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In approximate arithmetic, such as floating-point arithmetic, the distributive property of multiplication (and division) over addition may fail because of the limitations of arithmetic precision. For example, the identity 1 / 3 + 1 / 3 + 1 / 3 = ( 1 + 1 + 1 ) / 3 {\displaystyle 1/3+1/3+1/3=(1+1+1)/3} fails in decimal arithmetic , regardless of ...
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.
A term rewriting given by a set of rules can be viewed as an abstract rewriting system as defined above, with terms as its objects and as its rewrite relation. For example, x ∗ ( y ∗ z ) → ( x ∗ y ) ∗ z {\displaystyle x*(y*z)\rightarrow (x*y)*z} is a rewrite rule, commonly used to establish a normal form with respect to the ...
For cancellation of common terms, we have the following rules: If a + k ≡ b + k (mod m), where k is any integer, then a ≡ b (mod m). If k a ≡ k b (mod m) and k is coprime with m, then a ≡ b (mod m). If k a ≡ k b (mod k m) and k ≠ 0, then a ≡ b (mod m). The last rule can be used to move modular arithmetic into division.
Like terms are added together, [30] for example, + + is written as +, because the terms containing are added together, and, the terms containing are added together. Brackets can be "multiplied out", using the distributive property.
This can be computed by hand using the distributive property of multiplication over addition and combining like terms, but it can also be done (perhaps more easily) with the multinomial theorem. It is possible to "read off" the multinomial coefficients from the terms by using the multinomial coefficient formula.
In mathematics, the associative property [1] is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. In propositional logic , associativity is a valid rule of replacement for expressions in logical proofs .
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