In mathematics, you might have encountered the terms expression and equation very often. As both combines number and/or variables, people often misunderstood an expression for an equation. However, these two mathematical terms are not same, and a big difference lies in their arrangement, that explains what they represent. The best way, to identify, whether a given problem is an expression or equation is to check, if it contains an equal to sign (=) or not. If it does, it is an equation, but if it does not, then it is just an expression. Go through this article to understand the basic differences between expression and equation.
Content: Expression Vs Equation
|Basis for Comparison||Expression||Equation|
|Meaning||Expression is a mathematical phrase which combines, numbers, variables and operators to show the value of something.||An equation is a mathematical statement wherein two expressions are set equal to each other.|
|What is it?||A sentence fragment, that stands for a single numerical value.||A sentence that shows equality between two expressions.|
|Relation symbol||No||Yes, equal sign (=)|
|Sides||One sided||Two sided, left and right|
|Answer||Numerical value||Assertion, i.e. true or false.|
|Example||7x - 2(3x + 14)||7x - 5 = 19|
Definition of Expression
In mathematics, the expression is defined as a phrase that groups together numbers (constant), letters (variables) or their combination joined by operators (+, -, *, /), to represent the value of something. An expression can be arithmetic, algebraic, polynomial and analytical.
As it does not contain any equal to (=) sign, so, it does not show any relationship. Hence, it has nothing like left side or right side. An expression can be simplified by combining the like terms, or it can be evaluated, inserting values in place of the variables to arrive at a numerical value. Examples: 9x + 2, x – 9, 3p + 5, 4m + 10
Definition of Equation
In mathematics, the term equation means a statement of equality. It is a sentence in which two expressions are placed equal to one another. In order to satisfy an equation, it is important to determine the value of the variable concerned; this is known as solution or root of the equation.
An equation can be conditional or an identity. If the equation is conditional, then the equality of two expressions is true for a definite value of variable involved. However, if the equation is an identity, then the equality is true for all the values held by the variable. There are four types of equation, discussed below:
- Simple or Linear Equation: An equation is said to be linear is the highest power of the variable concerned in 1.
Example: 3x + 13 = 8x – 2
- Simultaneous Linear Equation: When there are two or more linear equations containing two or more variables.
Example: 3x + 2y = 5, 5x + 3y = 7
- Quadratic Equation: When in an equation, the highest power is 2, it is called as the quadratic equation.
Example: 2x2 + 7x + 13 = 0
- Cubic Equation: As the name suggests, a cubic equation is one which degree 3.
Example: 9x3 + 2x2 + 4x -3 = 13
Key Differences Between Expression and Equation
The points given below summarises important differences between expression and equation:
- A mathematical phrase that groups together numbers, variables, and operators, to show the value of something is called expression. An equation is described as a mathematical statement with two expressions set equal to one another.
- An expression is a sentence fragment that stands for a single numerical value. On the contrary, an equation is a sentence showing equality between two expressions.
- The expression is simplified, through evaluation where we substitute values in place of variables. Conversely, an equation is solved.
- An equation is indicated by an equal sign (=). On the other hand, there is no relation symbol in an expression.
- An equation is two sided, where an equal sign separates the left and right sides. Unlike, an expression is one-sided, there is no demarcation like left or right side.
- The answer of an expression is either an expression or a numerical value. As opposed to the equation, which could only be true or false.
Therefore, with the above explanation is clear that there exist a big difference between these two mathematical concepts. An expression does not reveal any relationship while an equation does. An equation contains an ‘equal to sign’, therefore, it shows solution or ends up representing the value of the variable. However, in the case of an expression, there is no equal sign, so there is no definite solution and cannot end up displaying the value of the variable involved.