The Product Formula Chart Aid: P = A × B

The Product Formula Chart Aid: P = A × B

A Learning and Memorization Aid

A lot of mathematical formulas, basic relationships in physics and other applications are often in the form of:

P = A × B

where P is the product of two factors, A and B.

Examples include:

Distance: distance = velocity × time

Ohm’s Law: power = current × voltage

Newton’s Second Law: force = mass × acceleration

A chart in a shape of a circle (some people use a triangle) can be used to illustrate the relationship between the three variables.  I see charts of this time in various math books and videos applied to many applications.  An example is Ohm's Law as illustrated by Electrician U (skip to https://youtu.be/-oHzc_DbaGw?t=17).

Going across means multiply, while vertically means divide.

P = A × B

A = P ÷ B

B = P ÷ A

Hope you find this helpful,

Eddie

Source:  

Electrician U.  "5 Formulas Electricians Should Have Memorized!"  March 15, 2023.   https://www.youtube.com/watch?v=-oHzc_DbaGw.  Accessed May 27, 2025

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

All posts are 100% generated by human effort.  The author does not use AI engines and never will.

Review: Victor 6500 Loan Calculator, HP 48G Retro Month

Review:  Victor 6500 Loan Calculator, HP 48G Retro Month

Victor 6500 Review

Quick Facts

Company:  Victor

Year Introduced:  about 2010, still in production

Battery:  Solar and 1 AA battery

Digits: 12

Memory Registers:  2: Independent (M) and Grand Total (GM)

Cost: About $20.00 to $25.00 US

Product Page:  https://www.victortech.com/product/6500

It is rare that a desktop calculator features advanced financial or scientific functions, and that is what attracted me to the Victor 6500.  The keys respond quickly which allows for fast typing.   The display has room for 12 large digits which makes reading the display easy.

Features

*  Fix Display Switch: Float, 0, 2, 4, Add Mode

*  Round Setting Switch:  cut (always round results down), 5/4 (regular rounding rules are followed), up (always round up)

*  Time Value of Money - will be discussed next

*  %, Δ%, √

*  Tax Rate:  setting, TAX+, TAX-

*  Double Zero Key

Memory Registers

There are two memory registers:

Independent Memory (M).  This the traditional memory register that comes with most desktop calculators.  Included are M+ and M-.  Recall and clear are combined in one key RCM.

Grand Total (GT).  The grand total memory is activated every time the equals key is pressed.   

Time Value of Money

The Victor 6500 have four finance keys:

Loan = PV

Pmt = Payment

Years = number of years = n * PYR

Int = annual interest rate

The cash flow convention (inflow/outflow) is not followed, all results are positive.  The number of payments per year is set through the P/Y setting.  

What is missing is the FV (future value) key, which leaves out some of the finance problems involving calculating balance or balloon payment.   However, we can still do a lot of calculations on the Victor 6500 fairly easier.  Here are several example calculations.  In these examples, the Victor 6500 is set to 2 Decimal Places with 5/4 rounding mode.

Example 1:  Calculating Payment of a Loan

Loan:  345,000.00

Years: 30

Interest Rate:  3.3%

[ ON/C ] [ ON/C ]

345000 [ Loan ]

30 [ Years ] 

3.3 [ Int ]

[ Pmt ]  returns 1,510.95

Example 2:  Calculating Payment of a Loan with a Down Payment

Loan:  260,000.00 with 15% down

Years: 27

Interest Rate:  3.2%

[ ON/C ] [ ON/C ]

260000 [ - ] 15 [ % ] [ Loan ]

27 [ Years ] 

3.2 [ Int ]

[ Pmt ]  returns 1,019.53

Example 3:  PITI (Payment with Principal Interest Taxes Insurance)

Loan: 300,000.00

Years: 30

Interest Rate: 3.25%

Annual Property Tax: 2,121.00

Annual Property Insurance: 541.00

[ ON/C ] [ ON/C ] [ MRC ] [ MRC ]

300000 [ Loan ]

30 [ Years ]

3.25 [ Int ] 

[ Pmt ] [ M+ ]

2121 [ + ] 541 [ = ] [ ÷ ] 12 [ = ] [ M+ ]

[ MRC ] (once)  

PITI:  1527.45

Verdict

I like the Victor 6500 since it offers a time value of money solver on a desktop calculator form.  I wish Victor would have included the future value variable.   The keys are fast and responsive.  The keyboard is pretty light but also feel stable.  

I am working on posting additional examples for the Victor 6500 in the near future.  

