Core Connections: Course 2
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3. Section 3.3
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Exercise 121 Page 175

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 evaluating the expression inside the parentheses completely before performing addition.

3+4(10-8) Notice also that even within this parenthetical expression, we must follow the order of operations. 10-8 Let's do it!

Operation Before Simplification After Simplification
Subtract terms 3+4( 10- 8) 3+4( 2)
Multiply 3+ 4( 2) 3+ 8
Add terms 3+ 8 11
The expression is equal to 11.

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 addition and subtraction. 3+4* 10-8 Let's do it!

Operation Before Simplification After Simplification
Multiply 3+ 4* 10-8 3+ 40-8
Add terms 3+ 40-8 43-8
Subtract terms 43- 8 35
The expression is equal to 35.

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. (3+4)(10-8) Let's do it!

Operation Before Simplification After Simplification
Add terms ( 3+ 4)(10-8) ( 7)(10-8)
Subtract terms (7)( 10- 8) (7)( 2)
Multiply ( 7)( 2) 14
The expression is equal to 14.

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.