🧮 the Secret Code of Math: Order of Operations
Introduction
Have you ever tried to solve a math puzzle and got two different answers? That happens when we forget the Order Of Operations—the special set of rules that tells us the right way to tackle a math problem. Think of it as the secret code that makes every calculation give the same, correct result, no matter who solves it!
1. What Is the Order of Operations?
The order of operations is a Sequence (a specific order) that decides which part of a math expression we do first, second, third, and so on. The usual rule is remembered with the easy‑to‑say acronym Pemdas:
| Letter | Means | What to do |
|---|---|---|
| P | Parentheses | Solve anything inside ( ) first. |
| E | Exponents | Deal with powers like (2^3) (2 cubed). |
| M | Multiplication | Multiply numbers. |
| D | Division | Divide numbers. |
| A | Addition | Add numbers. |
| S | Subtraction | Subtract numbers. |
Note: Multiplication and Division are on the same level, so we do them from left to right, just like Addition and Subtraction.
Why Does It Matter?
If we skip the code, we might end up with the wrong answer. For example,
[ 8 + 2 \times 3 = ? ]
- Wrong Way: Add first → (8 + 2 = 10); then multiply → (10 \times 3 = 30).
- Correct Way (Pemdas): Multiply first → (2 \times 3 = 6); then add → (8 + 6 = 14).
The Cause (ignoring the order) leads to the Effect (a wrong answer).
2. Real‑world Example: Baking Cookies 🍪
Imagine you’re making chocolate chip cookies. The recipe says:
- Mix 2 cups of flour Plus 1 cup of sugar.
- Multiply the mixture by 3 (to make three batches).
If you add the flour and sugar after you multiply, you’ll end up with way too much dough! The recipe follows the same idea as PEMDAS: you must Add the ingredients before you Multiply the whole mixture.
3. Mini Experiments You Can Try
Experiment 1: “math Treasure Hunt”
- Write three different expressions on sticky notes, like:
- (5 + 4 \times 2)
- ((5 + 4) \times 2)
- (6^2 - 10 ÷ 2)
- Solve each one twice: once following PEMDAS, once ignoring it.
- Compare the results. Which set of answers looks more “reasonable”?
Experiment 2: “parentheses Power”
Take a sheet of paper and draw a simple picture of a house. Write the expression (3 + (2 \times 5)) on the roof and ( (3 + 2) \times 5) on the door. Compute both. Notice how moving the parentheses changes the answer dramatically—just like moving a door changes where you can enter a house!
4. Did You Know?
- The order of operations is the same in Every Country that uses the standard arithmetic symbols, so mathematicians around the world speak the same “math language.”
- The exponent symbol “^” (as in (2^3)) is read “Raised To The Power Of.” The word exponent comes from the Latin exponere, meaning “to put out.”
Order of Operations Quiz
Keep using PEMDAS and you’ll always get the right answer!