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