Core Connections: Course 2
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3. Section 3.3
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Exercise 126 Page 176

Practice makes perfect
According to the order of operations, expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division, and finally addition and subtraction are evaluated last. We can use the acronym PEMDAS to help us remember the correct order!
pemdas

For the given expression, this means performing multiplication before subtraction. 3-2* 5 Let's do it!

Operation Before Simplification After Simplification
Multiply 3- 2* 5 3- 10
Subtract terms 3- 10 - 7
The expression is equal to - 7.

Alternative Solution

Using a Calculator

We can also evaluate this expression using a calculator. To do so, we type it as shown below.

According to the order of operations, expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division, and finally addition and subtraction are evaluated last. We can use the acronym PEMDAS to help us remember the correct order!
pemdas
For the given expression, this means evaluating the expression inside the parentheses completely before performing multiplication and addition.

7(4+3* 2) Notice also that even within this parenthetical expression, we must follow the order of operations. 4+3* 2 Let's do it!

Operation Before Simplification After Simplification
Multiply 7(4+ 3* 2) 7(4+ 6)
Add terms 7( 4+ 6) 7( 10)
Multiply 7( 10) 70
The expression is equal to 70.

Alternative Solution

Using a Calculator

We can also evaluate this expression using a calculator. To do so, we type it as shown below.

Whenever using a calculator for a complicated expression such as this, be very careful when placing the parentheses. A calculator will only do what it is told to do, not what you meant for it do.

According to the order of operations, expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division, and finally addition and subtraction are evaluated last. We can use the acronym PEMDAS to help us remember the correct order!
pemdas

For the given expression, this means performing multiplication before performing division, addition, and subtraction. 10-6Ă· 2* 4+2 Let's do it!

Operation Before Simplification After Simplification
Multiply 10-6Ă· 2* 4+2 10-6Ă· 8+2
Divide 10- 6Ă· 8+2 10- 0.75+2
Add terms 10- 0.75+ 2 10- 2.75
Subtract terms 10- 2.75 7.25
The expression is equal to 7.25.

Alternative Solution

Using a Calculator

We can also evaluate this expression using a calculator. To do so, we type it as shown below.