Distributive Property over Addition vs. MultiplicationDate: 12/11/2002 at 02:25:05 From: Kathy O'Neill Subject: Distributive property over addition vs. multiplication Please help me explain the following to my child: His math problem was (3x3) = (4+5) He understands that both sides of the equation equal nine. Then he was asked to multiply both sides by 2. Although 2(3x3) = 18 and 2(4+5) = 18 he wanted to use the distributive property. But then he got 36 equals 18. Why can't you use the distributive property when the integers in the parenthesis are being multiplied if it works when you ADD inside the parenthesis? Date: 12/11/2002 at 08:55:19 From: Doctor Peterson Subject: Re: Distributive property over addition vs. multiplication Hi, Kathy. The simple answer is that there is only a distributive property of multiplication over addition, not a distributive property of multiplication over multiplication. The closest you can get to the latter is the associative property: 2*(3*3) = (2*3)*3 because we can move the parentheses around. You might picture it this way. The distributive property says that multiplying a sum multiplies each part of the sum: * * * * * * * * * * * * * * * * * * * * * * * * * * * = * * * * + * * * * * \_______________/ \_____/ \_______/ 2*(4+5) = 2*4 + 2*5 But if we double two numbers, and multiply them together, we don't just double the product; we double it twice: * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * \_________/ \___________/ (2*3)(2*3) = (2*2)(3*3) That is, using the associative property, (2*3)*(2*3) = 2*3*2*3 = 2*2*3*3 = (2*2)*(3*3) = 4*(3*3) which is not 2*(3*3). Does that help? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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