Calculator Tricks - Part 5

Welcome to Part 5 of Calculator Tricks

Part 5 will cover:
* Solving 2 by 2 equations
* Finding roots of the quadratic equations

The above tasks will be accomplished by using a simple calculator. That means we have only the arithmetic functions, square roots, percents, and memory to work with.


Solving 2 by 2 Equations

Suppose we are assigned the task solving for x and y:

Ax + By = E
Cx + Dy = F

This is a system of two simultaneous equations with two unknowns, x and y. We can use matrices to visualize this problem:

Take the inverse of the coefficient matrix and left multiply both sides to get:

We can find the inverse of the coefficient matrix by:

The product A × D - B × C is called the determinant. Finally, we solve for x and y:

Now that we have our general solutions, how do we tackle this on a simple calculator?

2 × 2 System of Equations

We only have one memory in the register to work with. Here is a strategy:

1. Calculate the determinant. Keystrokes: A × D - B × C =. Note this number down on paper. The calculator's memory will be required to find x and y.

2. Solve for x. Use the sequence:
MC
D × E = M+
B × F = M-
MR ÷ determinant =

3. Solve for y. Use the sequence:
MC
A × F = M+
C × E = M-
MR ÷ determinant =

---------------
Example: Solve the System

2x + 3y = -1
x - 3y = 2

We have A = 2, B = 3, C = 1, D = -3, E = -1, F = 2

Step 1:
Keystrokes:
MC
2 × 3 +/- = M+
3 × 1 = M-
MR

The determinant is -9. Write this result down.

Step 2:
Keystrokes:
MC
3 +/- × 1 +/- = M+
3 × 2 = M-
MR ÷ 9 +/- =

x ≈ 0.3333333

Step 3:
Keystrokes:
MC
2 × 2 = M+
1 × 1 +/- = M-
MR ÷ 9 +/- =

y ≈ -0.5555555

----------------

Solving Quadratic Equations

Let's tackle on how we find the roots of the equation:

Ax^2 + Bx + C = 0

Our focus for this blog entry will be finding real roots.

Referring to the quadratic formula:

We can derive our algorithm for finding both roots:

1. Calculate the discriminant. Store this result in the calculator's memory.

Keystrokes:
MC
B × = M+
4 × A × C = M-

2. Find the first root:

Keystrokes:
MR √ - B ÷ 2 ÷ A =

3. Find the second root:

Keystrokes:
MR √ +/- - B ÷ 2 ÷ A =
---------------
Example: Find the roots of

x^2 + 5x - 6 = 0

Let A = 1, B = 5, and C = -6

Step 1: Discriminant
MC
5 × = M+
4 × 1 × 6 +/- = M-

Discriminant = 49

Step 2: First Root
MR √ - 5 ÷ 2 ÷ 1 =

One of the roots is x = 1.

Step 3: Second Root
MR √ +/- - 5 ÷ 2 ÷ 1 =

The other root is x = -6


I hope this series is helpful. This series has showed how to make various calculations with a simple calculator: arithmetic procedures including fractions, area of a circle, distance between two points, calculating the total shopping bill, solving 2 x 2 simultaneous equations, and solving quadratic equations.

Until next time,

Eddie


This blog is property of Edward Shore, 2012.

Calculator Tricks - Part 4

Welcome to Part 4 of Calculator Tricks. This is series is where accomplish mathematical tasks with a use of a regular, simple calculator. Part 4 will cover:

* Dealing with Percents
* Shopping
* Simple Interest

Dealing with Percents

With most calculators, if you have to add tax and subtract discounts, you can just execute the operation directly.

However, on some calculators, like the Casio SL-300VC, require a different sequence:
× n % + (to add) and × n % - (to subtract).

Here is how I prefer to work with percents, and it avoids the percent key altogether.

---------------
Add Percent

Let A be the number you want to add N% percent to it. In a shopping application, N represents the sales tax. In construction, N can be thought be allowance for waste.

A + N%
= A + (A × N/100)
= A × (1 + N/100)

Keystrokes: N ÷ 100 + 1 × A
---------------
Example: Add 10% to 19.95.

Keystrokes: 10 ÷ 100 + 1 × 19.95

Result: 21.945

(On most calculators, 19.95 + 10 % works too)
---------------
Subtract Percent

Let A be the number you want to subtract N% from. In terms of shopping, N represents a discount.

