4) decompose on a number line

ejemplo of finding factors using factor tree

1) PF: of 72 are 2*2*2*3*3 (*note that 1, 72 are a factor pair as well) 2) 1,2,3, 24, 36,72 3) 4,6,8, 9,12,18

find greatest common divisor (GFC)

1) factor out all prime factors of each number 2) multiply all common prime factors

using prime factorization to make distributive property

1) find all prime factors of each addend 2) multiply common prime factors 3) multiply all uncommon prime factors for each number seperately 4) step 2 is number you will distribute by multiplying from the results of step 3

use prime factorization to make distributive property

1) find all prime factors of each addends 2) multiply common prime factors and pullout 3)

Finding GCF using prime factorization (3 steps)

1) find all prime factors of each number 2) multiply all common prime factors once 3) write final answer i.e. find GCF of 8 and 4 1) pf 8: 2*2*2 pf 4: 2*2 2) 2*2=4 3)GCF of 8 and 4= 4

factors and multiples: days of the week (3)

1) if trying to find what day x is from day y divide x days by 7 2) day 1 is day 1 when counting 3) add reaminder from dividing starting with day 1

common divisibility using prime factorization (3)

1) use factor tree to find all prime factors 2) put all prime factors that aren't repeating across both numbers 3) any combination of those numbers are all common divisors

find least common multiple (3)

1) use factor tree to get all prime factors 2) put all prime factors that dont repeat 3) use answer from step 2 and multiply

why does divisibility using 6 work

2 and 3 are the prime factors of 6 so if a number is divisible by 6 it must also be divisible by these numbers

prime factor

A factor that is a prime number.

histogram

A graph of vertical bars representing the frequency distribution of a set of data.

box plot

A graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a box, and the median

stem and leaf plot

A method of graphing a collection of numbers by placing the "stem" digits (or initial digits) in one column and the "leaf" digits (or remaining digits) out to the right.

scientific notation

A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10. i.e. 34= 3.4 * 10^1

minuend

A number from which another number is subtracted.

rational number

A number that can be written as a fraction i.e. 1/2, 1.2, sqrt36

associative property of multiplication

Changing the grouping of the factors doesn't change the product i.e. (2*3)4=(2*4)3

why is divisibility of 9 work

same as rule of 3

whole numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

Factors

Numbers that are multiplied together to get a product

irrational numbers`

Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating. i.e. pie. sqrt3, 3.333333

order of operations (PEMDAS)

Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction *note all each go from left to right

greatest common divisor

The greatest number that divides into two or more numbers with no remainder.

Greatest common factor

The largest factor shared by two or more numbers i.e. gcf of 8 & 4 is 4

area

The number of square units required to cover a surface.

subtrahend

The number that is to be subtracted.

sum

The result of adding two or more addends

least common multiple

The smallest multiple (other than zero) that two or more numbers have in common.

place value

The value of a digit based on its position within a number i.e. 356 = 3 hundred + 50 tens + 6 ones

factor pair

Two whole numbers that are multiplied to get a product

bar graph

a graph that uses vertical or horizontal bars to show comparisons among two or more items

dot plot

a graphical device that summarizes data by the number of dots above each data value on the horizontal axis

addend

a number that is added to another number

prime numbers

a positive integer that has exactly 2 positive divisors. which is 1 and itself. essentially only 1 set of factor pairs i.e. 5: 5*1 is prime i.e. 4: 2*2 and 4*2 so its isnt prime

divisibility of numbers with 3

add sum of all digits and see if divisible by 3

The parts of addition equation

addends and sum or total addend+addend=sum

inverse operation of subtraction

addition i.e. inverse of -5 is 5

common divisibility

all numbers that are divisible by 2 or more numbers

commutative law of multiplication

any finite product is unaltered by reordering its terms i.e. a*b=b*a

commutative law of addition

any finite sum is unaltered by reordering its terms i.e. a+b=b+a

identity property of 0

any number added to 0 is itself i.e. 20+0=20

identity property of 1

any number multiplied by one and itself is itself i.e. 7*1=7

bar graph vs histogram

bars on a histogram touch to show that they are increasing, related variables whereas in a bar graph, they are not

perimitier

boundary of some area

associative property of addition

changing groupings of addends does not change the sum i.e. (2+3)+4=2+(3+4)

standard form

condensed form of expanded form i.e. 536

equivalent fraction

different fractions that are equal in value i.e. 2/4=1/2

parts of a division problem

dividend/divisor=quotient

inverse of multiplication

division i.e. inverse of 5 is (1/5)

ejemplo of prime factorization using distributive property

factor 18+24 1) pf 18: 3*3*2 pf 24: 2*2*3*2 2) common pf: 2*3=6 3) uncommon pf of 18: 3=3 uncommon pf of 24: 2*2=4 4) 6(3+4)

factor pair example

factor pairs of 8 are: 2*4 and 1*8

parts of a multiplication problem

factors, product factor*factor=product

how to identifying multiples

see if number can be divided by another number to create a whole number i.e. 15/2=7.5 so 2 15 isnt a multiple of 2 15/3=5 so 15 is a multiple of 3

parts of a subtraction problem

minuend, subtrahend, difference minuend-subtrahend=difference

inverse operation of division

multiplication i.e. inverse of 1/5 is *5

inverse property of multiplication

multiplying a number by its multiplicative inverse equals 1 i.e. 5*(1/5)=1

is one prime?

no

multiples

numbers you say when you skip count. Multiples of 2 are: 2,4,6,8,...

Inverse in math

operation that reverses the effect of the other i.e. the addition inverse of -5 is 5

pictograph

represents data with pictures

inverse property of addition

the inverse of a number = 0 i.e. 5+(-5)=0

divisor

the number that divides the dividend

dividend

the number that is being divided

distributive law of multiplication over subtraction

the product of a difference is equal to the difference of the products i.e. 3(2-6)=3(2)-3(6)

quotient

the result of division

product

the result of multiplying two or more factors

difference

the result of subtraction

reciprocal of multiplication

two numbers whose product is one

common divisibility ejemplo

what is the common divisibility of 12 and 20 1)prime factors of 12: 2*3*3 prime factors 20: 5*2*2 2)prime factors not repeating: 2*3*3*5 3) all numbers that are divisible by 12 and 20 are also divided by any combination of 2*3*3*5

natural number

whole positive numbers starting at 1

why does divisibility rule with 3 work

you can you distributive property to get a value that is divisible by 3 on the inside and the outside is the only number that needs to be considered