Chapter 10
Describing & Changing Calculations

Previous Section: 10 Finding Number, Using formulas backwards

4  Formulas as Potential Calculations

We have discussed or described two recipes or formulas for calculating areas and volumes without doing any arithmetic. Given the heights, lengths and widths involved, we could compute the areas and volumes. That is easy to do by hand. It is also easy or easier to use a calculator to do the arithmetic for us. Think in terms of potential calculations: formulas describe calculations that could be done (or avoided) as needed. We can postpone calculations, unless we need to do them. Note that when you see a formula for the first time, you may need to practice using it.

5  Further Readings

The following books (and others) cover ideas not included above.

1. Mathematics Made Simple by A. Sperling and M. Stuart, Doubleday 1981 edition, ISBN 0-385-17481-0.
2. Algebra, the Easy Way by D. Downing, 1989, Barron's Educational Series, Inc, 250 Wireless Boulevard, Hauppauge, New York 11788. ISBN 0-8120-4194-1.
3. How to Solve Algebra Word Problems by W. A. Nardi, Simon & Shuster Inc, Gulf+Western Building, One Gulf + Western Plaza, New York, NY 10023. ISBN 0-6680-06574-5.

6  Two Notions of What is a Variable

6.1  With and Without Symbols

Numbers and quantities which may change or vary are said to be variables. This first notion of a variable does not involve or require the presence of shorthand notation (symbols) to represent the number or quantity in question.

But there is a second notion of a variable employed in mathematics. A symbol or letter which represents a number or quantity is also be called a variable if the number or quantity concerned may change or vary, that is if the number or quantity represented is a variable according to the first notion. While a symbol or letter may be called a variable, not all variables are given or represented letters or symbols. We can talk about numbers and quantities without employing a written symbol for each one.

Remark.   A change may be required in mathematics texts and dictionaries to recognize both notions and not just the second.

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

Next Chapter: 11 Why Shorthand