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In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
Division can be calculated with an abacus. [14] Logarithm tables can be used to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm of the result. Division can be calculated with a slide rule by aligning the divisor on the C scale with the dividend on the D scale. The quotient can be found on the D ...
In mathematics, like terms are summands in a sum that differ only by a numerical factor. [1] Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression , like terms are those that contain the same variables to the same powers , possibly with different coefficients .
For associative algebras, the definition can be simplified as follows: a non-zero associative algebra over a field is a division algebra if and only if it has a multiplicative identity element 1 and every non-zero element a has a multiplicative inverse (i.e. an element x with ax = xa = 1).
Use divide and conquer to compute the product of the primes whose exponents are odd; Divide all of the exponents by two (rounding down to an integer), recursively compute the product of the prime powers with these smaller exponents, and square the result; Multiply together the results of the two previous steps
For example, a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator. [2] As another example, if a×b=a×c, then the multiplicative term a can be canceled out if a≠0, resulting in the equivalent expression b=c; this is equivalent to dividing through by a.
hcf – highest common factor of two numbers. (Also written as gcd.) H.M. – harmonic mean. HOL – higher-order logic. Hom – Hom functor. hom – hom-class. hot – higher order term. HOTPO – half or triple plus one. hvc – havercosine function. (Also written as havercos.) hyp – hypograph of a function.
All other arithmetic concepts can then be defined in terms of these primitive concepts. [147] 0 is a natural number. For every natural number, there is a successor, which is also a natural number. The successors of two different natural numbers are never identical. 0 is not the successor of a natural number.