Order of operations facts for kids
The order of operations is a special set of rules in mathematics. It helps us solve math problems correctly, especially when there are many different operations. Think of it like a recipe: you need to follow the steps in the right order to get the perfect result!
The main math operations are addition (+), subtraction (−), multiplication (* or ×), division (/), brackets (like (), [], and {}), and exponentiation (like ^n or n, also called powers).
Mathematicians around the world agree on this order. This means everyone solving the same problem will get the same answer. If you don't follow the rules, your answer will likely be wrong!
Contents
How to Solve Math Problems: The Rules
Always follow these rules from left to right in your math problem.
Step 1: Brackets and Exponents
First, look for anything inside brackets. Solve those parts of the problem first. Brackets tell you what to do right away!
Example with Brackets:
- 2 * 4 + (9 - 8) + 3
- First, solve what's inside the brackets: (9 - 8) = 1
- Now the problem looks like: 2 * 4 + 1 + 3
- Next, we'll do multiplication.
What are Exponents?
After solving everything inside brackets, look for exponents. An exponent tells you to multiply a number by itself a certain number of times. For example, 53 means 5 * 5 * 5, which equals 125. You solve these before multiplication, division, addition, or subtraction.
Step 2: Multiplication and Division
Once brackets and exponents are done, it's time for multiplication and division. Do these operations as you find them, moving from left to right across the problem. It's a common mistake to think multiplication always comes before division. They are equally important, so you just go from left to right!
Example with Multiplication and Division:
- 5 * 4 - 9 / 3
- First, solve the multiplication from left to right: 5 * 4 = 20
- Now the problem is: 20 - 9 / 3
- Next, solve the division: 9 / 3 = 3
- The problem becomes: 20 - 3
- Now, we'll do subtraction.
Step 3: Addition and Subtraction
Finally, after all the other steps, you solve any addition and subtraction. Just like with multiplication and division, you do these from left to right as you find them.
Remembering the Order: PEMDAS or GEMDAS
Many people use acronyms to remember the order of operations. Two popular ones are:
- PEMDAS
* Parentheses (same as Brackets) * Exponents * Multiplication * Division * Addition * Subtraction
- GEMDAS
* Grouping (same as Brackets) * Exponents * Multiplication * Division * Addition * Subtraction
Remember, for multiplication/division and addition/subtraction, you always work from left to right! For example, in 8 - 7 + 5, you would do 8 - 7 first, then add 5.
Let's Try Some Examples!
Here are a couple of examples showing all the rules in action.
Example One
Let's solve: (1 + 8) * (4 - 1) + 16 / 23
- Step 1: Brackets
* Solve the first bracket: (1 + 8) = 9 * Solve the second bracket: (4 - 1) = 3 * Now the problem is: 9 * 3 + 16 / 23
- Step 2: Exponents
* Solve the exponent: 23 (which is 2 * 2 * 2) = 8 * Now the problem is: 9 * 3 + 16 / 8
- Step 3: Multiplication and Division (left to right)
* Do the multiplication: 9 * 3 = 27 * Now the problem is: 27 + 16 / 8 * Do the division: 16 / 8 = 2 * Now the problem is: 27 + 2
- Step 4: Addition and Subtraction (left to right)
* Do the addition: 27 + 2 = 29
So, the answer is 29!
Example Two
Let's solve: (7 + 3) * (6 - 3) + 216 / 33
- Step 1: Brackets
* Solve the first bracket: (7 + 3) = 10 * Solve the second bracket: (6 - 3) = 3 * Now the problem is: 10 * 3 + 216 / 33
- Step 2: Exponents
* Solve the exponent: 33 (which is 3 * 3 * 3) = 27 * Now the problem is: 10 * 3 + 216 / 27
- Step 3: Multiplication and Division (left to right)
* Do the multiplication: 10 * 3 = 30 * Now the problem is: 30 + 216 / 27 * Do the division: 216 / 27 = 8 * Now the problem is: 30 + 8
- Step 4: Addition and Subtraction (left to right)
* Do the addition: 30 + 8 = 38
So, the answer is 38!
Related pages
See also
In Spanish: Orden de evaluación para niños
