Home » What is a Constant in Math? Definition, Examples, and Solved Problems

Table of Contents

Have you ever wondered why mathematicians use constants in an equation or “what is a constant in math?” In the systems of the world, everything does not remain the same. However, to measure the functions of a system or simplify the system, some values must remain unchanged. These values are called constants. Simply put, constants are parameters that remain unchanged in a system. The value of the constant is similar to the functions of a variable, which keep changing over time. Apart from the practical implications, the constant is an essential component in arithmetic expressions. If you want to learn more about this element of mathematics, read this blog. Here, we have explained the concept of constants in almost all the ways it is used in math, such as constant in math, arithmetic constant numbers, and constant function. Additionally, we have also provided sufficient examples to make it easily comprehensible.

## What is a Constant in Math?

In simple words, “constant” refers to a fixed value or a value that does not transform. A constant has a known value.

For example,

If you calculate the height of a wall or table at home, it will indicate a constant number. It will not change unless it breaks apart. However, if you calculate the height of a shrub in a pot or the length of an adolescent, it will keep changing as it grows. Hence, it is not constant.

Consider the following sentences to recognize this better:

- There are 365 days in a week, apart from leap years. Here, 365 is a constant.
- The USA celebrates July 4 as its Independence Day. Here, 4 is a constant.

## How to Define a Constant?

Once you know what a constant in math is, you can easily define it. In mathematical terms, a constant can be defined as a unit whose value does not alter all through the calculation. This unit can be in the form of a number, decimal, or fraction. You can also indicate a constant with a letter, a symbol, or a number.

Common illustrations of constants are: 2, 1.5, 2, and 34.

**Also read: Best Math Books To Augment Your Skills**

## What is a Constant Term in an Algebraic Expression?

Constants also play a significant role in algebraic expressions or equations.

Take a look at an algebraic equation:5x+4y=12

Here,

- x and y are variables. It is a quantity that can be altered.
- 5 is the coefficient of x.
- 4 is the coefficient of y.
- 12 is a constant.

Moreover, 5 and 4 are also indicated as numbers in the equation. However, if you consider the numbers as constants in the algebraic expression, you have made a mistake. They are the coefficients of the variables. You can multiply the coefficient with any assigned value to get the variable.

In that case, how can you identify a constant in Algebraic expressions? Well, you must look for the following elements:

- A known value.
- A unique number.
- For unknown values, it is a set number.
- Fractions, decimals, whole numbers, all real numbers

These are constants in an algebraic expression. However, the following element is not a constant:

- An exponent. For example, in the term 25, 5 is not a constant.

## What is a Constant Number in Mathematics?

In mathematics, all numbers can be called constant numbers. It can be in the form of real numbers, natural numbers, whole numbers, or integers. However, they cannot be in the shape of a different value.

### · Example:

**Problem: **Raven read 5 pages of a novel on Monday and 7 pages on Tuesday. How many pages did he read in two consecutive days?

**Solution:** Here, to determine the total number of pages that Raven read, you must add 5 and 7. They are constant numbers.

Therefore, the total number of pages read by Raven in the two days is 5 + 7 = 12 pages.

Again, 12 is also a constant.

**Also read : What Is A Term In Math, And How To Solve A Mathematical Term?**

## What is an Arbitrary Constant in Math?

If you have a clear idea of “what is a constant in math”, recognizing the meaning of arbitrary constant in math will never be an issue for you. Arbitrary constants refer to symbols that may have different assigned values. However, a change in the value of a variable in an equation never affects it. Most often, English alphabets are used to signify fixed, unknown values.

### · Examples of arbitrary constants:

Consider y = mx + c as the typical equation of a straight line. Here, m and c are arbitrary constants.

m = the slope of the line

c is the line that intercepts y.

Hence, if m = 3 and c = 4, the equation of a line can be obtained as:

y = 3x + 4

## What is a Constant Function?

When you are asked to find or state constant functions, do not confuse the question, “What is a constant function in math?” with “What is a function in math?” Both are opposite terms. A mathematical function refers to a rule. It states that the value of a dependent variable always corresponds to the value of independent variables. However, a constant function is a type of function that links every number to a constant. Hence, the result is a constant number for all values of input. Usually, a function is denoted by the expression f(x) = c. Here, f = function, f(x) = variable, and c = an unspecified constant.

