Math Calculators

These days math calculators require electricity or are battery-powered, some are even accessible on your smartwatches and phones. But this wasn't how it had always been.

Before the electronic calculator was invented, a more primitive calculator, the slide rule introduced around 1960, was commonly used. It consisted of a slat of wood called the slide that could be moved in and out of a reinforced pair of strips. Both the slide and the outer slats had calibrated numerical scales. 

Eventually, a manual calculator called the abacus was introduced. The abacus is still being used by students around the world. Like the slide rule, the abacus required no source of power as well, and calculations were done using beads to denote numbers. Both these primitive devices required a learning curve to become proficient with these calculators.

By the 1970s, we were able to perform math problems with much more complexity as calculators became more advanced. Unlike the older calculators, modern-day calculators are designed to allow multi-step calculations. 

Calculators have got better in the last few decades, thanks to the technological advancements. Today, we have a lot of different brands and calculators to choose from depending on our needs. Let’s look more into the different types available:

Basic Calculators

The most common and basic calculator. It is used to carry out basic arithmetic operations like addition and subtraction. 

Many basic calculators have 5 signs ( +, -, x, ÷, =). Some calculators may even have the % sign to calculate percentages. 

Here are some examples to show the calculations done in basic calculators:

Example 1: Add 10 and 15 using a calculator’s addition operation.
Solution: 10 + 15 = 25.

Explanation: On the calculator, we should type 10 and then click on the '+' sign and type 15. Once this is done, we click on the = sign. The result will then be displayed. 

Example 2: Solve for 27 ÷ 6 using a calculator. 

Solution 27 ÷ 6 = 4.5

Explanation: First we input 27 followed by the division sign and 6. Once we click the equal sign, the result will be immediately displayed on the screen. 

Scientific Calculators

Apart from basic mathematical operations, scientific calculators can also solve complex mathematical problems like trigonometric functions, calculus, or logarithmic equations. Usually scientific calculators have a larger display to accommodate the complex equations and calculations.

Most modern computers and smartphones have scientific calculators as a default application. 

Here are some examples of using scientific calculators:

Example 1: Find sin (7°) in radians using a scientific calculator

Solution: sin (7°) = 0.657 (approx)

Explanation: Click on the trigonometry option on the scientific calculator, and a list of all trigonometry functions will be available. First make sure to change the degree to radian and then input the number along with the trigonometry function. The answer will be displayed as soon as you click on the equal sign.

Example 2: Using the scientific calculator find the value of log10(10)

Solution: log10(10) = 1

Explanation: We can find the value of log10(10) by using a scientific calculator. Just type 10 and then click on the log button once to find the value.

Graphing Calculators

The graphing calculator is similar to the scientific calculator. However, unlike the scientific calculator, we can graph equations for advanced math like trigonometry on a coordinate plane. This is especially useful for those wanting to learn visually.

Let’s look into a few examples:
 

Example 1: Compute the graph for y = 2x

Solution: Substitute x with a few values 
    
    x = -3, y = -6
    x = -2, y = -4
    x = -1, y = -2
    x = 0, y = 0
    x = 1, y = 2
    x = 2, y = 4
    x = 3, y = 6

Plot these points on the calculator to get the graph
    

Online Calculators

These are software-based calculators available on apps or websites. Depending on our needs, we can find different kinds of calculators. For e.g., one can find their BMI or calculate their monthly payments (EMIs) using online calculators. They are user-friendly, provide fast and accurate results, and free to use.

The image above illustrates an online BMI calculator. Here, the weight, height, and age of a person have been given. Once the calculate button is clicked, it shows the BMI and the range of the BMI as well. 
Financial Calculators

As the name states, we use this calculator to solve financial problems such as interest or return on investment. This calculator can usually be used to compute any type of financial concept. 

Example 1: If the principal is 1000, rate is 5%, and time is 3 years, find the simple interest using a calculator.

Solution: Simple interest =  150 
        (1000 × 5 × 3 )/ 100 = 150
Explanation: Simple interest is calculated by entering each value in their respective fields. 

Programming Calculators

Calculators used by software developers are called programming calculators. The calculations are usually related to coding. They often include features for algorithms, debugging, etc. 

Example 1: Solve the binary of 1010 + 110 using the programming calculator.

Solution: The binary number for 1010 (10) + 110 (6) = 0001 0000 (16)

Explanation: In a programming calculator, to solve for binary numbers, we use the binary option. Just like a normal calculator, we input the binary numbers along with the operation sign. 

Math calculators are tools that carry out mathematical operations. They provide fast and accurate results, making them reliable and efficient. However, most calculators have similar functions.

Here are a few of the common functions in math calculator:

• Addition: Denoted by the symbol ‘+’, almost all calculators have this basic function.
   
• Subtraction: Another basic arithmetic operation, subtraction, which is represented by the symbol ‘-’, can be seen in all calculators.
   
• Multiplication: It is denoted by the symbol ‘×.’ Even this can be seen in all calculators. 
   
• Division: Splits numbers into equal parts by dividing with another number. We denote it with the symbol ‘÷’.
   
• Square Roots: When multiplied by itself, it gives us the number that equals the original number. We use the ‘√’ sign to denote the square root. 
   
• Exponentiation: We use it to determine the power of the base number. It is denoted with the symbol (xy). 

Advanced functions are present in scientific and graphic calculators. These calculators are used to solve complex problems, such as trigonometry and logarithms. They can even be used to draw graphs of lines, shapes, and parabolas.

Some of the advanced functions of a scientific or graphing calculator are mentioned below:

• Trigonometric functions: Trigonometric functions are used to calculate the angles and sides of a triangle. The symbols for the trigonometric functions are denoted as sin, cos, tan, etc.
   
• Logarithms: We solve problems involving powers and exponents, where the log is base 10. Denoted on the calculator as (log, ln).
   
• Calculus functions: To find the derivative of a function, we use the symbol ddx. To calculate the area under a curve, we use integration (∫).
   
• Statistical functions: Symbols like ∑, μ, and σ are used to solve complex problems. These problems are related to mean, median, and mode.

To use math calculators effectively: 

• We first try to understand the problem we are solving. 
   
• We then identify the correct function or formula.
   
• Make sure to input the values correctly and double-check for any errors, especially when it comes to advanced calculations like graphing etc.

Calculators were invented to make our lives easy. However, if not used correctly, we might lose the advantage of using a calculator. Here are a few tips and tricks to use a calculator efficiently.

• Memory functions: Make sure to use the memory keys ( i.e. M+, MR, MC) so we can store, recall, and clear the values for any kind of multi-step calculation without re-entering numbers. 
   
• Shortcut keys: Learning shortcuts like x2 can help solve problems quickly like when finding squares. This can save time during exams.
   
• Error checking: Make sure to review inputs and outputs, especially during long division. Use the clear or backspace buttons to fix errors instead of starting over.
   

We use math calculators almost in every field that uses math problems. Some of them heavily involve calculators, which are used to save time. Here are a few real-world applications where we use calculators.

1. Education: Students use calculators to solve problems in schools and colleges. 
    
2. Finance: Financial analysts use calculators to determine interest rates, loan payments, etc, in banks and other financial institutions. 
    
3. Engineering: Many engineers use scientific calculators to solve complex problems and for precise calculations. 
    
4. Scientific Research: Researchers rely on calculators for analysis, processing experimental data to ensure precise and accurate results in their research.