Real Numbers

Question 1

What is a Rational Number?

Answer 1

The fraction of a number represented as p/q. Where p and q are both integers and q cannot equal 0.

Question 2

What is an Irrational number?

Answer 2

All numbers that cannot be represented as p/q. Where p and q are both integers and q is not equal 0.

Question 3

What is a Real Number?

Answer 3

All rational and irrational numbers are real numbers.

Question 4

Which kind of number would you use to count the number of bullets in a gun?
A. Integers
B. Rational numbers
C. Irrational numbers

Answer 4

A. Integers

Question 5

What is “The Real Number Line” ?

Answer 5

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.

Question 6

What does “a

Answer 6

It means that the number a is always before b in the real number line. In other words: a is less that b

Question 7

What is “the absolute value” of an integer?

Answer 7

The distance the integer has to 0 in the real number line.

Question 8

What is the absolute value of -5?

Answer 8

5

Question 9

What is “an interval of the real number line”?

Answer 9

A group of real numbers within the real number line. (E.g. “(5, 8)” is an interval containing the numbers 6 and 8)

Question 10

Which numbers are contained in the following interval : “(3, 6]” ?

Answer 10

4, 5 and 6

Question 11

Which numbers are contained in the following interval: “[2, 5]”?

Answer 11

2, 3, 4 and 5

Question 12

What is an equation?

Answer 12

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.

Question 13

What are the 4 properties of an equation?

Answer 13

1. Reflexive
2. Symmetric
3. Transitive
4. Substitution

Question 14

The Reflexive property of an equation claims that…

Answer 14

“a = a” any number can be reflected in an equation to be equal as itself.

Question 15

The Symmetric property of an equation claims that…

Answer 15

If “a = b” then “b = a”. We can swap the left side of the equation with the right side and the equation remains true.

Question 16

The Transitive property of an equation claims that…

Answer 16

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.

Question 17

The Substitution property of an equation claims that…

Answer 17

If “a = b”, then whenever a appears on an equation it can be replaced by b.

Question 18

What are the 4 operations used with real numbers?

Answer 18

1. Addition
2. Multiplication
3. Subtraction
4. Division

Question 19

In the following addition, what are the “terms”?

5 + 6

Answer 19

5 and 6 are the terms of the sum.

Question 20

What are the number 5 and 6 called in the following multiplication?

5 * 6

Answer 20

The “factors” of the multiplication

Question 21

Which real number operations are commutative?

Answer 21

Addition and multiplication

Question 22

What does it mean when an operation is commutative?

Answer 22

That the order of the operation does not matter. 2 + 5 is the same as 5 + 2.

Question 23

What is the additive inverse?

Answer 23

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.

Question 24

What is the “reciprocal” of a number?

Answer 24

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.

Question 25

Turn 5 / 6 to a multiplication using the reciprocal of 6.

Answer 25

5 * (1/6)

Question 26

How do you turn a division into a multiplication?

Answer 26

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

Question 27

The quantity a/b is also known as the quotient of a and b. It may also be known as…

Answer 27

The ratio of a and b

Question 28

What are the 6 properties of real numbers?

Answer 28

Closure, commutative, associative, identity, inverse, distributive.

Question 29

The closure property of real numbers claims that…

Answer 29

Addition: a + b is a real number
Multiplication: a * b is a real number

Question 30

The commutative property of real numbers claims that…

Answer 30

Addition: a + b = b + a (the order is irrelevant)
Multiplication: a * b = b * a
Does not apply to division and subtraction

Question 31

What does the associative property of real numbers claim?

Answer 31

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.

Question 32

What does the identity property of real numbers claim?

Answer 32

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

Question 33

What does the inverse property of real numbers claim?

Answer 33

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.

Question 34

What does the distributive property of real numbers claim?

Answer 34

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.

Question 35

Multiplication is distributive in respect to addition. Knowing this, simplify the following equation.

2 * 3 + 2 * 5 + 2 * 6 = ?

Answer 35

2 * (3 + 5 + 6) = 2 * 14

Question 36

The product of two negative numbers is a _______ number.

Answer 36

Positive

Question 37

What is an exponent?

Answer 37

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.

Question 38

What is an Integer

Answer 38

A whole number with no decimals (e.g. 1, 2, 3, 55)