Numbers and Numerals
Numbers are basic mathematical objects used for counting, measuring, and labeling.
Mathematics
Mathematics has a rich history that dates back to ancient civilizations. Around 3000 BCE, the Sumerians in Mesopotamia developed a complex system of metrology and basic arithmetic for trade, taxation, and astronomy, while the Egyptians used geometry to build pyramids and developed a calendar based on star observations and the Nile's flooding cycle. In Ancient Greece, mathematicians like Pythagoras, Euclid, and Archimedes made significant contributions, with Pythagoras known for the Pythagorean theorem, Euclid for his comprehensive geometry work "The Elements," and Archimedes for advances in geometry and calculus. During the medieval period, the development of mathematics flourished in the Islamic world with scholars like Al-Khwarizmi, whose work in algebra and the preservation and expansion of Greek and Indian mathematical knowledge, including the concept of zero and the decimal system, was crucial. This knowledge returned to Europe during the Renaissance, leading to rapid advancements by figures like Galileo, Newton, and Leibniz, who developed calculus and modern mathematical analysis, setting the stage for the diverse field of mathematics we study today.
Arithmetic:
Basic Operations
Fundamental mathematical processes used to manipulate numbers.
Properties of Operations
Helping to simplify calculations and understand relationships between numbers.
Fractions
They consist of a numerator (the top number) indicating how many parts are being considered, and ...
Decimals
Decimals represent fractions in a base-10 system, using a decimal point to separate the whole number part from the fractional part.
Percentages
Compare ratios, represent proportions, and calculate increases or decreases in values. Written using the percent symbol (%).
Ratios and Proportions
Ratios compare two quantities, showing the relative size of one quantity to another. Proportions state that two ratios are equal.
Powers and Roots
Powers involve raising a number to an exponent, indicating repeated multiplication (e.g., ).
Order of Operations
Rules used to determine the sequence in which mathematical operations should be performed to ensure accurate results.
Factors and Multiples
Prime and composite numbers, prime factorization, least common multiple (LCM), and greatest common divisor (GCD).
Basic Algebra
Basic algebra involves using symbols and letters to represent numbers and quantities in equations and expressions.
Measurements
This includes understanding and converting between different units of measurement such as metric and imperial systems.
Data Handling
Collecting, organizing, and interpreting data. Key concepts include calculating measures of central tendency
