Do you like to solve problems related to mathematical equations like a pro?
Knowing the basic terminology associated with a concept increases your self-confidence and enables you to solve problems quickly.
In this article, we will learn about all the essential words you would have probably heard while dealing with equations in maths like constants, variables, coefficients, terms, expressions, etc.
Constants in Maths
Instead of starting directly with equations, we will first see the most fundamental building block of the equations. Constants are fixed numbers present in a mathematical quantity. For example, 2 and -3 are constants.
Note: Sometimes, constants are denoted by letters like $a, b, c$, etc., which are fixed numbers but arbitrary. Let’s see an example. In the equation $y = x + c$, we have $c$ a constant. Here, $c$ is a fixed number that remains so throughout the equation.
Variables in Maths
As their name suggest, variables have no fixed value. Often, these represent unknown quantities to be obtained. Usually, the ending alphabet letters $x, y$, and $z$ are used to denote variables.
For example, consider a shopkeeper who makes a profit of \$ 2 per book. He will earn \$ $2x$ in a day from selling books where $x$ is the number of books sold.
Terms in Maths
By learning about constants and variables, we will now create a term by multiplying them. So, a term is formed by constants, variables, and their multiplication.
For example, $2$, $x$, $2x$, and $-9x$ denote terms in mathematics.
We can have many variables present in a term. For example, $x^2$, $2x^3$, $-3xy$, and $2x^2 y z^2$ are also terms.
Coefficient of a Term
The numerical part of a term denotes its coefficient. For example, the coefficient of the term $9x$ is 9. Similarly, the coefficient of the term $-3x^2 y$ is $-3$.
Note: The coefficient of the term $x^2$ is 1.
Algebraic Expressions
Just like adding a new floor to existing floors of a building, we will now build a new concept from existing ones. An expression is formed by combining various terms using some operations like addition, subtraction, etc.
For example, few expressions are as follows
- $x+2$.
- $x^2 – 9x + 3$.
- $x^2 + 2xy-3y^2$.
Equations in Maths
We have a equation when two expressions are equal. For example, $x-2 = y-3$ is an equation in two variables. Here, $(x-2)$ and $(y-3)$ are two expressions.
Similarly, $ax+by+c = 0$ is an equation here with following details
- Two expressions $(ax+by+c)$ and $0$ which are equal.
- Three terms in the first expression, $ax$, $by$ and $c$.
- Constant term $c$.
- Two coefficients $a$ and $b$.
You must be know that this equation represents a line.
Expressions vs Equation
Before we close, I like to clarify the distinction between an expression and an equation. The former does not have any equality sign (=) and takes different values as we substitute values of variables. There is nothing like a solution of an expression.
For example, an expression $(x+y-2)$ will have following values
- -2 with $x = 0$ and $y=0$.
- 0 with $x = 1$ and $y=1$.
- 2 with $x = 2$ and $y=2$.
On the other hand, an equation $x+y-2 = 0$ will have following few solutions
- $x = 1$ and $y=1$.
- $x = 0$ and $y= 2$.
- $x = 2$ and $y=0$.
Summary
In this post, we have learned about basic terminology associated with equations in maths like constants, variables, terms, expressions, etc. These concepts are important for further building higher concepts in mathematics.
- Learn about a pair of straight lines.
If you’ve any questions related to this topic, then please leave a comment below. I will be more than happy to answer your questions.