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Questions and Answers
What is the first step in evaluating the expression 2 × (3 + 4)?
What is the first step in evaluating the expression 2 × (3 + 4)?
- Add 3 and 4
- Evaluate the exponentiation operation
- Multiply 2 and 3
- Evaluate the expression inside the parentheses (correct)
What operation is evaluated next in the expression 2 × 3 + 4^2, after evaluating the exponentiation operation?
What operation is evaluated next in the expression 2 × 3 + 4^2, after evaluating the exponentiation operation?
- Subtraction
- Multiplication (correct)
- Division
- Addition
In the expression 10 - 3 + 2, which operation is evaluated first?
In the expression 10 - 3 + 2, which operation is evaluated first?
- Subtraction
- Addition
- None of the above, we evaluate from left to right (correct)
- Both subtraction and addition are evaluated simultaneously
What is the final step in evaluating the expression 2 × (3 + 4)?
What is the final step in evaluating the expression 2 × (3 + 4)?
In the expression 5 × 2 - 3, which operation is evaluated last?
In the expression 5 × 2 - 3, which operation is evaluated last?
What is the correct order of operations to evaluate the expression 2^3 × 4 - 1?
What is the correct order of operations to evaluate the expression 2^3 × 4 - 1?
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Study Notes
Order of Operations
The order of operations is a set of rules used to evaluate mathematical expressions in the correct order.
PEMDAS
PEMDAS is a mnemonic used to remember the order of operations:
P - Parentheses
- Evaluate expressions inside parentheses first
- Follow the order of operations within the parentheses
E - Exponents
- Evaluate any exponential expressions next (e.g. 2^3)
M - Multiplication and Division
- Evaluate any multiplication and division operations from left to right
- In other words, evaluate any multiplication operations before moving on to division operations
D - Addition and Subtraction
- Finally, evaluate any addition and subtraction operations from left to right
- In other words, evaluate any addition operations before moving on to subtraction operations
Examples
- 2 × 3 + 4 = ?
- Multiply 2 and 3: 2 × 3 = 6
- Add 4: 6 + 4 = 10
- 10 - 3 + 2 = ?
- Subtract 3: 10 - 3 = 7
- Add 2: 7 + 2 = 9
- (2 + 3) × 4 = ?
- Evaluate the expression inside the parentheses: 2 + 3 = 5
- Multiply 5 by 4: 5 × 4 = 20
Order of Operations
- The order of operations is a set of rules used to evaluate mathematical expressions in the correct order.
PEMDAS
- PEMDAS is a mnemonic used to remember the order of operations.
Evaluating Expressions
- Evaluate expressions inside parentheses first.
- Follow the order of operations within the parentheses.
Exponents
- Evaluate any exponential expressions next (e.g. 2^3).
Multiplication and Division
- Evaluate any multiplication and division operations from left to right.
- Evaluate any multiplication operations before moving on to division operations.
Addition and Subtraction
- Evaluate any addition and subtraction operations from left to right.
- Evaluate any addition operations before moving on to subtraction operations.
Examples
Example 1
- 2 × 3 + 4 = 10
- Multiply 2 and 3: 2 × 3 = 6
- Add 4: 6 + 4 = 10
Example 2
- 10 - 3 + 2 = 9
- Subtract 3: 10 - 3 = 7
- Add 2: 7 + 2 = 9
Example 3
- (2 + 3) × 4 = 20
- Evaluate the expression inside the parentheses: 2 + 3 = 5
- Multiply 5 by 4: 5 × 4 = 20
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