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


which is wrong.  Or when solving an equation like


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


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.

Title associativity of multiplication
Canonical name AssociativityOfMultiplication
Date of creation 2013-03-22 15:09:22
Last modified on 2013-03-22 15:09:22
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Application
Classification msc 12D99
Classification msc 00A35