Numbers and Operations

Study Notes

Types of Numbers:
- Natural Numbers: 1, 2, 3, ... (counting numbers)
- Whole Numbers: 0, 1, 2, 3, ... (including zero)
- Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (including negative numbers)
- Rational Numbers: fractions, decimals, percentages (can be expressed as a ratio)
- Irrational Numbers: cannot be expressed as a ratio (e.g. π, e, sqrt(2))
Number Operations:
- Addition: combining two or more numbers to get a total or a sum
- Subtraction: finding the difference between two numbers
- Multiplication: repeated addition of a number
- Division: sharing or grouping a number into equal parts
Properties of Operations:
- Commutative Property: order of numbers does not change the result
- Associative Property: grouping numbers does not change the result
- Distributive Property: multiplying a number by a sum is the same as multiplying by each addend separately

Units of Time:
- Second (s)
- Minute (min) = 60 s
- Hour (h) = 60 min
- Day = 24 h
- Week = 7 days
- Month = 28-31 days
- Year = 12 months
Time Conversions:
- 1 h = 60 min = 3600 s
- 1 day = 24 h = 1440 min = 86400 s
Time-Related Concepts:
- AM/PM: morning (AM) and afternoon/evening (PM)
- Time zones: regions with uniform standard time

Units of Distance:
- Meter (m)
- Kilometer (km) = 1000 m
- Centimeter (cm) = 0.01 m
- Millimeter (mm) = 0.001 m
Distance Conversions:
- 1 km = 1000 m = 100,000 cm = 1,000,000 mm
- 1 m = 100 cm = 1000 mm
Distance-Related Concepts:
- Perimeter: distance around a shape
- Circumference: distance around a circle

Natural Numbers are counting numbers, starting from 1, such as 1, 2, 3, ...
Whole Numbers include zero, in addition to Natural Numbers, such as 0, 1, 2, 3, ...
Integers include negative numbers, whole numbers, and zero, such as ..., -3, -2, -1, 0, 1, 2, 3, ...
Rational Numbers can be expressed as a ratio, including fractions, decimals, and percentages
Irrational Numbers cannot be expressed as a ratio, such as π, e, and sqrt(2)
Addition is the process of combining two or more numbers to get a total or a sum
Subtraction is the process of finding the difference between two numbers
Multiplication is the repeated addition of a number
Division is the process of sharing or grouping a number into equal parts
The Commutative Property states that the order of numbers does not change the result
The Associative Property states that grouping numbers does not change the result
The Distributive Property states that multiplying a number by a sum is the same as multiplying by each addend separately

A Second (s) is a unit of time
A Minute (min) is equal to 60 seconds
An Hour (h) is equal to 60 minutes
A Day is equal to 24 hours
A Week is equal to 7 days
A Month is equal to 28-31 days
A Year is equal to 12 months
1 hour is equal to 60 minutes, which is equal to 3600 seconds
1 day is equal to 24 hours, which is equal to 1440 minutes, which is equal to 86400 seconds
AM/PM refers to morning (AM) and afternoon/evening (PM)
Time zones are regions with uniform standard time

A Meter (m) is a unit of distance
A Kilometer (km) is equal to 1000 meters
A Centimeter (cm) is equal to 0.01 meters
A Millimeter (mm) is equal to 0.001 meters
1 kilometer is equal to 1000 meters, which is equal to 100,000 centimeters, which is equal to 1,000,000 millimeters
1 meter is equal to 100 centimeters, which is equal to 1000 millimeters
Perimeter refers to the distance around a shape
Circumference refers to the distance around a circle