Real Number System Flashcards
is made up of a set of rational and irrational numbers.
Real Number System
consists of all rational and irrational numbers
Real Numbers
It includes any number that can be written as a fraction, mixed numbers, terminating and repeating decimals, whole numbers, integers.
Real Numbers
consists of integers, terminating, and repeating decimals
Rational Numbers
It can also be expressed as a fraction.
Rational Numbers
-7, 0, 8
Integers
1.12
Terminating Decimal
3.3333
Repeating Decimals
7/8
Fraction
consist of whole numbers and negative numbers.
Integers
are all the counting numbers.
-Zero
Natural numbers
consist of numbers that are non-terminating and non-repeating decimals
Irrational numbers
cannot be express as a fraction
Irrational numbers
is a great example of an irrational number
Pi
Are all numbers Rational numbers?
NO
Are all numbers Real numbers?
YES
Can a number be both rational and irrational?
NO
Zero is a whole number
YES
Terminating Decimal can be a fraction.
YES
−5 is a rational number
TRUE
√(3&8) IS RATIONAL
TRUE
√16 is a natural number
TRUE
-3.25 (with dash) is an integer
FALSE
2.434434443… is a rational number.
FALSE
Properties refer to rules that indicate a standard procedure or method to be followed.
Mathematical Properties
demonstration of the truth of a statement in mathematics.
proof
Properties or rules in mathematics are the result from testing the truth or validity of something by experiment or trial to establish a proof.
Mathematical Properties
changing the order in which you add or multiply numbers does not change the sum or product.
Commutative Property
changing the grouping of numbers when adding or multiplying does not change their sum or product.
Associative Property
For any numbers a and b , a + b = b + a
Commutative Property of Addition - (Order)
For any numbers a and b , a x b = b x a
Commutative Property of Multiplication - (Order)
7(mn) = (7m)n
Associative Property of Multiplication
(a + 3) + b = a + (3 + b)
Associative Property of Addition
x + (y + z) = x + (z + y)
Commutative Property of Addition
For any number a, a + 0 = a.
The sum of any number and zero is equal to that number.
Additive Identity Property
For any number a, a x 1 = a.
The product of any number and one is equal to that number.
Multiplicative Identity Property
For any number a, a x 0 = 0.
The product of any number and zero is equal to zero.
Multiplicative Property of Zero
for every nonzero number a/b, where a, b is not equal to 0, there is exactly one b/a such that a/b x b/a=1
Two numbers whose product is 1 are called multiplicative inverses or reciprocals.
Zero has no reciprocal because any number times 0 is 0.
Multiplicative Inverse Property
4 × (8 × 2) = (4 × 8) × 2
Associative Property of Multiplication
6 + 8 = 8 + 6
Commutative Property of Addition
12 + 0 = 12
Additive Identity Property
is an example that disproves a statement, or shows that it is false.
counterexample
