Use the order of operations to evaluate this expression

Oct 13, 2025 by windailys.com 29 views

Use the order of operations to evaluate this expression

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Evaluating the Expression

To evaluate the given expression, we will follow the order of operations:

${7+(5-9)^2+3(16 \div 8)}$

First, we will evaluate the expression inside the parentheses:

${5-9 = -4}$

Next, we will evaluate the exponent:

${(-4)^2 = 16}$

Now, we will evaluate the division:

${16 \div 8 = 2}$

Now that we have evaluated the expressions inside the parentheses and the exponent, we can substitute these values back into the original expression:

${7+16+3(2)}$

Next, we will evaluate the multiplication:

${3(2) = 6}$

Now, we can substitute this value back into the expression:

${7+16+6}$

Finally, we will evaluate the addition and subtraction operations from left to right:

${7+16 = 23}$ ${23+6 = 29}$

Therefore, the value of the expression is:

${29}$

The Final Answer

The final answer is: 29

Use the order of operations to evaluate this expression

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Evaluating the Expression

To evaluate the given expression, we will follow the order of operations:

${7+(5-9)^2+3(16 \div 8)}$

First, we will evaluate the expression inside the parentheses:

${5-9 = -4}$

Next, we will evaluate the exponent:

${(-4)^2 = 16}$

Now, we will evaluate the division:

${16 \div 8 = 2}$

Now that we have evaluated the expressions inside the parentheses and the exponent, we can substitute these values back into the original expression:

${7+16+3(2)}$

Next, we will evaluate the multiplication:

${3(2) = 6}$

Now, we can substitute this value back into the expression:

${7+16+6}$

Finally, we will evaluate the addition and subtraction operations from left to right:

${7+16 = 23}$ ${23+6 = 29}$

Therefore, the value of the expression is:

${29}$

The Final Answer

The final answer is: 29

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is important because it ensures that mathematical expressions are evaluated consistently and accurately. If the order of operations is not followed, the result of the expression may be incorrect.

Q: What happens if there are multiple operations with the same precedence?

A: If there are multiple operations with the same precedence, the order in which they are evaluated is determined by the order in which they appear from left to right.

Q: Can you give an example of an expression that requires the order of operations?

A: Yes, the expression ${7+(5-9)^2+3(16 \div 8)}$ requires the order of operations to be evaluated correctly.

Q: How do you evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations:

Evaluate expressions inside parentheses first.
Evaluate any exponential expressions next.
Evaluate multiplication and division operations from left to right.
Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the final answer to the expression ${7+(5-9)^2+3(16 \div 8)}$ ?

A: The final answer to the expression ${7+(5-9)^2+3(16 \div 8)}$ is 29.

Common Mistakes

Not following the order of operations
Evaluating expressions from right to left instead of left to right
Not evaluating expressions inside parentheses first
Not evaluating exponential expressions next

Tips and Tricks

Use the acronym PEMDAS to remember the order of operations
Evaluate expressions inside parentheses first
Evaluate any exponential expressions next
Evaluate multiplication and division operations from left to right
Finally, evaluate any addition and subtraction operations from left to right

Practice Problems

Evaluate the expression ${2(3+4)^2-5}$
Evaluate the expression ${10-3(2+1)+2}$
Evaluate the expression ${4(2-1)^2+3(16 \div 8)}$

Conclusion

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. Following the order of operations is important to ensure that mathematical expressions are evaluated consistently and accurately. By following the order of operations, you can evaluate expressions with multiple operations and arrive at the correct answer.