The Order of Operations and Variables:

Simplifying Expressions with Variables

If we have an equation (or expression) with variables, we can only solve what it is equal to when we know what the variables are. The following video will show how to solve an equation when given numbers for the variables.

Video Source (04:13 mins) | Transcript

Simplifying expressions with variables comes in handy a lot when we are given a formula for a certain type of problem. A formula is something that looks like pt = a. This is a formula for finding the amount when we know the percent and the total. We learned about this formula in last week’s lesson on percentages. In this case, p represents the percent and t represents the total. If we were told that the percent was 75% and the total was 20, we could find that the amount was 15. This is done by putting our values in for our variables in the formula. pt becomes \((.75)(20)\).

Additional Resources

Khan Academy: Variables, Expressions, & Equations (06:54 mins, Transcript)
Khan Academy: Evaluating an expression with one variable (01:59 mins, Transcript)

Practice Problems

Simplify the following expression to find it's value:

Given that d = 3:
7d = ?
Given that m = 20:
m − 12 = ?
Given that x = 2:
6x + 3 = ?

As we will explore later, the area of a rectangle can be found by multiplying the length of the rectangle by its width, or (L × W). Use this information to answer the following two questions:

Find the area of a rectangular-shaped floor, where the length is L = 3 meters and the width is W = 4 meters

Find the area of a rectangular-shaped computer monitor, where the length is L = 31 cm and the width is W = 17 cm.

Solutions

21, 7d = 7 × 3 = 21 (Written Solution)

A number next to a variable implies multiplication.

7d

Replace the d in the expression with 3 as given in the math problem. Include a multiplication symbol of your choice.

7 × 3

Finally, multiply 7 × 3, the answer is 21.
8, M − 12 = 20 − 12 = 8
15, 6x + 3 = 6 · 2 + 3 = 15 (Solution Video | Transcript | Written Solution)

In this problem, the x is the variable

\(6(\text x)+3\)

Replace the variable x with 2 because x = 2 is given in our math problem. Use parentheses or a dot to show multiplication and to distinguish the symbol for multiplication from the x variable.

\(6(2)+3\)

Now use the Order of Operations to solve the problem. First, multiply 6 and 2.

\(12+ 3\)

Lastly, add 12 + 3. The answer is 15
12, L × W = 3 × 4 = 12 (Solution Video | Transcript)
As we will study later in the course, the units on this answer are square meters. So, we say the room has a size of 12 square meters. At this time, we will not worry about the units.
527, L × W = 31 × 17 = 527.
As we will study later, the units on this answer are square centimeters (\({\text{cm}}^{2}\)). So, we say the monitor has a size of 527 square centimeters. At this time, we will not worry about the units.