Distributive PropertyDate: 10/13/2001 at 08:10:12 From: Susan Kinney Subject: Distributive property We are learning the distributive property in school. Why do we have to learn this, and how will we use it, and when? Susan Date: 10/13/2001 at 22:47:25 From: Doctor Peterson Subject: Re: Distributive property Hi, Susan. This and similar properties are the foundation of all of algebra. Once you get into algebra you will have to be able to rewrite an expression, using these properties, to transform it into another expression that means the same thing, but is easier to work with in some way. By knowing how numbers work, you will know what changes you can make. For example, suppose the letter x stands for some (unknown) number, and 2x means twice that number. Then if we know that x + 2x = 15 then we know that x is the same as 1x (1 times x), and we can use the distributive property to say that x + 2x = 1x + 2x = (1+2)x = 3x So we can rewrite our equation as 3x = 15 But now it's easy to find what x has to be; the number you can multiply by 3 to get 15 is 15 divided by 3, or 5. The distributive property is really just common sense. My equation might mean I bought one CD for me and two for my big sister. The total cost was $15. I forget how much a CD costs. Can you tell me? Well, one CD and two CDs is the same as 3 CDs; so 1 times the cost of a CD plus 2 times the cost of a CD is 3 times the cost of a CD. What I did to the equation is the same thinking without the words. Ultimately, algebra means solving problems with less thinking; and knowing the properties of numbers and their operations is what lets you do algebra. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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