Pre Algebra 1

Natural numbers

Counting numbers starting from 1 to infinity. They do not include decimals or fractions.

Whole Numbers

set of all natural numbers including 0. No decimals or fractions.

Integers

Includes whole and negative natural numbers. Are not decimals or fractions.

Rational Numbers

Numbers that can be written as decimals or fractions. They can terminate and repeat themselves. Ex. .333 = 1/3 .34715715…=34,681/999 √64=8=8/1

Irrational Numbers

Numbers that cant be written as a fraction. If written in a decimal it goes forever without repeating itself. π=3.141592….√68=8.24621125

Real Numbers

All sets of Natural, whole, integers, rational and irrational numbers. EVERYTHING in the number line. Imaginary numbers are not real numbers.

Imaginary numbers

“i” = √-1 Occurs when you try to do something impossible in the number line like √-9. No real number squares to equal -9. ( -3 x -3= 9, 3×3=9)

Its used to calculate waves and rotation in a grid (number lines) when u multiply √-1 once it rotates the plotted point 90 degrees. Do it again and now its 180 degrees from the original plotted point.

Commutative

Relates to the order of numbers. To move around

Associative

Relates to the grouping of the numbers

Commutative Property of Addition

Says that the order of two or more adding numbers does not matter a +b = b + a. Only works with addition and multiplication.

Commutative Property of Multiplication

Says that the order of two or more multiplying numbers does not matter a x b = b x a. Only works with addition and multiplication.

Associative Property of Addition

Says that when we are adding 3 or more numbers, the order in which we group does not matter. a + (b+c)= (a+b)+c

Associative Property of Multiplication

Says that when we are multiplying 3 or more numbers, the order which we group does not matter. a x (b x c)= (a x b) x c

Distribute

To share or give out.

Distributive Property of of Multiplication over Addition

Says that we get the same number when we multiply a group of numbers added together or when we multiply each number separately and then add them.

a(b x c)= (a x b) + (a x c)

Distributive Property of Multiplication over Subtraction

Says that we get the same number when we multiply group of numbers subtracted together or when we multiply each number separately and then subtract them.

a(b-c)= (a x b) - (a x c)