Saturday, April 11, 2020

Casio fx-CG 50 Update and Mental Math: Squaring a Number Ending in 5

Casio fx-CG 50 Update and Mental Math:   Squaring a Number Ending in 5

Casio fx-CG 50 Update

Casio released an update to the operating software for the fx-CG 50, version 3.40.   This update, among other things, expands the number of commands in Casio's Micropython.

There is a new module casioplot module has commands to draw pixels in any color and strings. 

The link to get the updated software is here:  https://edu.casio.com/download/index.php

Click on Graphing Models.

I have not had a chance to try the new drawing commands yet, it's on my list of things to do. 

Mental Math:   Squaring a Number Ending in 5

Squaring a positive integer whose last digit is 5 will result in the answer whose last digits are 25.

Why is this true?

Let n be a positive integer whose last digit is 5.   (n = 15, 25, 35, etc.). 

Let m = n - 5, then n = m + 5.   Note that m is a multiple of 10.

Then:

n^2 = (m + 5)^2
= m^2 + 2 * m * 5 + 25
= m^2 + 10 * m + 25
= (m^2 + 10 * m) + 25
= m * (m + 10) + 25

Since m is a multiple of 10, m^2 and 10 *  m are multiples of 100.  Because of this fact, squaring integers ending in 5 is used in mental math.

Examples

Example 1:  Calculate 45^2.

n = 45 = 40 + 5    (m = 40)
= (40 + 5)^2
= 40 * (40 + 10) + 5^2
= 40 * 50 + 25
= 2000 + 25
= 2025

45^2 = 2025

Example 2:  Calculate 165^2

n = 165 = 160 + 5    (m = 160)
= (160 + 5)^2
= 160 * (160 + 10) + 25
= 160 * 170 + 25
=  27200 + 25
=  27225

Eddie

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