Suppose the value of c is 3. In that case, the value of f (x) will be 3.

This expression is constant because the function (f) takes the same value for f(x), whatever the value of x is. These constant functions are also called generic functions. The best part of this function is that any real number can be the value of x, and you instantly get the value of its function since the value of variables and their function are the same. You only need to multiply the values of the function and the variable to obtain the constant. In a constant function, the value of a variable can be anything from 0, 1, π, to any real number.

## What is a Mathematical Constant?

Another common mistake most students make when asked “What is a constant in math?” is that they confuse it with a mathematical constant. Mathematical constants can be the same as “a constant in math” if the value of the multiplicative value of the variable and it’s function matches the constant. However, they are mostly independent. Typically, people use the term mathematical constant to indicate fixed and well-defined numbers. A few of the most popular mathematical constants include the following:

- π = 3.1415926536.
*i*= -1.^{2}- e = 207182818284.
- Constant of Pythagoras: = 1.4142135623
- Constant of Theodoras: = 1.7320508075
- Golden rule: = 1.618033

## Why Do Mathematicians Write Constants As Variables?

You can notice that mathematicians denote fixed values with the letter “c” when they don’t express their precise value in an expression or a word problem. In that case, “c” refers to a variable. However, its value is always fixed with a number when it is included in a polynomial or expression.

Take a look at the following quadratic expression:

ax^{2} + bx + c = 0.

In this expression,

c = the constant term used on a polynomial.

a and b = the coefficients of the variable x.

**Note:** *You may also call them parameters, as they represent a model of a quadratic equation. Parameters can have multiple values. But it never changes once they are assigned to take up a specific function. However, when the parameters of these values change, the function or equation also becomes different.*

**Read more: How to Solve Math Assignment Problems Faster?**

## Is There a Difference Between a Constant and a Variable?

Most mathematical expressions or equations have constants and variables. However, many students fail to understand the difference between the two. They often ask, “Are constants and variables different?” The truth is, there are many differences between them. The most common ones are:

**Values:**The value of a constant is known and fixed. It does not change over time. But variables never have fixed values. Any value can become a variable.**Symbolization**: The symbols of the constant are mainly numbers. Some well-known constants, like pi, are mostly identified with the standard symbol π. However, you can never relate a symbol to a variable. Typically, the English alphabet represents a variable.**Examples:**Popular examples of constants are 6, 45, -90, etc. In contrast, you can identify variables by alphabets or alpha numerals like x, 5y, 9z, etc.

## Typical Examples of Problems and Solutions Based on Constants

Following are the examples of problems and solutions based on constants.

### · Example 1

**Problem:**

*Find the value of the constant in the given expression: 3x ^{2}y – 5y + 10.*

**Solution:**

The only fixed term in the expression is 10. Therefore, the value of the constant is 10.

### · Example 2

**Problem:**

*Why is 16 a constant?*

**Solution:**

16 is an integer. It has a fixed value that will not change. Therefore, it is a constant.

### · Example 3

**Problem:**

*Find the constant in the given equation: 3 x -5 = y.*

**Solution:**

In the given expression, the solution has three terms:

- 3x
- -5
- y

Here, x and y are variables.

-5 represent a fixed variable or a variable that does not change.

Therefore, -5 is the constant.

### · Example 4

**Problem:**

*John took six hours to travel from Place A to Place B. In contrast, Jason needed 3 hours to cover the same distance. Which are the constants and variables in this statistical setting?*

**Solution:**

In this question, the time taken by John and Jason to move from positions A and B is not fixed. Hence, time is a variable. However, the distance between Place A and Place B never changes. Thus, they are constant.

**Also read: Importance of Math in Our Daily Life**

**The Bottom Line**

The constant is an important element of math. It is used in different parts of mathematics and denotes different things. If you define “what is a constant in math,” it will denote any fixed number. However, in an algebraic expression, it can be in the form of a known or unknown value, except for an exponent of a number series. Moreover, in mathematical constants, it can be the value of the symbol pi or theta. Till now, we saw a detailed explanation of the various concepts and uses of constants in a mathematical context. Nonetheless, if you are interested in learning more or need help solving any math problems, connect with our assignment helpers. They will give detailed solutions to your problems, clarify your issue at its roots, and help you score the best grades.