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#### Lesson 14: Complex Formulas

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### Introduction

A simple formula is a mathematical expression with one operator, such as 7+9. A complex formula has more than one mathematical operator, such as 5+2*8. When there is more than one operation in a formula, the order of operations tells Excel which operation to calculate first. In order to use Excel to calculate complex formulas, you will need to understand the order of operations

#### The order of operations

Excel calculates formulas based on the following order of operations:

1. Operations enclosed in parentheses
2. Exponential calculations (3^2, for example)
3. Multiplication and division, whichever comes first
4. Addition and subtraction, whichever comes first

A mnemonic that can help you remember the order is PEMDAS, or Please Excuse My Dear Aunt Sally.

Click the arrows in the slideshow below to learn more about how the order of operations is used to calculate formulas in Excel.

• While this formula may look complicated, we can use the order of operations step by step to find the right answer.

• First, we'll start by calculating anything inside the parentheses. In this case, there's only one thing we need to calculate: 6-3=3.

• As you can see, the formula already looks simpler. Next, we'll look to see if there are any exponents. There's one: 2^2=4.

• Next, we'll solve any multiplication and division, working from left to right. Because the division operation comes before the multiplication, it is calculated first: 3/4=0.75.

• Now, we'll solve our remaining multiplication operation: 0.75*4=3.

• Next, we'll calculate any addition or subtraction, again working from left to right. Addition comes first: 10+3=13.

• Finally, we have one remaining subtraction operation: 13-1=12.

• Now we have our answer: 12. This is the exact same result you would get if you entered the formula into Excel.

• #### Creating complex formulas

In the example below, we will demonstrate how Excel solves a complex formula using the order of operations. Here, we want to calculate the cost of sales tax for a catering invoice. To do this, we'll write our formula as =(D2+D3)*0.075 in cell D4. This formula will add the prices of our items together and then multiply that value by the 7.5% tax rate (which is written as 0.075) to calculate the cost of sales tax. Creating a complex formula

Excel follows the order of operations and first adds the values inside the parentheses: (44.85+39.90) = \$84.75. It then multiplies that value by the tax rate: \$84.75*0.075. The result will show that the sales tax is \$6.36. The completed formula and calculated value

It is especially important to enter complex formulas with the correct order of operations. Otherwise, Excel will not calculate the results accurately. In our example, if the parentheses are not included, the multiplication is calculated first and the result is incorrect. Parentheses are the best way to define which calculations will be performed first in Excel. Result of an incorrect formula

#### To create a complex formula using the order of operations:

In our example below, we will use cell references along with numerical values to create a complex formula that will calculate the total cost for a catering invoice. The formula will calculate the cost for each menu item and then add those values together.

1. Select the cell that will contain the formula. In our example, we'll select cell C4. Selecting cell C4
2. Enter your formula. In our example, we'll type =B2*C2+B3*C3. This formula will follow the order of operations, first performing the multiplication: 2.29*20 = 45.80 and 3.49*35 = 122.15. It then will add those values together to calculate the total: 45.80+122.15. Creating a complex formula
3. Double-check your formula for accuracy, then press Enter on your keyboard. The formula will calculate and display the result. In our example, the result shows that the total cost for the order is \$167.95. The completed formula and calculated value

You can add parentheses to any equation to make it easier to read. While it won't change the result of the formula in this example, we could enclose the multiplication operations within parentheses to clarify that they will be calculated before the addition. Including parentheses in a formula for clarity

Excel will not always tell you if your formula contains an error, so it's up to you to check all of your formulas. To learn how to do this, you can read the Double-Check Your Formulas lesson from our Excel Formulas tutorial.

### Challenge!

1. Open an existing Excel workbook. If you want, you can use our practice workbook.
2. Create a complex formula that will perform addition before multiplication. If you are using the example, create a formula in cell D6 that first adds the values of cells D3, D4, and D5 and then multiplies their total by 0.075. Hint: You'll need to think about the order of operations for this to work correctly.

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