chapter 3 Flashcards
The commutative property
In addition and multiplication, order does not matter.
5.2=10 2.5=10
The Associative property
in addition and multiplication grouping order does not matter
(3+6)+13 = 3 + (6+13)
The distributive property
multiplying number into () foiling.
Multiplication property of 0
anything times 0 = 0
Identity property of addition
A number n that when added to other numbers gives the number n
ex. adding 0 to any number will equal it self
Identity property of multiplication
when you multiply any number by 1 you will get the same answer.
Additive inverse
what you add to a number to get a sum of 0
Multiplicative inverse
the reciprocal
Mathematical induction
A way of proving a mathematical statement by saying if this case is true then the rest of the cases must also be true.
Mathematical induction steps
- Show n = 1 is true
- assume n = k is true
- show n = k +1 is true
greatest common divisor
biggest number that can go into two or more numbers without leaving a remainder
Prime factoring a GCD
- make a factor tree till left with only prime numbers.
- multiply together the numbers the prime numbers that are shared.
GCD: Euclids algorithm
Dividend = divisor x quotient + remainder
divisor moves to dividend, remainder moves to divisor. keep going till the quotient has no remainder then divisor is the answer.
Finding GCF
list all factors out then pick greatest one in common.
LCM
The smallest number that can be divided evenly by the original two numbers.
