How to Simplify Expressions with Integers

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  • 0:01 Integer Expressions
  • 0:48 Order of Operations
  • 2:48 Example 1
  • 3:46 Example 2
  • 4:33 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to simplify any integer expression by following the order of operations. Learn what to watch for and in what order to do your operations.

Integer Expressions

Suzie is just returning to school after a long and fun summer vacation. She went swimming in the ocean and camping in the mountains. She didn't have to think about math one bit! But now, on her first day back, what do you think her teacher decides to do? Her teacher decides to give everybody a surprise welcome back quiz! It's a short quiz, but a quiz is still a quiz. Suzie is not enjoying this at all. Suzie looks at her quiz and finds problems like this:

Simplify (1 + 2) * 3

These are called integer expressions because they are mathematical expressions with integers or numbers. Integers are our positive and negative whole numbers.

Order of Operations

Suzie immediately realizes that she needs to follow the order of operations, the mathematical rule that tells you in what order to do your operations. She is relieved because she remembers PEMDAS, the acronym that helps you remember your order of operations. She remembers the phrase 'Please Excuse My Dear Aunt Sally'.

See, Suzie has an aunt named Sally. This particular Aunt Sally is so silly that she is always getting herself into messes. Like, she will accidentally trip over something while holding a cake and then have the cake splatter all over somebody else's car. So, Suzie found herself repeating the phrase, 'Please Excuse My Dear Aunt Sally' so many times over summer vacation that it has become second nature to her.

This is a good thing, because it helps Suzie remember the different operations. The P stands for 'parentheses', the E stands for 'exponents', the M stands for 'multiplication', the D stands for 'division', the A stands for 'addition', and the S stands for 'subtraction'. This tells Suzie that she first needs to work on her parentheses. If she sees parentheses, she goes inside them and then starts her order of operations again to simplify what is inside the parentheses. Then, when she's done with the parentheses, she continues with the rest of the expression.

So, for Suzie, simplifying the problem (1 + 2) * 3 is a piece of cake. She sees parentheses, so she goes inside them first and simplifies that expression, the 1 + 2. She gets 3 * 3. She is done with the parentheses, so she continues. She sees multiplication so she does that next. She gets an answer of 9. And she is done with that first problem.

Example 1

Her next problem is this one:

8 + 2^3 + 2*3

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