Real Numbers Flashcards
What is a Rational Number?
The fraction of a number represented as p/q. Where p and q are both integers and q cannot equal 0.
What is an Irrational number?
All numbers that cannot be represented as p/q. Where p and q are both integers and q is not equal 0.
What is a Real Number?
All rational and irrational numbers are real numbers.
Which kind of number would you use to count the number of bullets in a gun?
A. Integers
B. Rational numbers
C. Irrational numbers
A. Integers
What is “The Real Number Line” ?
The real number line is an imaginary line where all the real numbers are placed in order. In the middle of the line we will find the number zero, all the numbers to the left are negative and decrease in value. All the numbers to the right are positive and increase in value.
What does “a
It means that the number a is always before b in the real number line. In other words: a is less that b
What is “the absolute value” of an integer?
The distance the integer has to 0 in the real number line.
What is the absolute value of -5?
5
What is “an interval of the real number line”?
A group of real numbers within the real number line. (E.g. “(5, 8)” is an interval containing the numbers 6 and 8)
Which numbers are contained in the following interval : “(3, 6]” ?
4, 5 and 6
Which numbers are contained in the following interval: “[2, 5]”?
2, 3, 4 and 5
What is an equation?
An equation is an statement declaring equality between two numbers or expressions. E.g. “2+3 = 5”. This equation claims that writing 2+3 is the same as writing 5.
What are the 4 properties of an equation?
- Reflexive
- Symmetric
- Transitive
- Substitution
The Reflexive property of an equation claims that…
“a = a” any number can be reflected in an equation to be equal as itself.
The Symmetric property of an equation claims that…
If “a = b” then “b = a”. We can swap the left side of the equation with the right side and the equation remains true.
The Transitive property of an equation claims that…
If “a = b” and “b = c” then “c = a”. If a real number equals a two different real numbers then those other two numbers also equal each other.
The Substitution property of an equation claims that…
If “a = b”, then whenever a appears on an equation it can be replaced by b.
What are the 4 operations used with real numbers?
- Addition
- Multiplication
- Subtraction
- Division
In the following addition, what are the “terms”?
5 + 6
5 and 6 are the terms of the sum.
What are the number 5 and 6 called in the following multiplication?
5 * 6
The “factors” of the multiplication
Which real number operations are commutative?
Addition and multiplication
What does it mean when an operation is commutative?
That the order of the operation does not matter. 2 + 5 is the same as 5 + 2.
What is the additive inverse?
The additive inverse of b is the number that when added to b equals 0.
E.g. The additive inverse of 6 is -6 … “6 + (-6) = 0”. Also known as the opposite, sign change and negation.
What is the “reciprocal” of a number?
The reciprocal of a is the number that if multiplied by a will equal to 1. The reciprocal of 5 is 1/5, if we multiply (1/5) by 5 we get 1.