Distributing DivisionDate: 11/23/2003 at 12:50:01 From: Kathryn Subject: Mathematics Explained For Primary Teachers Hi, Hope I'm not wasting your time but I hope that you can help. On page 91 of the book _Mathematics Explained For Primary Teachers_ (by Derek Haycock), I find this statement: The method is based on the distributive law for division over addition. Shouldn't this read '....distributive law for multiplication over addition'? Many thanks for your help. Kathryn Date: 11/23/2003 at 22:49:57 From: Doctor Ian Subject: Re: Mathematics Explained For Primary Teachers Hi Kathryn, Well, division _does_ distribute over addition, e.g., (1 + 2)/5 = 1/5 + 2/5 which is why we can add fractions with common denominators by simply adding their numerators. However, it's only left-distributive, (1 + 2)/5 = 1/5 + 2/5 Yes 5/(1 + 2) = 5/1 + 5/2 No whereas multiplication is both left- and right-distributive: 5(1 + 2) = 5(1) + 5(2) Yes (1 + 2)5 = 1(5) + 2(5) Yes Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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