"Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers."
The basics of arithmetic including addition, subtraction, multiplication, and division of natural numbers, integers, fractions, and decimals.
Numeral Systems: The study of different systems used for representing numbers.
Place Value: The value assigned to a digit depending on its position in a number.
Addition: The process of combining two or more numbers to obtain a sum.
Subtraction: The process of taking away one number from another to obtain a difference.
Multiplication: The process of repeated addition, or of combining groups of equal size.
Division: The process of distributing a quantity into equal parts or groups.
Factors and Multiples: Numbers that can be evenly divided into another number, and numbers that are products of a given number and another whole number.
Common Factors and Common Multiples: Factors and multiples that are shared by two or more numbers.
Prime and Composite Numbers: Numbers that can only be divided evenly by themselves and 1, and numbers that can be factored into smaller whole numbers.
Greatest Common Factor: The largest number that can divide two or more given numbers without a remainder.
Least Common Multiple: The smallest number that is a multiple of two or more given numbers.
Fractions: Numbers that represent a part of a whole, or a division of one quantity by another.
Mixed Numbers and Improper Fractions: Numbers that combine whole numbers and fractions, and fractions that have a numerator greater than or equal to the denominator.
Equivalent Fractions: Fractions that represent the same quantity, but are expressed with different numerators and denominators.
Comparing and Ordering Fractions: The process of determining which of two or more fractions is greater or smaller, and arranging fractions in order from least to greatest or greatest to least.
Adding and Subtracting Fractions: The process of finding the sum or difference of two or more fractions.
Multiplying and Dividing Fractions: The process of finding the product or quotient of two or more fractions.
Decimals: Numbers that represent parts of a whole using the base 10 system.
Comparing and Ordering Decimals: The process of determining which of two or more decimals is greater or smaller, and arranging decimals in order from least to greatest or greatest to least.
Rounding Decimals: The process of approximating a decimal to a given place value.
Adding and Subtracting Decimals: The process of finding the sum or difference of two or more decimals.
Multiplying and Dividing Decimals: The process of finding the product or quotient of two or more decimals.
Percents: Fractions expressed as a ratio of a number to 100.
Converting Fractions, Decimals, and Percents: The process of expressing a number as a fraction, decimal, or percent.
Ratio and Proportion: The relationship between two quantities expressed as a fraction or a proportion.
Unit Rates: The ratio of two quantities with different units, expressed as a rate per unit.
Word Problems: Problems that involve real-life situations, expressed in words, that require mathematical operations to solve.
"Arithmetic comes from the Ancient Greek words 'arithmós' meaning 'number' and 'tikḗ [tékhnē]' meaning 'art, craft'."
"The traditional operations studied in arithmetic are addition, subtraction, multiplication, division, exponentiation, and extraction of roots."
"Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms."
"Peano axioms are highly important to the field of mathematical logic today."
"Giuseppe Peano formalized arithmetic with his Peano axioms."
"The purpose of studying arithmetic is to understand the properties of the traditional operations on numbers."
"The Ancient Greeks contributed to the study of arithmetic by providing the terms 'arithmós' and 'tikḗ [tékhnē]' to describe it."
"In arithmetic, the elementary operations are addition, subtraction, multiplication, division, exponentiation, and extraction of roots."
"In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms."
"Arithmetic is an elementary part of mathematics that specifically focuses on the properties of the traditional operations on numbers."
"The Peano axioms are components that formalize arithmetic and are highly important to the field of mathematical logic today."
"The extraction of roots is one of the traditional operations studied in arithmetic."
"The Peano axioms are highly important to the field of mathematical logic today."
"Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which greatly contributed to the study of arithmetic."
"Arithmetic is an elementary part of mathematics that forms the foundation for studying other mathematical concepts."
"The Peano axioms, formulated by Giuseppe Peano, have historical significance as they formalized arithmetic and shaped the field of mathematical logic."
"Peano axioms provide a defined framework for arithmetic, allowing for the study of the properties of traditional operations on numbers."
"Before the formalization by Giuseppe Peano, the study of arithmetic involved understanding the properties of the traditional operations on numbers."
"The fundamental principles of arithmetic include the properties and rules governing the traditional operations on numbers."