Chapter 10
Describing & Changing Calculations

Previous Section: 10. Replacement Principle

3  To Find A Rectangle's Dimensions

The rectangle area formula is easy to compute if you are given the width W and the length L. But can we use the area formula A = L·W to find the width W when the area A and length L are given? The rectangle area formula says

A = L·W

From this formula we can directly compute A provided the other two quantities L and W are given or known.

If you multiply W by a non-zero number called it, and then divide by the same number called it you get back your original quantity W. This is a rule or property of arithmetic with whole numbers and fractions, etc. A description of these properties will be given later. So multiplying and then dividing W by the number L gives the same result as doing nothing to W. This suggests the expression [( W·L)/(L)] when calculated, gives you the width W. Now we can write W = [( W·L)/(L)]. The equality sign is used to signal that the expression on either side of it gives the same result. But the expression W ·L whenever computed is the same as the area A. So we replace the computation of W ·L by A with the understanding that A = W ·L always represents this product W ·L.

Now W can be obtained by calculating [(( W ·L))/(L)]. The latter gives the same result as [(A)/(L)]. So we have a new width formula W = [(A)/(L)] for computing W whenever L and A are given. This formula is correct if A = W ·L for every rectangle you meet. Similarly, the length formula L = [(A)/(W)] can be obtained by interchanging the roles of the actors L and W above.

Chapter Sections:  [ 10  Formullas & Shorthand Notation ] [ 10  Changing Calculations ] [ 10. Replacement & Substitution ] [ 10 Find a Number ] [ 10 Formulas as Potential Calculations ]

Next Section 10 Formulas as Potential Calculations

Next Chapter: 11 Why Shorthand