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Parentheses, Braces & Brackets in Math

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  • 0:03 Parentheses, Brackets,…
  • 0:38 Order of Operations
  • 2:16 Arrays and Sets
  • 3:21 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

They might look similar, but parentheses, brackets, and braces are not the same. Learn how each of them is used in mathematics, from order of operations to matrices.

Parentheses, Brackets, and Braces

Parentheses, brackets, and braces are ways of separating one part of an expression from another.

  • Parentheses ( ) are the curved signs that you might see in text just as much as in mathematics
  • Brackets look similar but are angular in shape [ ], and
  • Braces are also similar but are curly in shape { }

So, since they are all ways of separating parts of an expression, how do you know when to use each of them? There are actually multiple circumstances when you would want to use some of them, including order of operations, arrays, and sets. In this lesson we're going to go through each of these circumstances and explain how to use them.

Order of Operations

The most basic and common reason to use parentheses, brackets, and braces is to control the order of operations. Order of operations is a method for figuring out which part of a mathematical expression to complete first. You might've heard of acronyms like BEDMAS or PEDMAS or even PEMDAS. There are lots of versions, but they all have the same purpose: to tell you in what order to complete mathematical operations. For example, PEMDAS, which is the most popular version in the United States, stands for parentheses, exponents, multiplication, division, addition, and subtraction. You complete parentheses first, then exponents, then multiplication, and so on. This is important because if you evaluate an expression in the wrong order, it is quite possible that you will arrive at an incorrect answer.

The first thing on the list is parentheses. The truth is, the first thing on the list is any combination of parentheses, brackets, and braces. When used for order of operations, parentheses are used first and are most common. For example, in the expression below, you would calculate 5 minus 2 first, even though multiplication would normally come first if there were no parentheses:

8 * (5 - 2)

Sometimes you need multiple layers of parentheses. That's when you can use brackets and braces. The inside layer is made up of parentheses, the following layer is made up of square brackets, and the outer layer is made up of braces. This allows you to have a complex expression like this:

{4 - [8 * (5 - 2)] + 3} * 6

In this case you would calculate 5 minus 2 first (parentheses), then multiply by 8 (brackets), then complete the part inside the curly braces, and finally multiply by 6.

Arrays and Sets

There are a couple of other situations where you might use brackets and braces.

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