Whole Numbers are all positive numbers but not negative numbers including zero.
Natural Numbers are all positive whole numbers but not negative numbers excluding zero.
Integers are all whole numbers (not fractions or decmals) including zero and negative whole numbers.
Even Numbers when divided by 2 always equal zero. They are defined as any real numbers greater than but not equal to zero and negative numbers less than but not equal to zero.
Prime Numbers can only be divided by itself and 1. A prime number must be divisible by exactly 2 unique numbers so 1 and 0 are not prime. The smallest posible prime number is 2.
Rational Numbers The fundamental characteristics of a rational number is that it can be expressed as fraction, a quotient of two integers.
Irrational Numbers Pi is an irrational number. It is a non-repeating, non-termination decimal. irrational numbers can not be expressed as a fraction.
PEMDAS is a mnemonic for the order of operations in math, ensuring consistent calculations:Parentheses/ BracketsExponents/ OrdersMultiplication/ Division (left-to-right)Addition/ Subtraction (left-to-right)
The Associative Property of Addition or Multiplication states that no matter in what order you add or multiply two numbers the result remains the same.Example (a+b)+c=a+(b+c) or (ab)c=a(bc).To solve using the associative property, perform the operation within the parentheses first, then the operation outside. The outcome will be the same regardless of which grouping is solved first. You can only apply these when addition or multiplication is used individually. They will not work if you use addition and multiplication at the same time.
The Commutative Property of Addition or Multiplication states that when adding or multiplying numbers the order of operands does not change the result.Example a+b=b+a or ab=ba.This property does not apply to subtraction or division because changing the order of the numbers changes the outcome.
The Distributive Property of Multiplication over Addition states that for any numbers (a), (b), and (c), the expression a(b+c) is equal to ab+ac.Example a(b+c)=ab+ac.
The Distributive Property of Multiplication over Subtraction states that for any numbers (a), (b), and (c), the expression a(b-c) is equal to ab-ac.Example a(b-c)=ab-ac.
The Identity Property of Addition states that adding 0 to any number results in the original number.Example 10+0=10.
The Identity Property of Multiplication states that multiplying any number by 1 results in the original number.Example 10x1=10.
Simplifing by Addition and Subtraction of Expressions Containing Signed Numbers Ajacent signs are when two signs are next to each other. 5+(-5) or 5-(-5). To simplify these expressions, convert the two signs into one. The method is simple: If the two signs are different replace them both with a negative sign. 5+(-5) becomes 5-5, 5-5=0. If they are both the same, whether positive or negative, replace them with a single positive sign. 5-(-5) becomes 5+5, 5+5=10.The expressions may also contain signed numbers next to each other like -6-7. Both numbers have a sign. To simplify signed numbers like these think of these numbers as either adding to or in this case subtracting from. Since both numbers are subtracting from you would combine the two totals. -6 and -7 when combined equal -11.Straight lines surrounding an expression is asking for the absolute value. |-9|=9. The expression 5-|-9| becomes 5-9 and 5-9=-4
Simplifing by Multiplication and Division of Expressions Containing Signed Numbers When multipling and dividing signed numbers if the two signs are different the result is negative. 5*(-5)=-25 and 5/(-5)=-1. If they are both the same, whether positive or negative, the result is positive. -5*(-5)=25 and -5/(-5)=1.
Quotient A quotient is the result of a division, representing the number of times a divisor goes into a dividend.
Associative of or involving the action of associating ideas or things. Where associate is to have a relation to, like you associate a nurse as being a women.
Commutative of a calculation, giving the same result whatever order the values are in. Where commute is to give in exchange for another like in a court, commute a sentece to a lesser one.
Distributive Algebraically, distribution means to spread terms equally across an expression, such as in a(b+c)=ab+ac.
Identity a close similarity or affinity.