Some equations have just one operator (+, -, ×, ÷), like this:
s = 3 + 4
Some have multiple operators, like this:
2 × 3 + 8 ÷ 2 = s
Some equations even have parentheses:
8 + 2 × (2 + 3) = d
Parentheses ( ) are a pair of round brackets that group numbers and operations together.
Equations can have even more operations.
For example, equations can have exponents.
Exponents are a shortcut for writing repeated multiplication.
Tip: The exponent 8 squared is a shortcut for writing 8 × 8. It's also pronounced 8 to the power of 2.
8 cubed is a shortcut writing for 8 × 8 × 8. It's also pronounced 8 to the power of 3.
You'll learn more about exponents in later grades.
Now, if we can have many different operators like addition, exponents, and parenthesis in the same equation, which one do we do first?
It turns out there's an official order to follow.
It's called the order of operations. ✨
In math, the order of operations tells us which operation to do first.
First, we always solve what's inside parentheses.
If there are multiple parentheses, simplify the left first.
If we don't follow this order, we won't get the right answer.
Tip: A popular acronym for the order of operations is PEMDAS. Does it sound like anything to you? 🧘
PEMDAS may help you remember the order of operations: 1. Parenthesis, 2. Exponents, 3. Multiplication or Division, then 4. Addition or Subtraction.
Now, let's try to solve this equation:
2 × 3 + 8 ÷ 2 = s
What operation do we do first?
There are no parentheses ( ) here.
What's below parentheses in the order of operations?
Right, it's exponents. We don't have any exponents, like 2 squared, in this equation.
The next operation to look for is multiplication or division.
We see that this expression has both multiplication and division.
The rule says to go from left to right.
So, we multiply first.
What's next?
Correct, we divide.
What's the last thing to do?
You got it. We add the simplified terms.
The answer is 10. ✅
Let's try solving the same equation just by going from left to right.
2 × 3 + 8 ÷ 2 =
6 + 8 ÷ 2 =
14 ÷ 2 =
7 = s ❌
Woops, we got the wrong answer.
You have to follow the order of operations to get the right answer.
Let's solve this together:
8 × 1 - (2 + 3) = d
What's the first thing to do?
We have parentheses, so let's simplify what's inside them.
What's the next thing to do?
Yes. 👏 We multiply.
What's next?
The only operation left is subtraction.
That's it. We have our answer.
3 = d
Great job following the order of operations.
To review, we follow a certain order when performing multiple operations in an equation.
Parentheses
Exponents
Multiplication or Division
Addition or Subtraction
Tip: The acronym PEMDAS may help you remember this order.
When there are two similar operations in one equation, we go from left to right.
Take a look:
12 × 2 + 8 × 9 = h
There are two multiplication signs.
Which one should we do first?
Correct, we go from left to right.
So we simplify the 12 × 2 first, then 8 × 9.
12 × 2 + 8 × 9 =
24 + 8 × 9 =
24 + 72 =
96 = h
Fantastic job. 👏
Tip: Rewrite your equation after each simplification step so you don't get confused.
When there are multiple operators (+, -, ÷, ...) in one equation, the order or operations (PEMDAS), tells you which to solve, or simplify, first.
PEMDAS can help you memorize the order of operations: 1. Parenthesis, 2. Exponents, 3. Multiplication or Division, then 4. Addition or Subtraction.
Now, try the practice. It'll help you learn more and remember for longer.