A - N%
= A - (A × N/100)
= A × (1 - N/100)

Keystrokes: N ÷ 100 +/- + 1 × A
---------------
Example: Subtract 10% from 19.95.

Keystrokes: 10 ÷ 100 +/- + 1 × 19.95

Result: 17.955

(On most calculators, 19.95 - 10 % works too)
---------------

Shopping

Ever though what your bill would be as you shop? This section will show you what the potential bill will be and hopefully will lead you to make smart shopping decisions, and keep in budget.

Approach:
1. Clear Memory. We will use the memory register to keep track of our purchases.
2. Determine whether the item is subject to sales tax. You can press MR at any time to get a subtotal.
3. Add the total.
4. *If all of your items are subject to sales tax, add sales tax to the total.

If your purchases are "mixed", buying both non-taxable and taxable items (grocery store comes mind):

If the item or service is not subject to sales tax, use the keystroke sequence price M+ .

If the item or service is subject to sales tax, use the keystroke sequence tax factor × price M+ .

where tax factor = (1 + tax%/100)


In California, where I live, generally food, grocery items, and most services are generally not subject to sales tax, while sales of tangible goods are subject to sales tax.


Let's illustrate this strategy by a few examples.
---------------
Example 1: We are at a hardware store and purchasing the following items:

Hammer: $19.99
Nails: $3.95
Staple Gun: $14.95
Measuring Tape: $3.99

All items are subject to 8.5% sales tax.

Well, since we are dealing with just taxable purchases, we can total everything and add sales tax at the end.

Keystrokes:
MC
19.99 M+
3.95 M+
14.95 M+
3.99 M+
8.5 ÷ 100 + 1 = × MR =

Total: $46.52
---------------
Example 2: From an office store, we are purchasing:

Ream of 500 sheets of paper: 3 at $8.99 each
Pack of pencils: $2.99
Pack of pens: $3.95
Calculator: 2 at $9.95 each

All items are subject to 8.5% sales tax. In this case, we can add the sales tax at the end.

Keystrokes:
MC
3 × 8.99 = M+
2.99 M+
3.95 M+
2 × 9.95 = M+
8.5 ÷ 100 + 1 = × MR =

Subtotal: $53.81
With Sales Tax: $58.38
---------------
Example 3: At a grocery store, we are purchasing:

Bag of Grapes: $2.45
Apples: 5 at 99¢ each
Bananas: 6 at 24¢ each
Bread: $4.09 with a 5% discount coupon
Water: 2 gallons at $1.09 each
Box of Ziploc Bags: $3.99 with a 50¢ coupon

Only the Ziploc bag is subject to 8.5% sales tax. Assume coupons take affect immediately (before sales tax). Here we must use the "mixed purchases" strategy. Enter $3.49 for the Ziploc bags.

MC
2.45 M+ (grapes)
5 × 0.99 = M+ (apples)
6 × 0.24 = M+ (bananas)
5 ÷ 100 +/- + 1 = × 4.09 = M+ (bread)
2 × 1.09 = M+ (water)
8.5 ÷ 100 = + 1 = × 3.49 = M+ (Ziploc bags)
MR (final total)

Total bill: $18.69
---------------


Simple Interest

The simple interest formula is:

I = P × R% × T

I = amount of interest
P = amount of the principal
R% = annual interest rate (as expressed as a decimal)
T = time, in years

The total amount paid is principal and interest, in other words, P + I.

---------------
Example 1: A bank makes a short term loan to Fred and Suzy of $1,000. The bank charges 9.6% interest on short term loans. Fred and Suzy have to pay the loan in two months. If Fred and Suzy wait for the two months, how much interest have they paid?

We are looking for I. We have the following:
P = principal = 1000
R% = annual interest rate = 9.6/100
T = time = 2 months * 1 year/12 months

Note have to convert months to years. So the interest paid is:

Keystrokes:
1000 × 9.6 ÷ 100 × 2 ÷ 12 =

The total interest paid is $16.
---------------
Example 2: Terrell is looking over his credit card bill. The balance is $1,540.29. His credit card charges an annual rate of 15.99%. Terrell is planning to make a $300.00 payment. Assuming Terrell does not use his credit card for the next month, what will be his balance?

