Math Calculators

The earliest known existence of calculators dates back to approximately 2000 BCE in Mesopotamia, where the abacus was invented. Later, it was used in other parts of the world, including China, Japan, and other countries. The abacus was used primarily for simple operations such as addition, subtraction, multiplication, and division. In 1642, Blaise Pascal created the "Pascaline," the first mechanical calculator that used gears to perform addition and subtraction.
Since then, the evolution of calculators has been happening, and after numerous developments through the years, pocket calculators were invented in the 1970s. These pocket calculators used microchips for faster and more accurate performance. Pocket calculators expanded the operations from basic addition, multiplication, subtraction, and division to more complex scientific and arithmetic operations. Then, later, in the year 1985, the world's first graphing calculator was invented. Throughout the 1990s, significant developments occurred in the field of math calculators. In the 2000s, fully digital calculators were introduced, and they have since become the most commonly used physical calculators.
 

Calculators are electronic devices that are used to perform mathematical operations. There are different types of calculators for other purposes. The basic electronic math calculator is used for performing simple operations such as addition, subtraction, multiplication, and division. For more advanced calculations and operations, additional calculators are available. Operations related to trigonometry, root calculations, and solving algebraic equations are done using scientific calculators. Basic calculators and scientific calculators are the most commonly used types of calculators. Apart from the basic calculator and scientific calculator, there are several other types of calculators, including graphing calculators, banking calculators, and specialized calculators. All of these calculators have various functions and can be used for many purposes.

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:

1. Basic Calculators

A basic calculator is the most common type and is used to carry out simple arithmetic operations like addition and subtraction. 

Many basic calculators have 5 signs (+, −, ×, ÷, =). 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. 

2. 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 rad) ≈ 0.657

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.

3. 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
    

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

5. 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 1010₂ (10) + 110₂ (6) = 10000₂ (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. 

Begin your journey into Math Calculators by exploring key concepts. Understand important math calculators topics in detail by selecting from the list below:

 

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 a 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 (x^y). 

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 d/dx. 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: 

• Understand the problem you are solving.  
• Identify the correct function or formula.
• Input the values correctly and double-check your answers.

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 (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.

• Use parentheses for accuracy: Parentheses should be used to imply correct operations at correct places.

• Correct mode setting: While working on scientific calculators and other specially designed calculators, the mode in which the answers are required and in which the equation values are inserted should be correctly used.

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. 

5. Business and Trade: Calculators are widely used by local business as well as traders in daily lives.

From Numbers to Geometry and beyond, you can explore all the important Math topics by selecting from the list below: