Basic Arithmetic and Number Systems

Study Notes

Basic Arithmetic Operations

Addition: Combining two or more numbers to find their total. The sum is the result.
Subtraction: Finding the difference between two numbers. The result is the difference.
Multiplication: Repeated addition of a number. The product is the result.
Division: Splitting a number into equal parts. The quotient is the result.

Number Systems

Natural Numbers (counting numbers): 1, 2, 3, ...
Whole Numbers: 0, 1, 2, 3, ... (includes zero)
Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (includes negative numbers)
Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. Examples include 1/2, 3/4, -2/5.
Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers. Examples include √2, π.
Real Numbers: The set of all rational and irrational numbers.

Properties of Numbers

Commutative Property: Changing the order of numbers in addition or multiplication does not change the result.
Associative Property: Changing the grouping of numbers in addition or multiplication does not change the result.
Distributive Property: Multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
Identity Property: The sum of any number and zero is the number itself. The product of any number and one is the number itself.
Inverse Property: The sum of a number and its opposite is zero. The product of a number and its reciprocal is one (except for zero which has no reciprocal).

Fractions

Fractions represent parts of a whole. A fraction has a numerator and a denominator.
Equivalent Fractions: Fractions that represent the same portion of a whole.
Simplifying Fractions: Reducing a fraction to its lowest terms by dividing the numerator and denominator by their greatest common factor (GCF).
Adding and Subtracting Fractions: Requires finding a common denominator.
Multiplying Fractions: Multiply the numerators and multiply the denominators.
Dividing Fractions: Multiply the first fraction by the reciprocal of the second fraction.

Decimals

Decimals represent parts of a whole using place value.
Converting between decimals and fractions.
Adding, Subtracting, Multiplying, and Dividing Decimals.

Exponents and Radicals

Exponents represent repeated multiplication.
Evaluating expressions involving exponents and radicals.

Algebra

Variables represent unknown quantities.
Equations express equality between two expressions.
Solving equations involves isolating the variable.
Inequalities compare two expressions using symbols like <, >, ≤, ≥.
Linear equations: Equations that can be graphed as straight lines.
Systems of equations: Two or more equations with the same variables.

Geometry

Basic shapes (triangles, circles, squares, rectangles).
Perimeter, area, and volume of common shapes.
Angles and their properties.
Lines and their properties.

Measurement

Units of measurement (length, weight, volume, time, temperature).
Converting between different units of measurement.

Data Analysis

Collecting data and organizing it in tables or graphs.
Measures of central tendency (mean, median, mode).
Measures of variability (range, standard deviation).
Interpreting data presented in graphs and tables.

Probability

Likelihood of events occurring.
Basic probability calculations.
Probability distributions.

Statistics

Collecting and analyzing numerical data.
Descriptive statistics summarize data (mean, median, etc).
Inferential statistics uses sample data to draw conclusions about a wider population.

Problem Solving

Steps for solving math problems.
Identifying unknowns, creating equations, solving equations, and verifying the results.

Special Topics

Significant figures/rounding
Pythagorean theorem
Functions

Description

Test your understanding of basic arithmetic operations and number systems with this quiz. Covering addition, subtraction, multiplication, and division, as well as various types of numbers including natural, whole, integers, rational, and irrational numbers, this quiz will solidify your foundational math skills.