Math Lesson 1.4.6 - Types of Parenthesis and Their Order of Priority

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Welcome to our Math lesson on Types of Parenthesis and Their Order of Priority, this is the sixth lesson of our suite of math lessons covering the topic of Order of Operations and PEMDAS Rule, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Types of Parenthesis and Their Order of Priority

So far, we have used only one type of brackets (parenthesis) - the curved (or round) ones. However, an arithmetic expression may be more complicated and require other types of parenthesis in addition to the round ones, ( ). Two other types of brackets that are commonly used in arithmetic expressions are the square brackets, [ ] and curled ones { }. These, like operations brackets, also have their order of priority. The priority order for completing calculations with math problems containing multiple bracket types is: round brackets are solved first, then square brackets and finally the curled ones. IT is normally easy to understand this order of priority without knowing the above rule as the curled brackets usually include the square ones and square parenthesis include the round ones. Look at the scheme below:

According to the math rules of brackets, part A of the expression enclosed inside the round brackets is solved first, then we continue with the part/s B inside the square brackets, then with the part/s C inside the curled brackets and only then, we solve the part D outside the brackets. Let's see a couple of examples to clarify this point.

Example 7

Calculate the value of the arithmetic expression below.

Solution 7

Based on the rule of parenthesis, we begin with the round brackets as they are the innermost ones in the long part of expression. We can simultaneously solve the two round brackets as they are independent from each other, i.e.

Now that the round brackets are gone, we continue with the square ones following the known math rules (we have one division and immediately after it, a multiplication, so we do the division first). We have

Now that square bracket are gone too, we focus on the part of the expression inside the curled brackets. Thus,

Now, it is the turn for the expression outside brackets. We do the two multiplications simultaneously as they are independent (they are not consecutive). We have

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7. Continuing learning arithmetic - read our next math tutorial: Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF

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