Numbers, Numbers, Numbers
{1, 2, 3, 4, 5...}
What are the natural numbers?
Translate 'a number n plus a number x', into algebraic symbols.
What is n + x?
-7 _____ 3
-7 < 3
What is less than?
3 + (-6)
What is -3?
3 - 8
What is -5?
{0, 1, 2, 3, 4, 5...}
What are the whole numbers?
Translate 'a number m subtracted from n', into algebraic symbols.
What is n - m?
-4.78 ______-5.011
-4.78 > -5.011
What is greater than?
(-2.1) + (-1.1)
What is -3.2?
-8 - (-2)
-8 + 2 = -6
What is -6?
{...-3, -2, -1, 0, 1, 2, 3...}
What are integers?
Translate 'twice some number x', into algebraic symbols.
What is 2x?
|-3|______|3|
|-3| = |3|
What is equal to?
(-3/5) + 2/5
What is -1/5?
-6 - (-8)
-6 + 8 = 2
What is 2?
Any number that can be expressed as a/b as long as b≠0, for example -3/1 or 23/2
What are the rational numbers?
Translate 'the product of eight and some number x', into algebraic symbols.
What is 8x?
-(-8) ______-|-8|
-(-8) > -|-8|
What is greater than?
(-44) + 1.5
What is -42.5?
7 - (-10.5)
7 + 10.5 = 17.5
What is 17.5?
Describes the set of numbers that have decimal notation that does not terminate or repeat (like pi or √2)
What are irrational numbers?
Translate 'six less than two times a number x', into algebraic symbols.
What is 2x-6?
-36/48 ______ -25/30
-36/48 = -3/4
-25/30 = -5/6
5/6 > 3/4 when positive, but when negative:
-3/4 > -5/6 because -3/4 is to the right (closer to zero) than -5/6
so... -36/48 > -25/30
What is greater than?
(-3/8) + 5/12
-3/8 = -9/24 (multiply top and bottom by 3)
5/12 = 10/24 (multiply top and bottom by 2)
(-9/24) + 10/24 = 1/24
What is 1/24?
(-3/8) - 3/4
3/4 = 6/8 (multiply top and bottom by 2)
(-3/8) - 6/8 = -9/8
What is -1 1/8?