Variables:
P = $1,540.29 - $300.00 = $1,240.29
R% = 15.99%
T = 1/12 (1/12 of a year)

Keystrokes:
MC (Clear memory)
1540.29 - 300 = M+ (Subtract payment, interest will accrue on $1,240.29.)
MR × 15.99 ÷ 100 ÷ 12 = (Months interest: $16.53)
M+ MR (Add interest to memory)

Terrell's new balance next month would be $1,256.82.
---------------
Example 3: Lita deposited $500 in a Double Your Money CD. The bank will pay her $1,000 when the CD doubles in value. The bank pays 7.5% interest on these deposits. How long will Lita wait?

This time we are looking for T.

Variables:
P = $500
R% = 7.5%
I = $500

Why is I = $500? Lita deposits $500 and will wait for her account to grow $500, to earn $500 in interest. Solving for T, time:

T = I / (P × R%/100) = I × (P × R%/100)^-1 = (P × R%/100)^-1 × I

Keystrokes:
500 × 7.5 ÷ 100 =
÷ ÷ = (37.5^-1)
× 500 = (Display: 13.333333)

So it takes 13 1/3 years to double Lita's CD. She may want to rethink this investment.
---------------

So this wraps up Part 4 of our Calculator Tricks series. Coming up in Part 5 we will tackle two common algebra problems.

Eddie

This blog is property of Edward Shore, 2012.

Calculator Tricks - Part 3

Welcome to Part 3 of the Calculator Trick series using the Simple Calculator. This part covers:

* Squaring Numbers
* Reciprocals
* Geometric Applications

Just a reminder, a simple calculator has the following functions: arithmetic (+, -, ×, ÷), square root (√), percent (%), and memory (M+, M-, MR, MC). If your calculator has a MRC clear, this means press MRC once to recall memory, twice to clear it.

Squaring Numbers

---------------
To square a number, use the following key sequence:

× =
--------------
Example 1: 7^2

Keystrokes:
7 × =
---------------
Example 2: √(3^2 + 4^2) = 5

Use the memory keys to solve this problem. Squaring a number is multiplying a number by itself. Apply the square root last.

Keystrokes: MC (Again, always a good idea to clear memory to start)
3 × = M+ (3^2 = 9)
4 × = M+ (4^2 = 16)
MR (3^2 + 4^2 = 25)
√ (√25 = 5)
----------------

Reciprocals

---------------
To find the reciprocal of a number, use the following key sequence:

÷ ÷ =
(Yes, press the division key twice)
---------------
Example 1: 1/7 ≈ 0.142857

Keystrokes: 7 ÷ ÷ =
---------------
Example 2: 1/(1/5 + 1/3.2) ≈ 1.9512195

Strategy: Tackle the denominator first. Of course, anytime you have mixed operations, chances are you will be using the memory register.

Keystrokes:
MC
5 ÷ ÷ = M+ (1/5 = 0.2)
3.2 ÷ ÷ = M+ (adding 1/3.2 = 0.3125)
MR (1/5 + 1/3.2 = 0.5125 )
÷ ÷ = ( 1/(1.5 + 1/3.2) ≈ 1.9512195)
---------------

Geometric Applications

Area of the a Circle:
A = π r^2

where r is the radius and π is the constant pi. In this series, I am working with an 8 digit calculator, I will use the approximation π ≈ 3.1415927. I can use less digits, but I want as much accuracy as possible.

---------------
Area of a Circle: A = π r^2

Keystrokes: radius × = × 3.1415927 =
---------------
Example: Find an area of a circle with a radius of 14.5 inches.

Keystrokes: 14.5 × = × 3.1415927 =

The area is approximately 660.51986 square inches.
---------------


Distance between two Cartesian points (x1, y1) and (x2, y2):
√((x2 - x1)^2 + (y2 - y1)^2)

---------------
Distance between (x1, y1) and (x2, y2):

Keystrokes: MC
x2 - x1 = × = M+
y2 - y1 = × = M+
MR √
---------------
Example: Find the distance between the points (5,6) and (1,9).

Note: (x1, y1) = (5, 6) and (x2, y2) = (1, 9)

Keystrokes: MC
1 - 5 = × = M+ (Display: 16 M)
9 - 6 = × = M+ (Display: 9 M)
MR √ (Display: 5 M)

The distance between the points (5, 6) and (1, 9) is 5 units.
---------------

Right Triangles

Area = 1/2 × A × B

Pythagorean Theorem: H^2 = A^2 + B^2

---------------
With A = 3.9 inches, B = 2.4 inches. Find the area and the hypotenuse (H).

