Grouping Terms, Parentheses

Background

Sometimes when writing expressions and equations, we want one operation or set of operations to be done before other ones. We do that using parentheses (also known as brackets). The two words are used pretty much interchangeably, and so parentheses and brackets will typically refer to the same thing.

Question

What's 5 + (3 - 2) - 4

Answer

5 + (3 - 2) - 4 = 2

Analysis

When we work through a problem like this, we're being told to work the operation within the parentheses/brackets first. Let's go ahead and work this problem:

5 + (3 - 2) - 4

Notice that the 3 - 2 term is inside the brackets (I'll highlight it to make it more obvious):

5 + (3 - 2) - 4

So we work the 3 - 2 first. 3 - 2 = 1. And so we put 1 inside the brackets (the equal sign tells us that 3 - 2 is the same thing as 1 so we can do that substitution):

5 + (1) - 4

Since there is only the number 1 inside the brackets now, we can remove them (we can do this because there is no other operation inside the brackets that need to be done):

5 + 1 - 4

We now work the problem from left to right:

6 - 4

2

Therefore, 5 + (3 - 2) - 4 = 2

Vocabulary used:

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Where might you have come from?

Fact-orials Index

Operations:

• Addition
• Subtraction
• Multiplication
• Division

Operations with different kinds of numbers:

• Addition, Subtraction, and Whole Numbers

Where might we go?

Operations:

• Order of Operations

Properties:

• Associative Property