Think of brackets like packing for a trip. You’ve got your backpack, but inside that backpack is your lunchbox, and inside your lunchbox are your snacks, sandwich, and drink. You can’t zip up the backpack until everything is packed in the right order.
Math problems with more than one step work the same way, and brackets help us organize those steps so nothing gets out of place. They show us exactly where to begin and what to do next.
Read on for clear definitions, step-by-step examples, practice problems, and answers to common questions, all designed to help you understand and master brackets in math with confidence.
Brackets are symbols we use in math to help organize numbers and operations. They tell us what to solve first in a problem, almost like giving us step-by-step directions.
For example, when we see a problem like this:
(2 + 3) × 4
Without brackets, we might start with the multiplication step because, as we learned in the order of operations, we do multiplication before addition. But, there is something that comes before multiplication: brackets! (Or, parentheses, which are one type of bracket.)
We often see brackets in math expressions and equations, but they also pop up in geometry to show things like the length of a side or the measure of an angle.
As we progress on our math journey, they help us:
Get ready for more advanced math topics, like algebra
Work with shapes and measurements in geometry
Write formulas in tools like Excel or computer programs
And more
In math, brackets come in different shapes, but they all do the same thing: they group numbers and operations to show what to solve first.
Let’s look at the three main types of brackets we’ll encounter in math problems:
Parentheses are the most common type of brackets.
We use them to organize math expressions and show which part to solve first.
For example:
(2 + 3) × 4=?
What do we do first?
That’s right! We solve what's inside the parentheses:
( 2 + 3) × 4
= 5 × 4
= 20
So the result is (2 + 3) × 4=20
Without parentheses, we might follow the usual order of operations and multiply first. Parentheses help us stay on the right track!
Square brackets are used when we need to group things inside of other groupings. This is called a nested expression.
Think of it like packing a lunchbox inside a bigger lunchbox. Each set of brackets helps us keep everything organized!
Here’s an example:
[18 ÷ (4 + 2)] × 2
What should we solve first?
We start with the parentheses and work our way to square brackets, like so:
[18 ÷ (4 + 2)] × 2
= (18 ÷ 6) × 2
= 3 × 2
= 6
And we get the final answer [18 ÷ (4 + 2)] × 2 = 6 .
Square brackets are not as common in elementary school but become more useful in advanced math, especially with intervals (number ranges) or multi-step problems.
Curly braces, or curly brackets, don’t show up much in elementary math, but they’re good to know!
We often use them in set notation to show a set of numbers or group many steps together in advanced problems.
For example, {1, 2, 3} is a set of three numbers.
Sometimes we use curly braces when there are lots of nested groupings, like so:
{2 + [3 × (1 + 2)]}
Here, each bracket type helps keep the expression organized and easy to solve.
The type of brackets tells us which operation to solve first
Let’s clear up a common math question: Are brackets and parentheses the same thing?
Not exactly. Here's how to think about it:
“Brackets” is a general word. It includes all the grouping symbols we use in math: parentheses ( ), square brackets [ ], and curly braces { }. So whenever we talk about grouping parts of a math problem, we can say “brackets” to describe any of these symbols.
But “parentheses” is the name of one specific type of bracket—the round ones: ( ). These are the ones we use first and most often in math problems to show what needs to be solved first.
So when your teacher says “use brackets,” they might mean any kind. But if they say “use parentheses,” they mean the round ones specifically.
Here’s a helpful way to remember it:
All parentheses are brackets, but not all brackets are parentheses.
Think of “brackets” as the big family and parentheses are one member of that family, along with square brackets and curly braces.
Solving a math problem is a bit like baking cookies: we must follow the recipe, and follow the right steps in the right order. If we skip ahead or mix things up, the result won’t turn out exactly as we wanted.
In math, there’s a special rule that tells us the correct order to do operations in math, and brackets play a huge role in that. The rule is called PEMDAS, also known as BODMAS.
Let’s break each letter of the rule down:
P = Parentheses (solve these first!)*
E = Exponents (you’ll learn these soon, they’re like shortcuts for multiplying)
M and D = Multiplication and Division (left to right)
A and S = Addition and Subtraction (left to right)
*The alternative, BODMAS, may be a little more helpful here, as instead of P for parentheses, we have B for brackets.
So when you see brackets in a problem, they’re telling you, “Start here!”
Practice makes perfect, so let’s try some more examples together.
10 − (2 + 3)=?
What should we solve first in this problem? There’s a subtraction sign and some parentheses.
