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Question 8126: can you give me an example and explination for distributive properties?
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! Ah! Distributive property! That's when a(b + c + d + e + ...) = ab + ac + ad + ae + ....
Actually, you'll usually see it as a single number in front of a set of parentheses that contain two or more terms. What happens is that you multiply that number in front to EVERY SINGLE TERM inside the parentheses. In the above example, we multiplied the a to the b,c,d, and e, and whatever else term might have been there.
Alright. Does this actually really work? Let's see.
Does 5(2 + 3 + 8 - 6) really equal 5*2 + 5*3 + 5*8 - 5*6? You bet.
5(2 + 3 + 8 - 6) ==> 5(7) = 35
5*2 + 5*3 + 5*8 - 5*6 = 10 + 15 + 40 - 30 = 35
So WHY do you need to know this? Here's a real life example. Say that the sales tax is 5%. You decide to buy a video game for $50.00 and you want to know how much tax you'll pay. You know that it's 5% of $50.00, so that's 0.05*50 which is $2.50. So say that you needed to buy that new joystick because it works better with that new game than the old 4-button controller you have at home. That's $45.00. How much tax will you pay for that new joystick? That 0.05*45.00 which brings you to $2.25. Then you decided you got bored with the CDs you have in your car, so you buy a new album, costing $17.00. You know that the tax for that would be 0.05*17.00 or $0.85.
So how much would you be taxed for those 3 products? So, it's the video game, the joystick, and the CD. You initially calculated it as 0.05*50 + 0.05*45 + 0.05*17 to find out that you'll be paying $5.60 in taxes. Now that you've got the distributive property, you know that you can add up the sale prices first, which were 50.00, 45.00, and 17.00 to get $112, then multiply that total amount by the 0.05 (AKA 5% sales tax) to get $5.60. That's a lot easier and a lot less work than multiplying each item's cost by the percent tax, and then adding all of those values together.
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