Area:
Keystrokes: 3.9 × 2.4 ÷ 2 =

The area is 4.68 square inches.

Finding the Hypotenuse:
Keystrokes: MC 3.9 × = M+
2.4 × = M+
MR √

The hypotenuse is approximately 4.5793012 inches.
---------------

Next time in Part 4, we will cover shopping and short-term loans with simple interest.

Eddie


This blog is property of Edward Shore, 2012.

Calculator Tricks - Part 2

Fractions

Welcome to Part 2 of the Calculator Tricks series. We are using a simple ("four banger" calculator) to tackle common mathematical problems. If you missed Part 1,
you can check it right here by clicking on this link.

Simple Fractions

Simple calculators do not have the ability to display numbers as fractions, just their decimal equivalents.

Here are the decimal equivalent of some fractions that are handy to remember:

1/8 = 0.125
1/4 = 0.25
1/3 ≈ 0.3333333
3/8 = 0.375
1/2 = 0.5
5/8 = 0.625
2/3 ≈ 0.6666667
3/4 = 0.75
7/8 = 0.875

Remember the order you press the keys is critical, since the simple calculator operates in Chain Mode.

This blog assumes that you are working with an 8-digit calculator.

1. Adding and Subtracting Fractions

Adding and subtracting fractions will require the use of memory. Remember to always clear memory before beginning a calculation.

---------------
Adding Fractions: A/B + C/D

Keystrokes:
MC (clear memory because we will need it)
A ÷ B = M+
C ÷ D = M+
MR
---------------
Subtracting Fractions: A/B - C/D

Keystrokes:
MC
A ÷ B = M+
C ÷ D = M-
MR
---------------
Example 1: 4/11 - 3/99 = 1/3 ≈ 0.3333333

The decimal equivalent (0.3333333 on a 8-digit calculator) is what we are after in this example.

Keystrokes:
MC (Yes, I can't emphasize clearing the memory at the start enough!)
4 ÷ 11 = M+
3 ÷ 99 = M-
MR (Display: 0.3333333 M)
--------------
Example 2: 1/7 + 3/8 - 4/9 = 37/504 ≈ 0.073412698

We can use this technique to add and subtract more than two fractions.

Keystrokes:
MC
1 ÷ 7 = M+ (adding 0.1428571)
3 ÷ 8 = M+ (adding 0.375)
4 ÷ 9 = M- (subtracting 0.4444444)
MR (Display: 0.0734127 M)

Depending on the calculator the last digit may be rounded or not. This result is correct to eight decimal places.

2. Multiplying and Dividing Fractions

Let's multiply the fractions A/B × C/D. Using some algebra, we can simplify this expression.

A/B × C/D
= (A × C)/(B × D)
= (A × C)/B × 1/D
= (A × C) ÷ B ÷ D

---------------
Multiplying Fractions: A/B × C/D

Keystrokes: A × C ÷ B ÷ D =

Multiply the numerators, divide the denominators.
---------------
Example: 4/7 × 2/3 = 8/21 ≈ 0.3809524

Keystrokes: 4 × 2 ÷ 7 ÷ 3 =
---------------

Let's divide the fraction A/B by C/D. (Calculate A/B ÷ C/D) To divide number by a fraction, multiply it by the fraction's reciprocal.

A/B ÷ C/D
= A/B × D/C
= (A × D)/(B × C)
= (A × D)/B × 1/C
= (A × D) ÷ B ÷ C

----------------
Dividing Fractions: A/B ÷ C/D

Keystrokes: A × D ÷ B ÷ C =
---------------
Example: 7/9 ÷ 2/5 = 7/9 × 5/2 = 35/18 ≈ 1.9444444

Keystrokes: 7 × 5 ÷ 9 ÷ 2 =
----------------

Mixed Fractions

A strategy is to to covert mixed fractions to simple (improper fractions) first.

Adding Mixed Fractions

For the mixed fraction A B/C is converted into the simple fraction (A × C + B)/C. Adding two mixed fractions will require the use of the memory register.

---------------
Adding Mixed Fractions:

A B/C + D E/F = (A × C + B)/C + (D × F + E)/F

Keystrokes: MC
A × C + B ÷ C = M+
D × F + E ÷ F = M+
MR
---------------
Example: 8 1/9 + 7 3/5 = 15 32/45 ≈ 15.711111

Keystrokes: MC
8 × 9 + 1 ÷ 9 = M+
7 × 5 + 3 ÷ 5 = M+
MR
---------------

Multiplying Mixed Fractions

Unlike multiplying simple fractions, multiplying mixed fractions will require the use of memory. We can get a form for an algorithm by simplifying.

