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单词 AssociativityOfMultiplication
释义

associativity of multiplication


It’s important to know the following interpretationMathworldPlanetmathPlanetmath of the associative law

a(bc)=(ab)c(1)

of multiplicationPlanetmathPlanetmath in arithmeticsPlanetmathPlanetmath and elementary algebra:

A product (bc) is multiplied by a number (a) so that only one (b) of the product is multiplied by that number.

This rule is sometimes violated even in high school e.g. like

102.50.3=253=75,

which is wrong.  Or when solving an equation like

x2x-13=1

one would like to multiply both sides by 3 for removing the denominator, getting perhaps

3x(2x-1)=3;

then the both of left side have incorrectly been multiplied by 3.

The reason of such mistakes is very likely that one confuses the associative law with the distributive law;  cf. (1) with this latter

a(b+c)=ab+ac,(2)

which two different operationsMathworldPlanetmath, multiplication and addition; both addends must be multiplied separately.

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更新时间:2025/5/4 15:37:46