Numbers Flashcards
If you include a 0 with natural numbers, you have ________ numbers
Whole
Counting numbers like; 1,2,3,4,5… are also called ________ and ________ numbers
Natural, positive
What kind of correspondence are numbers on a number line represented with dots or dashes to designate where on the in each number appears called?
One-to-One correspondence
Numbers shown on a number line are called ________
integers
What kinds of numbers do integers include?
Positive and Negative numbers
What kinds of numbers are between numbers?
Fractions, decimals, or radicals
What kind of numbers are fractions, decimals, and radicals known as, and what number system are they included in?
Non-integral rational numbers, rational number system
A number that is calculated, but never ends is called an ________?
(√5)
Irrational number
What kind of numbers make up real numbers?
Rational and irrational numbers
What is a digit?
A single number
What are numerals?
Sets of digits.
Example: 635, number: six hundred thirty-five, numeral: 635
What is an expression, what does it do, and what can it contain?
An expression tells “how many” in terms of a number, or some representation of a number. It can contain words as well.
Equivalent expressions use?
An equals sign, =
What does a number sentence do?
It is a way of showing that two expressions have a relationship
What does this sign mean? ≠ or ^1
Examples: 5 ≠ 15, 6^1seven
Is not equal to.
What does this sign mean? <
Is less than
What does this sign mean? >
Is greater than
What does this sign mean? £ or ≤
Example: 10≤10
Is less than or equal to
What does this sign mean? ³ or ≥
Example: 25≥25, 100 ³ 25
Is greater than or equal to
The following is an example of _________?
Examples: 21n
32+6x
5(3-2n)
Algebraic expressions
The following are examples of ____________?
Examples: 21n>60
32+6x=44
5(3-2n)= -5
Algebraic sentences or equations
What is a variable?
Example: often use a letter for a variable, ‘x’
A symbol that holds the place for numerals in expressions or number sentences. Represents an unknown quality.
What is an open sentence?
A number sentence that contains a variable
What is a closed sentence?
A number sentence that does NOT contain a variable
What is a constant?
Example: 2 tens + 6 ones = 32, false number sentence
2 tens + 6 ones = 26, true number sentence
2 tens + x ones = 26, x= 6, 6 is the constant
One value that makes the variable true
What is an equality or an equation?
Example: 3+2=5
What number plus six equals thirteen? x+6=13
A number sentence in which expressions to the left of the equals sign is equivalent to the expressions on the right of the equals sign.
What are axioms?
The 3 equations that are true for all numbers, laws for numbers.
Can be called properties of numbers or properties of equality.
What does the Reflective Axiom or Reflective Property state?
Any quantity is equal to itself.
Example: A=A
What does the Symmetric Axiom, or Symmetric Property state?
If one quantity is equivalent to another, you can switch which side of the equals sign they are on.
Example: If A=B, then B=A
What does the Transitive Axiom, or Transitive Property state?
It two quantities are equal to a third quantity, then they are equal to each other.
Example: If A=B and B=C, then A=C
What does the Substitution Principle state, and what properties does it apply to?
The substitution principle states that for any numbers A & B, if A=B, then A and B may be substituted for each other. This applies to the Symmetric and Transitive Properties
Why are numbers called constants?
Because they constantly have the same value.
