## Chef Henri runs a small restaurant on the outskirts of Paris called Le Jardin de la Joie. He is well known for his exquisitely light and scrumptiously delicious chocolate mousse. "Ze secret," says Chef Henri, "is ze order in which I add ze ingredients."To make his famous chocolate mousse, Chef Henri follows the steps in a specific order. When we simplify expressions in mathematics, we must also follow a certain order. This is called the Order of Operations. Chef Henri must follow his recipe in the proper order, or his mousse would not set properly every time he made it. In math, if the order of operations is not used, people may get different values for the same expression. For example, if for the expression 3+5×4 you multiply the 5 times the 4 first, you get 20, and then add the 3, the value of the expression is 23. On the other hand, if you add the 3 and the 5 first, you get 8, and the value of 8 times 4 is 32. Therefore, we have a set of rules called the Order of Operations which help avoid confusion.

### The rules for the Order of Operations are as follows:

1. Do all work in parentheses first.
2. Find the value of each expression with an exponent.
3. Do all the multiplications and divisions in order from left to right.
4. Do all the additions and subtractions in order from left to right.

It is helpful to write each step on a separate line to avoid making a mistake.

#### Example 1:

7+2×9

7+18
Multiplication Done First

25

#### Example 2:

(7+2)×9

9×9
Work in Parentheses Done First

81
Multiplication Next

#### Example 3:

18+36÷3²+5

18+36÷9+5
Exponential Expression Simplified

18+4+5
Multiplications/Divisions Done From Left to Right

22+5
Additions/Subtractions Done From Left to Right

27
Additions/Subtractions Done From Left to Right

#### Example 4:

27×2÷3×5

54÷3×5
Multiplications/Divisions Done From Left to Right

18×5
Multiplications/Divisions Done From Left to Right

90
Multiplications/Divisions Done From Left to Right Chef Henri uses the order of operations when finding his profit from the sale of chocolate mousse each week. Henri sold 88 servings of mousse at 15 francs each this week. He made 100 servings which cost him 4 francs each to produce during this week. Help Henri calculate his profit for the week: 88×15-100×4=

Continue with Order of Operations | Number Theory Main

 Art: Zach Sterba Writing: Nikki Siegel