Basic Arithmetic and Number Systems

Study Notes

Basic Arithmetic Operations

Addition: Combining two or more numbers to find their sum. Example: 2 + 3 = 5
Subtraction: Finding the difference between two numbers. Example: 5 - 2 = 3
Multiplication: Repeated addition of a number. Example: 2 x 3 = 6 (2 added 3 times)
Division: Splitting a number into equal parts. Example: 6 ÷ 2 = 3 (6 split into 2 equal groups)

Order of Operations (PEMDAS/BODMAS)

Parentheses/Brackets: Operations inside parentheses are performed first.
Exponents/Orders: Calculations with exponents are done next.
Multiplication and Division (from left to right): Performed from left to right in the expression.
Addition and Subtraction (from left to right): Performed from left to right in the expression.

Number Systems

Natural Numbers: Counting numbers (1, 2, 3,...).
Whole Numbers: Natural numbers plus zero (0, 1, 2, 3,...).
Integers: Whole numbers and their opposites (-3, -2, -1, 0, 1, 2, 3,...).
Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers, and q is not zero. Examples: 1/2, 3/4, -2/5.
Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers. Examples: π (pi), √2.
Real Numbers: The set of all rational and irrational numbers.

Fractions

Numerator: The top number of a fraction, representing the parts.
Denominator: The bottom number of a fraction, representing the whole.
Equivalent Fractions: Fractions that represent the same value.
Simplifying Fractions: Reducing a fraction to its lowest terms.
Adding/Subtracting Fractions: Need a common denominator.
Multiplying Fractions: Multiply the numerators and denominators.
Dividing Fractions: Multiply by the reciprocal of the divisor.

Decimals

Place Value: Understanding the value of digits based on their position.
Converting Between Fractions and Decimals.

Percentages

Representing a part of a whole as a fraction of 100.
Calculating percentages.
Converting between fractions, decimals, and percentages.

Exponents and Radicals

Exponents: Repeated multiplication of a number. Example: 2³ = 2 x 2 x 2 = 8
Roots: Finding a number that, when multiplied by itself a certain number of times, equals a given number. Example: √9 = 3
Square Roots: Finding the number that when multiplied by itself equals a given number.
Cube Roots: Finding the number that when multiplied by itself three times equals a given number.

Geometry

Basic Shapes: Understanding two-dimensional shapes like squares, rectangles, triangles, circles, and three-dimensional shapes like cubes, spheres, and cones.
Perimeter: The distance around the outside of a two-dimensional shape.
Area: The space inside a two-dimensional shape.
Volume: The space occupied by a three-dimensional object.

Algebra

Variables: Symbols used to represent unknown values. Examples: x, y, z
Equations: Statements of equality between two expressions. Examples: x + 2 = 5.
Solving Equations: Finding the value of the variable that makes the equation true.

Data Analysis and Statistics

Mean: Average of a set of numbers.
Median: Middle value in a sorted set of numbers.
Mode: Most frequent value in a set of numbers.
Range: Difference between the largest and smallest values in a set.

Problem Solving

Developing a strategy to approach a mathematical problem.
Using different approaches to solve problems; logical deduction, guess and check, working backwards.

Measurement Units

Length (meters, centimeters, inches, feet)
Weight/Mass (grams, kilograms, pounds)
Volume (liters, cubic centimeters)
Time (seconds, minutes, hours)
Temperature (degrees Celsius, degrees Fahrenheit)

Description

This quiz covers fundamental arithmetic operations including addition, subtraction, multiplication, and division. It also addresses the order of operations and various number systems such as natural numbers, whole numbers, integers, and rational numbers. Test your understanding of these essential math concepts!