Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms.
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any non-negative integer using a combination of ten fundamental numeric symbols, called digits. In addition to their use in counting and measuring, numerals are often used for labels, for ordering, and for codes. In common usage, a numeral is not clearly distinguished from the number that it represents.
A multiplication algorithm is an algorithm to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic.
Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows two columns of three apples and two apples each, totaling at five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5".
Subtraction is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 − 2 peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches. Therefore, the difference of 5 and 2 is 3; that is, 5 − 2 = 3. While primarily associated with natural numbers in arithmetic, subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.
Rote learning is a memorization technique based on repetition. The method rests on the premise that the recall of repeated material becomes faster the more one repeats it. Some of the alternatives to rote learning include meaningful learning, associative learning, spaced repetition and active learning.
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A binary number may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two.
Mental calculation consists of arithmetical calculations using only the human brain, with no help from any supplies or devices such as a calculator. People may use mental calculation when computing tools are not available, when it is faster than other means of calculation, or even in a competitive context. Mental calculation often involves the use of specific techniques devised for specific types of problems. People with unusually high ability to perform mental calculations are called mental calculators or lightning calculators.
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are potentially limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision.
The suanpan, also spelled suan pan or souanpan) is an abacus of Chinese origin, earliest first known written documentation of the Chinese abacus dates to the 2nd century BCE during the Han dynasty, and later, described in a 190 CE book of the Eastern Han dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue. However, the exact design of this suanpan is not known. Usually, a suanpan is about 20 cm (8 in) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads on each rod in the bottom deck. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. The suanpan can be reset to the starting position instantly by a quick jerk around the horizontal axis to spin all the beads away from the horizontal beam at the center.
Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada. It is the primary model for standards-based mathematics.
Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools.
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of an integer numerator, displayed above a line, and a non-zero integer denominator, displayed below that line. If these integers are positive, then the numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates 3/4 of a cake.
Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers. It is mathematically identical to the more commonly used long multiplication algorithm, but it breaks the process into smaller steps, which some practitioners find easier to use.
In elementary arithmetic, a standard algorithm or method is a specific method of computation which is conventionally taught for solving particular mathematical problems. These methods vary somewhat by nation and time, but generally include exchanging, regrouping, long division, and long multiplication using a standard notation, and standard formulas for average, area, and volume. Similar methods also exist for procedures such as square root and even more sophisticated functions, but have fallen out of the general mathematics curriculum in favor of calculators. As to standard algorithms in elementary mathematics, Fischer et al. (2019) state that advanced students use standard algorithms more effectively than peers who use these algorithms unreasoningly. That said, standard algorithms, such as addition, subtraction, as well as those mentioned above, represent central components of elementary math.
Arithmetic is an elementary branch of mathematics that is widely used for tasks ranging from simple day-to-day counting to advanced science and business calculations.
Investigations in Numbers, Data, and Space is a K–5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts, United States. The curriculum is often referred to as Investigations or simply TERC. Patterned after the NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula. As opposed to referring to textbooks and having teachers impose methods for solving arithmetic problems, the TERC program uses a constructivist approach that encourages students to develop their own understanding of mathematics. The curriculum underwent a major revision in 2005–2007.
Mirifici Logarithmorum Canonis Descriptio and Mirifici Logarithmorum Canonis Constructio are two books in Latin by John Napier expounding the method of logarithms. While others had approached the idea of logarithms, notably Jost Bürgi, it was Napier who first published the concept, along with easily used precomputed tables, in his Mirifici Logarithmorum Canonis Descriptio.
The Chinese multiplication table is the first requisite for using the Rod calculus for carrying out multiplication, division, the extraction of square roots, and the solving of equations based on place value decimal notation. It was known in China as early as the Spring and Autumn period, and survived through the age of the abacus; pupils in elementary school today still must memorise it.
