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
What do you need to record when moving decimals?
The number of spaces moved
What is the final step after multiplying the numbers?
Place decimals back into the solution
What is the first step in dividing rational numbers?
Determine if the solution will be negative or positive
What should you do with the divisor’s decimal point in division?
Move it to the right till you have a whole number
What must you do to the dividend’s decimal point during division?
Move it the same amount as the divisor
What is the final step in performing division with rational numbers?
Perform long division
What is the first step in adding negative fractions?
Move negative signs to the numerator
What must be done to fractions before adding them if necessary?
Make fractions improper if necessary
What is the third step in the process of adding negative fractions?
Find common denominators
After finding common denominators in adding negative fractions, what do you do next?
Add numerators
What must be kept the same when adding negative fractions?
Keep common denominator
What is the final step after adding negative fractions?
Reduce or simplify
What is the first step in subtracting negative fractions?
Move negative signs to the numerator
What should be done to fractions before subtracting them if necessary?
Make fractions improper if necessary
What is the third step in the process of subtracting negative fractions?
Find common denominator
What is the next step after finding common denominators in subtracting negative fractions?
Subtract numerators
What must be kept the same when subtracting negative fractions?
Keep common denominator
What is the final step after subtracting negative fractions?
Reduce or simplify
What does ‘square a number’ mean?
Multiply a number by itself
What does ‘square root’ of a number mean?
Find out which number times itself gives you the value under the square root sign
What is a ‘perfect square’?
A number that has two identical factors
Is 144 a perfect square? Why?
Yes, because its identical factors are 12
Can decimals and fractions be perfect squares?
Yes
What is the square root of 25?
5
What is the square root of 4?
2
How do you find the square roots of non-perfect squares?
Find the two whole numbers closest to the non-perfect square
True or False: 0.64 is a perfect square.
True
Fill in the blank: To estimate the square root of a non-perfect square, find the two whole numbers closest to the non-perfect ______.
square
