Order of Operations - Practice Problems

Background

Let's work a few examples focusing on the Order of Operations

Question

Evaluate:

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•  

Answer

• 

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Analysis

Let's first remember Order of Operations:

• P = Parentheses (also known as Brackets)
• E = Exponentials
• M = Multiplication (same weight as Division)
• D = Division (same weight as Multiplication)
• A = Addition (same weight as Subtraction)
• S = Subtraction (same weight as Addition)

Using this order, let's work the questions:

Question 1

There are a couple of parts here: there's the fraction on the left side of the minus sign (in the middle) and then a series of brackets to work through on the right. 

Ok - in the fraction we have a parenthesis, so we'll work that first. Also, on the right side, there is a parenthesis inside the square brackets - we'll work that first as well:

We still have brackets to work through - the numerator of the fraction (the top number) is an implied bracket, as is the denominator (the bottom number of the fraction) - so let's work those. We also have the brackets on the right hand side of the minus sign. 

Ok - details as to what we're going to do in the next couple of steps:

• In the numerator, we'll square the 5
• In the denominator, we'll do the multiplication first, then the addition
• In the right hand term, we'll square the -1, then do the multiplication, and lastly the addition.

And now we work the division in the fraction and then do the subtraction:



Therefore,



Question 2



We have 3 terms: the -2 being cubed, the division in the middle, and then a more complicated fraction on the right side. We can work the different parts of the expression:







Therefore we can say that:

Vocabulary used:


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Fact-orials Index

Operations:

• Order of Operations (PEMDAS)

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