Heidi T. answered • 09/03/19
MS in Mathematics, PhD in Physics, 7+ years teaching experience
Translating word problems into mathematical expressions is a lot like learning a new language. You need to learn what each word/expression means. So let's break down your problem.
First it says "the product of". A product is formed when you multiply two numbers or expressions. The word "and" is used to divide the two items being multiplied. So "The product of 8 and ---" means that you are multiplying 8 and what ever follows the "and" in the problem, in this case it is "the sum of a number and 7". Since what follows the "and" is another expression, it would be written in parentheses. To this point we have: 8 * ( ?? ), where the ?? replaces the expression.
The words "the sum" means that we are adding two numbers or expressions. As with multiplication, "and" separates the two addends. The first addend in the sum is "a number" - thus we know it isn't another expression and that we need to use a variable, because we aren't told the number. You can choose any letter or figure for your variable name, so lets call it "n". The part following the "and" is the number 7. Putting it together results in (n + 7), which will now be combined with the 8 * in the product, resulting in 8 * (n + 7).
The next thing that comes in your problem is "results in". This means "is equal to" and may also be written "is". Mathematical replacement is "=". Following the "=" is another expression: "the difference between 7 and the number". A difference is subtraction and, again, the "and" represents the break between the two values. The first number is 7 the second number is "the number" meaning the same number as before, so we use the same variable. The "difference between 7 and the number" is written: 7 - n
Putting it all together: "The product of 8 and the sum of a number and 7results in the difference of 7 and the number." Translates into math as:
8 * (n + 7) = 7 - n
at this point you can solve for n, if finding "the number" is the goal, or it may be left in this form.
