Real Numbers
What is a real number?
A real number is any number that can be found on the number line, including both rational and irrational numbers.
What is a rational number?
A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b≠0
What are integers?
Integers are whole numbers that can be positive, negative, or zero.
Define whole numbers.
Whole numbers are non-negative integers, including 00 and all positive integers.
What is a fraction?
A fraction is a way to represent a part of a whole, expressed as a/b.
Give an example of a real number that is not an integer.
An example of a real number that is not an integer is 2.5 or the square root of 2.
Is 3/4 a rational number? Why or why not?
Yes, 3/4 is a rational number because it can be expressed as a fraction.
List three examples of integers.
Three examples of integers are −3, 0, and 5
Are negative numbers considered whole numbers? Why or why not?
No, negative numbers are not considered whole numbers because whole numbers are non-negative.
Simplify the fraction 6/8.
3/4
Are all rational numbers real numbers? Explain your answer.
Yes, all rational numbers are real numbers because they can be represented on the number line.
Can a rational number be a negative number? Give an example.
Yes, a rational number can be a negative number. An example is −1/2.
What is the absolute value of −5?
The absolute value of −5 is 5.
What is the smallest whole number?
The smallest whole number is 0.
What are equivalent fractions? Give an example.
Equivalent fractions are different fractions that represent the same value, for example, 1/2 and 2/4.
What is the square root of 1616? Is it a real number?
The square root of 16 is 4, and yes, it is a real number.
Convert the decimal 0.75 into a fraction.
The decimal 0.75 can be converted into the fraction 3/4.
Are all whole numbers integers? Explain.
Yes, all whole numbers are integers because whole numbers include 00 and positive integers.
How many whole numbers are there from 0 to 10?
There are 11 whole numbers from 0 to 10 (inclusive).
Can an irrational number be expressed as a fraction? Why or why not?
No, an irrational number cannot be expressed as a fraction because it has a non-terminating, non-repeating decimal expansion.
Name three real numbers that are also irrational.
Three real numbers that are also irrational include square root of 2
What are the two parts of a fraction called?
The two parts of a fraction are called the numerator (top number) and denominator (bottom number).
What is the sum of −3 and 4?
The sum of −3 and 4 is 1.
List the first five whole numbers.
The first five whole numbers are 0, 1, 2, 3, and 4.
What is the square root of 2? Is it a rational or irrational number?
The square root of 2 is an irrational number because it cannot be expressed as a fraction.