What Are Parentheses in Math?
Learn exactly how parentheses are used in math and how to solve problems that include them.
Have you ever come across parentheses in math and wondered how they’re used? Or maybe you remember learning something about parentheses in math class, but you’re not sure when to perform operations that are in parentheses.
These important symbols can help you solve equations and math problems correctly. However, first, you have to know what parentheses are and how they fit into the order of operations in math.
Parentheses are these symbols: (). They may also be called round brackets. Parentheses are used to group numbers, operations, or variables together in math.
Parentheses are also part of the order of operations in math.
What Is the Order of Operations in Math?
Math problems can be complex and confusing. For example, if you look at a problem like this one: (3+5) – 4 x 5 + 5², what should you do first? Should you go from left to right? Should you do the exponent first? What should you do?
The order of operations tells us exactly how to solve math problems. If you don’t use this important order of operations, you will probably get the answers to your math problems wrong!
The order of operations can easily be remembered by the acronym PEMDAS which stands for:
– Multiplication and Division (whichever comes first from left to right)
– Addition and Subtraction (whichever comes first from left to right)
When solving an equation, you should do the operations in this order.
How Does the Math Order of Operations Work?
That may all sound fine. It’s when you get into the math problems that it gets messier. So, let’s use our example to learn in detail how to solve a math problem using the order of operations in math:
(3+5) – 4 x 5 + 5²
To solve this problem, we follow PEMDAS. So, first, we do what’s in the parentheses, which is 3+5. We do this operation first even though addition comes later in the order of operations. Because it’s in parentheses, we do it first. When you’re done solving 3+5, you can replace the answer in the equation without using parenthesis anymore. So now we have:
8 – 4 x 5 + 5²
Next, come exponents which is 5². So now we have:
8 – 4 x 5 + 25
Next, come multiplication and division. There is no division in this equation. So we solve for 4 x 5. So now we have:
8 – 20 + 25
Next, come addition and subtraction. You do whatever comes first from left to right, so we solve for 8-20 first, and then the addition problem that results:
-12 + 25
Finally, the solution is:
-12 + 25 = 13
See? It’s really simple. Using parentheses in math is easy if you know the order of operations. All you have to do is follow the order operations, solve each part of the problem, and eventually, you’ll get your answer.
Remember, follow PEMDAS or you might get the answer wrong!
Parentheses in Math = Multiplication
Parentheses in math also has another meaning: multiplication. Let’s take a look at a problem to see how it works.
(3 + 4)5 – 6
To solve this problem, we also follow PEMDAS. So, first we do what’s in the parentheses:
(7)5 – 6
Next comes multiplication and division. Because the parentheses stands for multiplication, we do this next. (7)5 is the same as 7 x 5.
So we solve and get:
35 – 6
The final answer is 29.
Do you have any special tricks for remembering the order of operations or how to use parentheses in math? Tell us about them on social media.