Rational Numbers Flashcards
What is a rational number?
Any number that can be expressed in the form of a ratio a/b, where a and b are integers and b ≠ 0
A number divided by 0 is undefined.
What are natural numbers?
Counting numbers not including 0 (1, 2, 3, 4, …)
Natural numbers are used for counting.
What are whole numbers?
Counting numbers including 0 (0, 1, 2, 3, 4, …)
Whole numbers are a subset of natural numbers.
What are integers?
Positive and negative whole numbers including 0 (-1, 0, 1, 2, 3, …)
Integers do not include decimals or fractions.
What do real numbers include?
All rational and irrational numbers
Real numbers encompass both types of numbers.
What are irrational numbers?
Numbers that cannot be written as a ratio of integers
Examples include the square root of a non-perfect square and numbers like π and √2.
What characterizes the square root of a non-perfect square?
It is non-terminating and non-repeating
This indicates that it cannot be expressed as a simple fraction.
Fill in the blank: A decimal is irrational if it is _______ and _______.
non-terminating and non-repeating
This property distinguishes irrational numbers from rational numbers.
True or False: All integers are whole numbers.
False
Integers include negative numbers, while whole numbers do not.
Fill in the blank: The set of natural numbers is represented by the symbol _______.
N
This notation is commonly used in mathematics.
Fill in the blank: The set of integers is represented by the symbol _______.
Z
This notation comes from the German word ‘Zahlen’ meaning ‘numbers.’
Fill in the blank: The set of rational numbers is represented by the symbol _______.
Q
This notation is derived from the word ‘quotient.’
What is the result of adding two positive integers?
A more positive number
What is the result of adding two negative integers?
A more negative number
How do you determine the outcome of a combination of numbers?
It depends on which number is larger
What visual aid can help in understanding addition and subtraction of rationals?
A number line
What should you do if the signs of the numbers are different when adding or subtracting?
Subtract the smaller absolute value from the larger absolute value
What is the result of subtracting a negative number?
It equals a positive
Calculate: -2 - (-4)
-2 + 4
What is the sign of the product or quotient of two rational numbers with the same sign?
Positive
What is the sign of the product or quotient of two rational numbers with different signs?
Negative
What does BEDMAS stand for?
Brackets, Exponents, Division, Multiplication, Addition, Subtraction
What is the first step in solving a problem using BEDMAS?
Determine if the solution will be negative or positive
What should you do with the decimals before multiplying two rational numbers?
Move decimals to the right till you have a whole number