HP 48G Retro Month - July 2021

For the month of July 2021, every Saturday from July 10 to July 31 will have a post on the legendary HP 48G/48GX/48G+ calculator.  

Next post will be on July 10, 2021 (taking the Fourth of July weekend off).   Have a great day and thank you!  

Eddie 

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Fun with the TI-73 Part I: Logarithmic Regression, Percent, Square Root Simplification

 Fun with the TI-73 Part I: Logarithmic Regression, Percent, Square Root Simplification

TI-73 Program:  LNREG - Logarithmic Regression

Introduction:

The program LNREG fits the data to the equation:

y = a * ln x + b

The lists used are:

L_1:  x list  

L_2:  y list

Access L_1 by pressing [ 2nd ] [ STAT ] (LIST), 1.

Access L_2 by pressing [ 2nd ] [ STAT ] (LIST), 2

You can edit lists by pressing [LIST].  

The lower case a and b are from the VARS, Statistics, EQ menu.

Program:

"EWS 2021"

Disp "FIT Y=A LN X +B","USES X=L1,Y=L2:

ln(L_1) → L_1

LinReg(ax+b) L_1,L_2

a → A

b → B

Output(4,1,"A=")

Output(4,5,A)

Output(5,1,"B=")

Output(5,5,B)

Output(6,5,r²)

e^(L_1) → L_1

Pause

Menu("PLOT?","YES",1,"NO",2)

Lbl 1

PlotsOff

FnOff

"A*ln(X)+B"→Y_1

Plot1(xyLine,L_1,L_2,□)

ZoomStat

Lbl 2

Example:

X:  L_1 = {1, 2, 3, 4, 5, 6}

Y:  L_2 = {-1.26, 2.1018, 4.0683, 5.4635, 6.5458, 7.43}

Results:

y = A ln x + B

A = -1.259978557

B = 4.849985251

r^2 ≈ 1

TI-73 Program: PERCENT - Percent Calculations

Introduction:

The program gives the users four options:

1.  Adding tax (plus percent)

2.  Subtracting tax (minus percent)

3.  Percent Change

4.  Percent Total

The percent key divides the amount by 100.  Example:  5% turns to 0.052.

Program:

"EWS 2021"

Menu("PERCENT","TAX+",1,"TAX-",2,"%CHG",3,"%TOT",4)

Lbl 1

Prompt N

Input "X% ",X

N*(1+X%)→Y

Pause Y

Stop

Lbl 2

Prompt N

Input "X% ",X

N*(1-X%)→Y

Pause Y

Stop

Lbl 3

Input "OLD=",O

Input "NEW=",N

(N-O)*100/O→Y

Pause Y

Stop

Lbl 4

Input "PART=",P

Input "WHOLE=",W

100*P/W→Y

Pause Y

Stop

Example:

TAX+:   Add 15% to 19.95

N: 19.95, X%:  15

Result:  22.9425

TAX-:  Subtract 15% from 19.95

N:  19.95, X%:  15

Result:  16.9575

%CHG:  Old (O):  11700, New (N):  15420

Result:  31.79487179

%TOT:  Part (P):  11700, Whole (W):  15420

Result:  75.7548638

TI-73 Program: SQROOT - Simplification Square Root

This program tries to factor √N to A√B.  N, A, and B are integers.

Program:

"EWS 2021"

Disp "√(N)->A√(B)"

Prompt N

iPart(√(N))→X

While X≠0

If fPart(N/X^2)=0

Then

X→A

N/X^2→B

Goto 1

Else

X-1→X

End

End

Lbl 1

Disp "A=",A,"B=",B

Pause

Examples:

N = 88;   √88 = 2√22

N = 1225;  √1225 = 35√1

Notes:

*  There is no ALPHA key for the TI-73 (family).   Text is entered by use of the [ 2nd ] [ MATH ] (TEXT) key sequence.  Letters are selected by using the arrow keys and selecting them with the ENTER key.

*  The underscore character ( _ ) acts like a space.

*  The TEXT has the letters A-Z, _, <, =, >, ≤, ≠, ≥, and the logic functions and, or.  For the question mark character, ?, press [ 2nd ] [ PRGM ] (CATALOG) [ ↑ ] [ ENTER ]. 

* The programming language of the TI-73 is the robust as the TI-83 family (TI-83, TI-83 Plus, TI-84 Plus family, TI-82).  

* The main difference is that results are shown on a separate screen for output.   When a program terminates, the TI-73 returns to the Home screen.  It is necessary to include a Pause at the end to keep the results on the screen.

Stay tuned tomorrow for more programs for the TI-73.  

