Expressions Vs. Equations

Expressions and equations look similar in math; however, there are distinct differences between them. An expression in math has numbers, symbols and variables to be calculated. Expressions in an equation that are separated by an equals sign is an equation.

Higher levels of mathematics have both expressions and equations. Since both use variables and numbers it can be confusing at first, however, there is an easy way to distinguish between the two. An expression has different combinations of variables, symbols and numbers for you to calculate. An equation has expressions in it that are separated by an equals sign. So, look for an equals sign to identify an equation easily. In simple terms, an equation has an equals sign to link two equivalent expressions, while expressions are more like "mathematical phrases."

In order to get the correct answer in math, you must use the correct order of operations. You will need to understand this fundamental before you solve equations and expressions. The acronym PEMDAS helps you remember the order of operations. It stands for Parentheses, Exponents, Multiply, Divide, Add and Subtract.

You do the math functions inside the parentheses first, then the exponents such as powers and square roots, then multiply and divide from left to right and finally add or subtract from left to right. Here is an example:

\(\begin{aligned}
30 ÷ 5 + (5 – 3) 2^2 – 3 &= 30 ÷ 5 + 2 × 2^2 – 3\)
\(&= 30 ÷ 5 + 2 × 4 -3\)
\(&= 6 + 8 – 3\)
\(&= 14 – 3\)
\(&= 11
\end{aligned}\)

A balanced symbol equation has an equals sign. When you solve the problem, both sides of the equals sign have the same number, so you know your answer is correct. Consider this example of a simple equation:

\(x – 4 = 5\)

Solve the easiest side first. Since you have the answer on the right, you can easily decide that ​x​ equals 9 because that is the only number that will make the numbers on each side of the equals sign be the same. Here is a more complicated equation where ​y​ = 2. You simply plug in the variables and solve the equation using PEMDAS:

\(y + 7 + 3 × (4 + 5) = (y × 12) + 12\)
\(2 +7 + 3 × (4 + 5) = (2 × 12) + 12\)
\(2 + 7 + 3 × (9) = (24) + 12\)
\(2 + 7 + 27 = 36\)
\(36 = 36\)

In order to solve a mathematical expression, you need to know what the variables are, place them in the expression and solve it using PEMDAS. For example, solve the following expression where ​a​ = 2, ​b​ = 3 and c = 4:

\(\begin{aligned}\)
\(5a × (a + 2b) – &(5a + 2b) + b × (2a + c)\)
\(&= 5 × 2 × (2 + 2 × 3) – (5 × 2 + 2 × 3) + 3 × (2 × 2 + 4)\)
\(&= 5 × 2 × (8) – (16) + 3 × (8)\)
\(&= 80 – 16 +24\)
\(&= 88\)
\(\end{aligned}\)