# ASVAB Preparation: Math Expressions and Equations

The ASVAB will expect you to have a firm grasp on certain mathematical expressions and equations. Math without expressions and equations is like a fire hydrant without a dog; they just go together. So what’s the difference between a mathematical *expression* and an *equation?*

An

*expression*is any mathematical calculation or formula combining numbers and/or variables. Expressions don’t include equal signs (=). For example, 3 + 2 is an expression, and so is*x*(*x*+ 2) – 3.An

*equation,*on the other hand, is a mathematical sentence built from expressions that use one or more equal signs (=). For example, 3 + 2 = 5 is an equation, and*x*(*x*+ 2) – 3 = 30 is also an equation.

## Obey the order of operations

In math, you must solve equations by following steps in a proper order. If you don’t, you won’t get the right answer. Many of the most frequent math errors occur when people don’t follow the *order of operations* when solving mathematical problems.

Keep in mind the following order of operations:

Start with any calculations in brackets or parentheses.

When you have

*nested*parentheses or brackets (parentheses or brackets inside other parentheses or brackets), do the inner ones first and work your way outward.Do any terms with exponents and roots.

Complete any multiplication and division, in order from left to right.

Do any addition and subtraction, in order from left to right.

An easy way to remember this order is to think of the phrase “**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally” (**P**arentheses, **E**xponents, **M**ultiply, **D**ivide, **A**dd, **S**ubtract).

Take the following expression out for a ride.

Solve: 3 × (5 + 2) + 5^{2} ÷ 2.

Do the calculations in the parentheses first:

3 × (5 + 2) + 5^{2} ÷2 = 3 × 7 + 5^{2} ÷ 2

Next, simplify the exponents:

3 × 7 + 25 ÷ 2

Do multiplication and division from left to right:

21 + 12.5

Finally, perform addition and subtraction from left to right:

33.5

## Keep equations balanced

One of the coolest things about equations is that you can do almost anything you want to them as long as you remember to do the exact same thing to both sides of the equation. This rule is called keeping the equation *balanced.*

For example, if you have the equation 4 + 1 = 3 + 2, you can add 3 to both sides of the equation, and it still balances out: 4 + 1 + 3 = 3 + 2 + 3. You can divide both sides by 3, and it still balances: (4 + 1) ÷3 = (3 + 2) ÷ 3.

Equation balancing becomes especially handy in algebra.