When we see parentheses in a math problem, what do they tell us to do?
They tell us to solve what’s inside the parentheses first!
The expression inside the parentheses is:
(2 + 3)
Let’s solve that first:
10 − (2 + 3)=
= 10 − 5
= 5
Final Answer: 10 − (2 + 3) = 5
What would’ve happened if we had subtracted 10 − 2 first instead?
We would’ve gotten 8, and then added 3 to get 11, which is the wrong answer.
That’s why using brackets correctly is so important. They guide us through the problem step by step, so we don’t guess or go out of order.
2 × [6 − (1 + 1)]=?
This problem might look tricky at first, but don’t worry. It’s a great example of how brackets help us know exactly what to do and in what order.
Since we see both square brackets and parentheses, this is a nested expression, which means one set of brackets is inside another.
Let’s solve it step by step, starting the innermost brackets which, in this case, are parentheses:
2 × [6 − (1 + 1)]=
= 2 × [6 − 2]
= 2 × 4
= 8
Final answer: 2 × [6 − (1 + 1)] = 8
Brackets guided us every step of the way. First, they told us to solve the parentheses. Then, they showed us what to do next inside the square brackets. Finally, we finished the problem by multiplying.
3 + (2 × [7 − 4])=?
This problem has three different types of math operations: addition, multiplication, and subtraction, and it uses both parentheses and square brackets.
How do we know where to start?
In math, the order of solving expressions depends on the position, not the shape of the brackets.
Parentheses () and square brackets [] are just visual tools to help us organize nested expressions clearly. The actual rule from PEMDAS is: solve the innermost grouping symbols first, regardless of whether they’re () or [].
So in our example:
3 + (2 × [7 − 4])
We would still start with the expression inside the square brackets [7 − 4], because it's the innermost part.
Inside the square brackets, we see:
3 + (2 × [7 − 4]) =
= 3 + (2 × 3)
= 3 + 6
= 9
Final answer:3 + (2 × [7 − 4]) = 9
See brackets in action! Check out our Order of Operations Series:
Ready to test your skills? Solve the following expressions:
6 + (4 × 2)
[10 − (3 + 2)] × 2
(5 + 3) × (2 + 1 + 1)
12 ÷ (6 − 4)
[8 + 2 × (5 − 3)] − 4
(3 + 2) × (4 + 1)
[15 − (2 × 5)] + 6
When you finish solving the exercises, check your answers at the bottom of the guide.
Brackets show up in math from the very beginning, and they keep coming back in more complex ways as we move into algebra, geometry, and beyond. Because brackets help us solve problems in the correct order, students often have questions about how and when to use them.
Here are some of the most common questions we hear about brackets in math, along with clear answers to help you understand how they work and why they matter:
Not entirely. Parentheses are just one type of bracket.
Parentheses are the most common type of bracket you’ll see in elementary math.
Other types include square brackets and curly braces.
All of them are called brackets because they group parts of a math problem. We use different types when problems have layers, so it’s easier to tell which part to solve first.
Yes! According to PEMDAS (or BODMAS), brackets come first. Start with the innermost brackets, then work outward. This keeps your steps in the right order and helps avoid mistakes.
Sometimes, yes! In very simple problems, brackets might not be written, but they’re still implied.
For example, in 3 + 2 × 4, you do the multiplication first as if there were brackets around it: 3 + (2 × 4). Brackets are often added to make things extra clear.
Absolutely! When breaking a word problem into steps, brackets help you group related actions so you can solve them one part at a time.
At Mathnasium of Blue Ash, questions are always welcome! Our tutors encourage students to speak up, explore ideas, and build a deep understanding of any topic, including expressions.
At Mathnasium of Blue Ash, we help K–12 students of all skill levels develop a strong understanding of math, including essential topics like brackets and the order of operations.
Our specially trained tutors provide face-to-face instruction in a caring and fun group environment, available both in-center and online. Whether your student is learning how to solve problems with parentheses in elementary school or working through complex, bracket-filled algebraic expressions in middle or high school, we’re here to guide them every step of the way.
Each student begins with a diagnostic assessment that helps us identify their strengths, skill level, and knowledge gaps. From there, we build a personalized learning plan designed to help them master concepts at their own pace.
Whether your student needs to catch up, keep up, or get ahead in math, schedule an assessment and enroll at Mathnasium of Blue Ash today.
Schedule your free assessment at Mathnasium of Blue Ash today!
If you’ve given our practice exercises a go, check your answers here:
14
10
32
6
8
25
11
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