Thursday, October 11, 2012

Calculator Tricks - Part 1

First of all, I am home taking care of my dad today. He's doing fine, recovering from surgery.

I also want to thank everyone who reads this blog and leaves comments. I appreciate the input and conversation.




Don't have a scientific calculator and only have a simple calculator with you? Interested in maximizing the abilities of a simple calculator? Want to impress your friends and co-workers? This series is for you.

What do I mean by a simple calculator? it is the calculator that you find everywhere, not just produced by the big calculator manufacturers Hewlett Packard, Texas Instruments, Sharp, and Casio, but as a novelty item from companies with almost any color or design you like. If you prefer, there are thousands of calculator apps on almost any cell phone, tablet, or iPod Touch. I refer to this type of calculator as a "four-banger" because it's primary functions are the arithmetic functions (+, -, ×, ÷).

Part 1 will cover:

* Chain Mode
* The Memory Keys
* Arithmetic Operations

Chain Mode

I estimate that 99% of simple calculators operate on chain mode. That is calculations take place as you enter them, without regard to the Order of Operations. You may remember the expression "My Dear Aunt Sally" or it's expanded version "Please Excuse My Dear Aunt Sally" as a mnemonic for the Order of Operations.

Order of Operations:
Please (everything in Parenthesis gets priority)
Excuse (Exponents, roots, [sine, cosine, tangent, logarithm])
My Dear (Multiplication, Division)
Aunt Sally (Addition, Subtraction)

Here is how to know whether your calculator is operating in Chain Mode:

Type, in order: 4 + 2 × 3 =

Now using the proper order of operations, 4 + 2 × 3 = 10. However, calculators in chain mode don't "know" the order of operations. In that case, that calculator completes 4 + 2 first before multiplying the result by 3, giving a result of 18.

So if you type 4 + 2 × 3 = , in that order, and get 18, your calculator operates in Chain Mode. This means we have to manually take the Order of Operations into account to ensure we get the correct answer of 10.

One way to do this is rearrange the expression to 2 × 3 + 4. Typing the expression in this order will give us the correct answer, 10.

For this series, we will work with calculators operating in Chain Mode, which covers about 95% of simple calculators.

The Memory Keys

The simple calculator has four memory operations:
M+: Add whatever is in the display to Memory.
M-: Subtract whatever is in the display from Memory.
MR: Recall the contents of Memory.
MC: Clears the contents of Memory.

Often, you will see the key MRC. Press this key once to recall the contents of memory, twice to clear it.

For this series, I will keep MR and MC separate. Just remember if you are working with the MRC key, pressing MRC twice will clear memory.

The memory register is a key to advanced calculations on a simple calculator. One, it can help keep our calculations in proper operation. Second, it can store a number for later use.

Your calculator will give an indicator ("M" or "MEMORY") whenever a number other than zero is stored in memory. The memory is consider cleared when 0 is stored and the calculator does not display a memory indicator.

On to the Arithmetic Section.

Arithmetic Section

Let's tackle some common arithmetic calculations with the simple calculator to get the correct answers. Remember the order you press the keys is critical, since the simple calculator operates in Chain Mode.

For each section, I will give a proper keystroke to tackle the problem. Then I will give an example. Each capital letter (A, B, C, etc.) represents a variable.

1. A × B + C

This is a fairly simple expression. Just keep "Please Excuse My Dear Aunt Sally" in mind and you're gold.

A × B + C

Keystrokes: A × B + C =
Example: 8 × 6 + 3 = 51

Keystrokes: 8 × 6 + 3 =

The result is 51, which the correct result with the Order of Operations.

2. A × B + C × D

Now we have two multiplications to do before the addition. This is where the memory keys (M+, M-, MR, MC) come in handy. Before you start any operation involving memory, clear it first! Remember if your calculator has a MRC key, press it twice to clear memory.

A × B + C × D

A × B = M+
C × D = M+

Example: 4 × 1.95 + 3 × 0.99 = 10.77

4 × 1.95 = M+
(Display: 7.8 M)
3 × .99 = M+ (Display: 2.97 M)
MR (Display: 10.77 M)

3. A × B - C × D

This is similar to problem 2.

A × B - C × D

A × B = M+
C × D = M-

Example: 4 × 8.25 - 3 × 1.95 = 27.15

MC (always want to clear memory before beginning)
4 × 8.25 = M+ (Display: 33 M)
3 × 1.95 = M- (Display: 5.85 M)
MR (Display: 27.15 M)

The answer is 27.15.

4. A × (B + C)

Note the parenthesis around the addition of B and C. This time we work the addition first.

A × (B + C)

Keystrokes: B + C × A
Example: 8 × (6 + 3) = 72

Keystrokes: 6 + 3 (Display: 9)
× 8 = (Display: 72)

5. (A + B) ÷ (C + D)

A strategy is to work the denominator first, store the result in memory. Then work left to right.

(A + B) ÷ (C + D)

Keystrokes: MC
C + D = M+
(store denominator in memory)
A + B
÷ MR =

Example: (48 - 16) ÷ (3 + 1) = 8

Keystrokes: MC
3 + 1 = M+
(4 is stored in memory)
48 - 16 (working the numerator)
÷ MR = (divide by memory)

Display: 8 M

This ends Part 1 of our series. In part 2, we will work with fractions. Thanks,


This blog is property of Edward Shore, 2012.

1 comment:

Σ(1 / (a^n)) from n=1 to m

 Σ(1 / (a^n)) from n=1 to m This blog entry covers the sum of the series: Σ[1 / (a^n), n=1 to m] with n and m positive integers Specific Cas...