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.
Turn 5 / 6 to a multiplication using the reciprocal of 6.
5 * (1/6)
How do you turn a division into a multiplication?
You times the reciprocal of the divisor by the dividend. E.g 3/4 is the same as 3 * (1/4) which is the same as 3 * .25
The quantity a/b is also known as the quotient of a and b. It may also be known as…
The ratio of a and b
What are the 6 properties of real numbers?
Closure, commutative, associative, identity, inverse, distributive.
The closure property of real numbers claims that…
Addition: a + b is a real number
Multiplication: a * b is a real number
The commutative property of real numbers claims that…
Addition: a + b = b + a (the order is irrelevant)
Multiplication: a * b = b * a
Does not apply to division and subtraction
What does the associative property of real numbers claim?
Addition: (a + b) + c = a + (b + c) = a + b + c
Multiplication: (ab)c = a(bc) = abc
Equations made up of only additions or only multiplications is not affected by order of operations.
What does the identity property of real numbers claim?
Addition: a + 0 = 0 + a = a
Multiplication: a * 1 = 1 * a = a
Any number multiplied by 1 will equal the same number. Any number we add zero to will equal the same number
What does the inverse property of real numbers claim?
For every real number a there exists another number which we can add for it to equal 0. All numbers except 0 have an inverse multiplicative (reciprocal) which if we multiply it with its matching real number will equate to 1.
What does the distributive property of real numbers claim?
Multiplication: a(b + c) = ab + ac
The definition of multiplication states that we are adding a number to itself a number of times. So if we add all the times the factor is being multiplied the multiplication is simplified and the equation remains true.
Multiplication is distributive in respect to addition. Knowing this, simplify the following equation.
2 * 3 + 2 * 5 + 2 * 6 = ?
2 * (3 + 5 + 6) = 2 * 14
The product of two negative numbers is a _______ number.
Positive
What is an exponent?
When we want to perform the same multiplication multiple times we use an exponent. Also known as “to the power”. E.g 5 to the power of 3 is 5 multiplied by itself 3 times.
What is an Integer
A whole number with no decimals (e.g. 1, 2, 3, 55)