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Review: Ativa 2-Line Calculator DD-2361

 Review:  Ativa 2-Line Calculator DD-2361

Just the Facts:

Model:  DD-2361 (I was stated in the manual)

Company: Ativa (Office Depot)

Type: Four Function

Battery:  Solar with backup battery LR1130

Logic: Algebraic

Memory Registers: None

Price:  $8.99

A Two Line Screen

The Ativa DD-2361 calculator has a two lines: the top line shows the entered expression.  Each calculation can have up to 79 characters.   The bottom line shows answers, which can have up to 12 characters.  

Functions include the percent function which, works like four function calculators.  

Example:  

Top:  7 x 8 - 2 x 9

Bottom:  38

The order of operations are used.  

The keys on the keyboard are huge and responsive.  Expressions can be edited using left and right arrow keys.  Characters are replaced in editing.  

Verdict

I like the big keys.  The DD-2361 does lack a few key features: square root, an independent memory register, and due to the calculator following the order of operations, parenthesis.  This is one of few two-line four-function calculators where you can buy it a store, and not just online.  

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP Prime: The Percent Function

 HP Prime:  The Percent Function

The Percent Function

The HP Prime has three percent functions.   They are not easily found (through the catalog or in program edit mode, Cmds-More menu).  The functions are:

%

%CHANGE

%TOTAL

% Function

%(x, y)  returns x * y /100.  This returns either x% of y or y% of x.  Due to the communicative multiplication property, you can use the arguments in either order.  

%CHANGE

This the percent change function where the arguments are %CHANGE(old, new).  Formula:  %CHANGE(x, y) = (y - x) / x * 100%

%TOTAL

This calculates the % total given a part and a whole.  Syntax:  %TOTAL(whole, part).  Formula:  %TOTAL(x, y) = y / x * 100%

The program POPTOWN uses the percent functions.  It is a simple game where you invite a certain population to live in a town, and the birth (growth) and death rates are determined by random.

HP Prime Prime Program:  POPTOWN

RESULTS(y,n,g,d,p)

BEGIN

// subroutine

PRINT();

PRINT("Year: "+STRING(y));

PRINT("Population: "+STRING(n));

IF y>0 THEN

PRINT("Growth: "+STRING(g)+"%");

PRINT("Death: "+STRING(d)+"%");

PRINT("Δ%: "+%CHANGE(p,n));

END;

WAIT(0);

END;

// main program

EXPORT POPTOWN()

BEGIN

MSGBOX("You start with 10 

residents, inviting up to 50 

new residents each year.  Can 

growth beat death?");

// 2020-10-24 EWS

// Growth and Death

LOCAL n,y,w,g,d,c,p;

LOCAL v; // number of invites

n:=10;

RESULTS(y,n,g,d,p);

// The game

FOR y FROM 1 TO 5 DO

INPUT({{c,{0,10,20,30,40,50}}},

"Year "+STRING(y),"Invite:");

// all invites move in at the

// beginning of each turn

p:=n;

w:=10*(c-1)+n;

v:=10*(c-1)+v;

g:=RANDINT(5,20);

d:=RANDINT(1,25);

n:=w+IP(%(w,g))-IP(%(w,d));

// empty town scenario

IF n≤0 THEN

MSGBOX("No one survived.");

n:=0; 

END;

RESULTS(y,n,g,d,p);

END;

// End the game results

PRINT("Final Results");

PRINT("Population Change: "+

STRING(n-10));

PRINT("Invited: "+STRING(v));

PRINT("Percent Invite: "+

STRING(ROUND(%TOTAL(n,v),2))

+"%");

END;

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

A Choice of Discounts

A Choice of Discounts

Situation

We are ready to purchase two items.  Let A be the cost of the more expensive item, while B is the cost of the less expensive item (A > B).  We have two coupons:

Coupon 1:  Take 10% off of all purchases  (10% off the cost of both A and B)

Coupon 2:  Take 20% off of the most expensive item  (20% off of A, B remains at full price)

The store allows for only one coupon to be used per transaction.  Which coupon gives us the best benefit?  Let's assume that we are only buying two items.

We will not worry about sales tax in this situation.

Calculating the Costs After Discounts

Using Coupon 1:  Let T1 be the total cost using coupon 1.

T1 = (100% -10%) * (A + B)
T1 = 90% * (A + B)
T1 = 0.9 * (A + B)

Using Coupon 2:  Let T2 be the total cost using coupon 2.

Here, A is more expensive, so:

T2 = (100% -20%) * A + B
T2 = 80% * A + B
T2 = 0.8 * A + B

In summary, the total costs are:

T1 = 0.9 * (A + B)
T2 = 0.8 *A + B

Comparing the Two Coupons

Is there a price point of both A and B where the total costs of the two items is the same?  This occurs when T1 = T2.

