Order of Operations
Have you ever seen a math problem with more than one kind of operation, like \(+\) and \(\times\) in the same question? To make sure everyone in the world solves it the same way and gets the same answer, mathematicians created a special set of rules called the Order of Operations. It's like a recipe for solving math puzzles!
Why the Order Matters
Hugo has 4 apples and 2 baskets. Each basket contains 3 oranges.
- His brother Louis calculates it like this: "I'll do \(4 + 2\) first, which is 6. Then I’ll multiply by 3. The answer is 18 fruits!"
- Hugo replies: "No, you have to do \(2 \times 3\) first, which is 6. Then you add my 4 apples. The answer is 10 fruits."
Hugo is right! The picture shows 4 apples and a separate group of \(2 \times 3 = 6\) oranges, making 10 fruits in total.
To prevent this kind of confusion, the rules of math state that some operations are more powerful than others and must be done first.Rule: Always do multiplication before addition. Let’s solve \(4 + 2 \times 3\) using the correct order:
To prevent this kind of confusion, the rules of math state that some operations are more powerful than others and must be done first.
- Step 1 (Multiply): First, find the total number of oranges.$$2 \times 3 = 6$$
- Step 2 (Add): Now, add the apples to that total.$$4 + 6 = 10$$
Method Order of operations
To evaluate an expression, we follow these steps in order:
- Parentheses (): Always solve what's inside parentheses first.
- Multiplication (\(\times\)) and Division (\(\div\)): Do them next, working from left to right.
- Addition (+) and Subtraction (-): Do them last, also working from left to right.
Example
Calculate \(4+2 \times 3\)
We follow the order:$$\begin{aligned}4+2 \times 3 & = 4 +6&&\text{(Do the multiplication } 2 \times 3)\\
& = 10&&\text{(Do the addition } 4 + 6)\end{aligned}$$