Think of a situation that would require us to calculate a mathematical expression that can be simplified.
See solution.
Let's start by writing an example problem.
Example Problem
Imagine that we have 4 different duct tapes rolls. They are all 325 centimeters long, but their widths are different. The widths are 1, 2, 2, and 5 centimeters.
Roll 1
Roll 2
Roll 3
Roll 4
Length (cm)
325
325
325
325
Width (cm)
1
2
2
5
We want to find the total area we can cover using all the tape rolls. How can we find it?
Solving the Example Problem
The tape pieces will be like very long rectangles. The area A of a rectangle is the product of its length l and its width w.
A = l * w
The total area will be equal to the sum of all the individual areas.
Now let's think — is there an easier way than calculating all the products and then adding them? Notice that the sum of the products above resembles the Distributive Property.
a(b+c+d+e) = ab + ac + ad+ ae
We can rewrite the sum of the products and find our result in a easier a way.
Notice that this is only one example of applications of the Properties of Real Numbers. There are infinitely many cases in which we can use them in algebraic problems to simplify algebraic expressions.