T1 = T2

0.9 * (A + B) = 0.8 * A + B
0.9 * A + 0.9 * B = 0.8 * A + B
0.1 * A + 0.9 * B = B
0.1 * A = 0.1 * B
A = B

The costs are the same when the cost of both items are the same.

But we assume that A > B.    So, either T1 will be more or T2 will be more.  To determine this, we will need to perform a subtraction.  Let's pick T1 - T2.

If T1 -T2 > 0, then T1 costs more and using the second coupon, 20% of the more expensive item,  is preferable.

If T1 - T2 < 0, then T2 costs more and using the first coupon, 10% of both items, is preferrable.

T1 - T2
= 0.9 * A + 0.9 * B - (0.8 * A +  B)
= 0.1 * A - 0.1 * B
= 0.1 * (A - B)

Since A represents the cost of the more expensive item, A > B, and A - B > 0.  Therefore 0.1 * (A - B) > 0 and T1 > 0.   The second coupon is preferable.

Case Studies

A = $29.99,  B = $24.99:  T1 = $49.48,  T2 = $48.98  (not much difference)

A = $29.99,  B = $13.99:  T1 = $39.58,  T2 = $37.98

A = $29.99, B = $5.99;  T1 = $32.38,  T2 = $29.98  (difference between T1 and T2 increase as discrepancy of costs increase)

Hopefully this helps on all of our future shopping trips,

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Review: Texas Instruments TI-15

Review: Texas Instruments TI-15

Website:  https://education.ti.com/en/us/products/calculators/elementary-calculators/ti-15-explorer/tabs/overview#tab=specifications

Production:  Since 2000

Power: Solar with CR2025 backup

Price: Depending on where you shop, $14-$22. I won one as a door prize. 

I won a TI-15 as a door prize (among a Raspberry Pi Zero and HP 49G) on HHC 2016.   

A Curious Calculator 

This is a curious calcualtor, destined for elementary school students.  More advanced than a regular four-function calculator yet it isn't a scientific calculator.  To start, the TI-15 operates algebraically, like most scientific calcualtors.  That is, you enter an expression, press [ Enter = ], using the order of operations.  The TI-15 also features a power key [ ^ ], a pi key [ π ], and set a fraction keys.  Furthermore, pressing [ π ] inserts the π the character instead of its approximation (3.141592653590).  Any results in the form of n * π, where n is an integer (like 3 π ) as such.  Converting answers to their decimal approximation will require pressing the [ F <-> D ] key. 

For something really unique, try the [>%] key. It converts decimals to percent form (0.19 to 19%). 

Fractions 

Fractions are a major feature of the TI-15.  Entering fractions require entering the part number and the appropriate button indicate which part to be entered.  For example: to enter 3 1/4, press 3 [Unit] 1 [n/] 4 [/d].  The entire two-line screen is used to display fractions.  Fractions can be simplified, converted to decimal approximation, and conversions between mixed and improper forms are available.  After simplifying the fraction, you can press [Fac] to display the factor used to simplify fractions. 

For example, enter 105/220.  Assume that manual simplification mode is set.  105 [n/] 220 [/d] [ Enter = ]. Press [Simp] [Enter=] to get 21/44. Pressing [Fac] returns 5, meaning a factor of 5 was used to reduce 105/220 to 21/44. 

Programming?

The TI-15 is programming calcualtor.  Well, sort of. The two programming keys [Op1] and [Op2] allows for storing a single operation (+, -, *, ÷, Int ÷ , ^) and single number operation.   Testing the TI-15, I couldn't get it work beyond this limitation. 

Place Value

Results can be rounded to 3 decimal places by pressing [Fix], then [1], [0.1], [0.01], [0.001] for 0, 1, 2, or 3 places respectively.  That is not surprising.  However, this might be one of the few calculators (if not only) to a round to tens, hundreds, or thousands mode. 

Problem Solving and Quiz

The elementary calculator has a quiz mode with three difficulty levels of basic arithmetic.  You can also write your own problems, replacing a number or operation with a ?, and try to quiz yourself.  

Review: The Verdict

The TI-15 is available only online (that I know of). I think it is an interesting and curious calculator to add to the collection, and can be enjoyable for those who want more options but are intimidated or don't desire by scientific calculators.  The keyboard is nice and big, I wish the screen was bigger but it is very readable. 

I wish the basic four-function calculators would consider adding a π and power button to their calculators.  If you want a TI-15, shop around.  

Eddie

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