Sum of Products

Date: 11/01/1999 at 12:38:16
From: Tasha
Subject: Products of math

When in a word problem it asks for the sum of a product, is the 
product the answer of all of the sums added together?

Date: 11/14/1999 at 19:54:44
From: Doctor TWE
Subject: Re: Products of math

Hi Tasha - thanks for writing to Dr. Math.

You ask a good question. In math, when we use the word "sum," we mean 
add the numbers. When we use the word "product," we mean multiply the 
numbers. So the "sum of the products" means we want to add (sum) the 
results of numbers being multiplied (products). Let me give you an 
example.

Suppose we have 3 nickels, 4 dimes and 2 quarters. To find the value 
of the nickels, we multiply (find the product of)

     3 * 5 cents = 15 cents.

To find the value of the dimes, we find the product of

     4 * 10 cents = 40 cents.

Likewise, to find the value of the quarters, we multiply

     2 * 25 cents = 50 cents.

To find the total value of all the coins, we add up (sum)

     15 cents + 40 cents + 50 cents = 105 cents, or $1.05.

Here, we added up ("took the sum of") all the results of the 
multiplications ("the products.")

I hope this example helps clear it up. Write back if you have any more 
questions!

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/