A B/C × D E/F
= (A × C + B)/C × (D × F + E)/F
= ((A × C + B) × (D × F + E))/(B × C)
= ((A × C + B) × (D × F + E)) ÷ B ÷ C

---------------
Multiplying Mixed Fractions

A B/C × D E/F = ((A × C + B) × (D × F + E)) ÷ C ÷ F

Keystrokes:
MC
A × C + B M+
D × F + E =
× MR =
÷ B ÷ F
---------------
Example 1: 4 1/2 × 8 1/3 = ((4 × 2 + 1) × (8 × 3 + 1)) ÷ 2 ÷ 3 = 37.5

Keystrokes:
MC (Start with the memory cleared!)
4 × 2 + 1 = M+ (Store 4 × 1 + 2 = 9 in memory)
8 × 3 + 1 = (Display: 25 M)
× MR = (numerator is done, Display: 225)
÷ 2 ÷ 3 = (no divide by the denominators)

The display should be 37.5 (with the memory indicator). This is a complex algorithm, so it will take some practice. Let's do another example.
---------------
Example 2: 5 5/9 × 16 2/3 = ((5 × 9 + 5) × (16 × 3 + 2)) ÷ 9 ÷ 3 ≈ 92.59259

Keystrokes:
MC (Start with the memory cleared!)
5 × 9 + 5 = M+ (Store 4 × 1 + 2 = 50 in memory)
16 × 3 + 2 = (Display: 50 M)
× MR = (numerator is done, Display: 2500 M)
÷ 9 ÷ 3 = (no divide by the denominators)

The display should have 92.59259.
---------------

In the next example we will add and multiply mixed fractions. Be willing to write immediate results on a note pad with complex problems.

---------------
Example 3:
4 1/8 + 3 3/7 × 6 2/3 = 1511/56 ≈ 26.982143

The Order of Operations says we must multiply the mixed fractions first. However, we only have one memory register, and we don't have the ability to "switch" whatever is in the display with memory. Tackling this problem requires a plan. Here is one way:

1. Change 4 1/8 into a fraction and write it down.
2. Multiply the mixed fractions 3 3/7 × 6 2/3.
3. Add the resulting decimal equivalent of 4 1/8 to the result obtained from step 2.

Step 1 Keystrokes:
4 × 8 + 1 ÷ 8 =
Note the result, which is 4.125. Don't store this number in memory, but on a notepad.

Step 2 Keystrokes:
MC
3 × 7 + 3 = M+ (Display: 24 M)
6 × 3 + 2 = (Display: 20 M)
× MR = (Display: 480 M)
÷ 7 ÷ 3 = (Display: 22.857142 M)

Step 3 Keystrokes:
Add 4.125 obtained from step 1 to 22.857142 obtained from step 2.
+ 4.125 = (Display: 26.982142 M)

We have arrived at our result.

The lesson here is to plan your calculation.

Another strategy to calculate 4 1/8 + 3 3/7 × 6 2/3 is to change all fractions to their decimal equivalents first, noting the decimal equivalents on paper. Let's see how this works out:

1. Change each mixed fraction to their decimal equivalent.
2. Complete the calculation.

Step 1 Keystrokes:
4 × 8 + 1 ÷ 8 = (4 1/8 = 4.125)
3 × 7 + 3 ÷ 7 = (3 3/7 ≈ 3.4285714)
6 × 3 + 2 ÷ 3 = (6 2/3 ≈ 6.6666666)

Now we have 4.125 + 3.4285714 × 6.6666666

Step 2 Keystrokes:
3.4285714 × 6.6666666 + 4.125 =
Result: 26.982142


The next time we meet, we will work with square numbers, reciprocals, and some geometry.

Eddie


This blog is property of Edward Shore, 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.

Eddie

---------------

Introduction

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

Keystrokes:
MC
A × B = M+
C × D = M+
MR
---------------
Example: 4 × 1.95 + 3 × 0.99 = 10.77

Key:
MC
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

Keystrokes:
MC
A × B = M+
C × D = M-
MR
---------------
Example: 4 × 8.25 - 3 × 1.95 = 27.15

Key:
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,

Eddie



This blog is property of Edward Shore, 2012.