What is difference between an expression and an equation in mathematics?
Both use numbers and variables; however it is all based on the arrangement.
So let's take look at both to determine their use and relationship.
An expression is a combination of numbers, variables, and symbols
to be calculated. An equation contains expressions that are separated
by an equals sign.
A further look at the mathematical expression can be explained with
numbers and variables such as: 7x + y - 4. The only way that you solve
this expression is that you need to know what the variables represent.
It can be as simple as 8x - 2 or as complicated as 5x(x + 2y) - (5x
+ 2y) + y(2x + z). In either of these expressions all you have to
do is define the variables and using PEMDAS simplify and solve the
problem. If you calculate the expression 5x(x + 2y) - (5x + 2y) +
y(2x + z), we need to define the variables: x = 2, y = 3, z = 4. So
let's solve the expression:
Expression |
|
5x(x + 2y) - (5x + 2y) + y(2x + z) |
The Problem |
5 * 2(2 + 2 * 3) - (5 * 2 + 2 * 3) + 3(2 * 2 + 4)
|
Variables defined |
5 * 2(8) - (16) + 3(8) |
Parentheses |
80 - 16 + 24 |
Operations |
88 |
Answer |
An equation is the combination of two expressions that are separated
by an equals sign. So this means that both expressions must equal
each other. This makes the problem relatively simple to solve, because
you can solve the side that is easiest first and then solve the other
side. Let's take a look at an equation and solve it: x - 4 = 5. Since
we know that the both expressions must equal each other, the "x" can
only be a 9: 9 - 4 = 5, 5 = 5.
Let's take a look at a more complicated equation. x + 7 + 3(4 + 5)
= (x * 12) + 12. The only way you can solve this problem without doing
a lot of guessing and checking is to know the value of "x." In this
case we will have x = 2. So let's solve the equation:
Equation |
|
expression = expression |
|
x + 7 + 3(4 + 5) = (x * 12) + 12 |
The Problem |
2 + 7 + 3(4 + 5) = (2 * 12) + 12 |
Variables defined |
2 + 7 + 3(9) = (24) + 12 |
Parentheses |
2 + 7 + 27 = 36 |
Addition |
36 = 36 |
Answer |
Let's take a look at some examples to prove that these rules are
correct:
5 + 36 = 36 + 5
|
36 - 5 = 36 - 5
|
41 = 41
|
31 = 31
|
|
|
2 * 36 = 36 * 2
|
36 / 2 = 36 / 2
|
72 = 72
|
18 = 18
|
Equations and expressions are used in higher levels of mathematics
that require special calculations to solve graphical problems and
geometric figures. They are also used in explanations of lines, cartoons,
and diagrams. They have their place in computer software and used
for developing animations.