LESSON III. These are simply some suggestions as to how you can analyze problems and convert various numbers to equivalents with which YOU are familiar. In this way you will be able to do most math problems in your head or at least estimate answers accurately enough that, when done on a calculator or computer, you will be fairly sure that that you have produced the correct answer.

[ These are ONLY examples, and fairly random, at that. Their value is in indicating to you what you can do IF you will analyze and simplify and force all problems to within the boundaries of your knowledge - especially by using the fraction/decimal/per cent equivalents from Lesson II. ]

Think in terms of numbers - recognize 25 as exactly the same number as .25, 2500, 2.5, 1/4, 2 1/2 x 10, 1/2 x 50, 5 x 5, 4 x 1/16, 1/4 x 100, 4 x .0625, etc. This gives you the flexibility of using whatever form of the number best fits your particular problem.

Examples: 5 x 5 = 25; 1/2 x 1/2 = 1/4 (EQUIVALENTS!).

25 x 48 = 100 x 1/4 x 48 = 100 x 12 = 1200

15 x 36 = 10 x 1 1/2 x 36 = 10 X (36 + 18) = 10 x 54 = 540

1/4 x 1/4 = 1/16; 25 x 25 = 625 (NUMBERS - not decimals or zeros)

50 / .17 = 50 / 1/6 = 50 x 6 = 300 (ESTIMATE; ans: 294.12)

960 x 69 = 10 x 96 x 11/16 x 100 = 1000 x 66 = 66000 (ESTIMATE; ans: 66,240)

42,000 / 1.76 = 42,000 / 1 3/4 = 42,000 / 7/4 = 42,000 x 4/7 = 6,000 x 4 = 24,000 (ESTIMATE; ans: 23,863.54)

Examples: n 1/2 x n 1/2 = n(n+1) + 1/4; This says that any number and a half times the same number can be calculated by multiplying the number by the next largest number and adding 1/4; so 6 1/2 x 6 1/2 would be 6 x 7 + 1/4 = 42 1/4.

..1 1/2 x ..1 1/2 = ..2 1/4 = ..2.25 (..15 x .15) = ...225)
..2 1/2 x ..2 1/2 = ..6 1/4 = ..6.25 (..25 x .25) = ...625)
..3 1/2 x ..3 1/2 = .12 1/4 = .12.25 (..35 x .35) = .1,225)
..4 1/2 x ..4 1/2 = .20 1/4 = .20.25 (..45 x .45) = .2,025)
..5 1/2 x ..5 1/2 = .30 1/4 = .30.25 (..55 x .55) = .3,025)
..6 1/2 x ..6 1/2 = .42 1/4 = .42.25 (..65 x .65) = .4,225)
..7 1/2 x ..7 1/2 = .56 1/4 = .56.25 (..75 x .75) = .5,625)
..8 1/2 x ..8 1/2 = .72 1/4 = .72.25 (..85 x .85) = .7,225)
..9 1/2 x ..9 1/2 = .90 1/4 = .90.25 (..95 x .95) = .9,025)
.10 1/2 x .10 1/2 = 110 1/4 = 110.25 (.105 x .105) = 11,025)
.11 1/2 x .11 1/2 = 132 1/4 = 132.25 (.115 x .115) = 13,225)
.12 1/2 x .12 1/2 = 156 1/4 = 156.25 (.125 x .125) = 15,625)

E T C... [ DO NOT MEMORIZE A TABLE - LEARN THE CONCEPT!!!! ]

Bart Jones     1128-A Beville Road      Daytona Beach, FL  32114-5769 Ofc:  (386)  252-4366      Alt:  252-4278      Fax:  252-6385 e-mail: Math