Order of Operations
In math, we often solve problems that use more than one operation, like addition, subtraction, multiplication, or division. The order in which we do these steps matters. That’s why mathematicians made a rule called the Order of Operations.
Order of operations
Hugo has 4 apples and 2 baskets, each containing 3 oranges.
- His brother Louis reads it and says: "I’ll add 2 to 4, which gives me 6. Then I’ll multiply the result, which is 6, by 3. I get 18 fruits!"
- Hugo replies: "No, you must multiply 2 and 3 first, then add 4. I have 10 fruits."
To avoid confusion (and maybe an argument between Hugo and Louis!), mathematicians created rules for the Order of Operations. These rules say:Do multiplication before addition. Let’s solve \(4 + 2 \times 3\) step by step:
- First, multiply:$$2 \times 3 = 6$$
- Then, add:$$4 + 6 = 10$$
Definition Order of operations
The order of operations is:
- parentheses
- multiplication and division (from left to right)
- addition and subtraction (from left to right).
Example
Calculate \(4+2 \times 3\)
$$\begin{aligned}4+2 \times 3 & = 4 +6&&\text{(evaluate the multiplication } 2 \times 3)\\& = 10&&\text{(evaluate the addition } 4 +6)&\end{aligned}$$