What Is The Value Of This Expression? 42 − { ( 7 + 14 ) ÷ 7 } × 4 42-\{(7+14) \div 7\} \times 4 42 − {( 7 + 14 ) ÷ 7 } × 4 A. 6 B. 28 C. 30 D. 156

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Understanding the Expression

The given expression is $42-\{(7+14) \div 7\} \times 4$. To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate the expressions inside the parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Evaluating the Expression Inside the Parentheses

The expression inside the parentheses is $(7+14) \div 7$. To evaluate this expression, we need to follow the order of operations:

1. Parentheses: Evaluate the expression inside the parentheses.
2. Division: Divide 21 by 7.

$(7+14) \div 7 = 21 \div 7 = 3$

Evaluating the Expression

Now that we have evaluated the expression inside the parentheses, we can substitute the result back into the original expression:

$42-\{(7+14) \div 7\} \times 4 = 42 - 3 \times 4$

Evaluating the Multiplication

To evaluate the multiplication, we need to multiply 3 by 4:

$3 \times 4 = 12$

Evaluating the Subtraction

Now that we have evaluated the multiplication, we can substitute the result back into the expression:

$42 - 3 \times 4 = 42 - 12$

Final Evaluation

To evaluate the subtraction, we need to subtract 12 from 42:

$42 - 12 = 30$

The final answer is $\boxed{30}$.

Conclusion

In this article, we evaluated the expression $42-\{(7+14) \div 7\} \times 4$ using the order of operations (PEMDAS). We first evaluated the expression inside the parentheses, then substituted the result back into the original expression. We then evaluated the multiplication and subtraction operations to arrive at the final answer of 30.

Frequently Asked Questions

• What is the order of operations (PEMDAS)? The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for:
  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.
• How do I evaluate an expression using the order of operations? To evaluate an expression using the order of operations, follow these steps:
  1. Evaluate any expressions inside parentheses.
  2. Evaluate any exponential expressions.
  3. Evaluate any multiplication and division operations from left to right.
  4. Evaluate any addition and subtraction operations from left to right.

Related Topics

• Order of Operations (PEMDAS)
• Evaluating Expressions
• Algebra

References

• "Order of Operations" by Math Open Reference
• "Evaluating Expressions" by Khan Academy
• "Algebra" by Wikipedia
  

Q&A: Evaluating Expressions

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for: + Parentheses: Evaluate expressions inside parentheses first. + Exponents: Evaluate any exponential expressions next. + Multiplication and Division: Evaluate any multiplication and division operations from left to right. + Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: How do I evaluate an expression using the order of operations?

A: To evaluate an expression using the order of operations, follow these steps: 1. Evaluate any expressions inside parentheses. 2. Evaluate any exponential expressions. 3. Evaluate any multiplication and division operations from left to right. 4. Evaluate any addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve numbers. However, multiplication involves combining numbers to get a product, while division involves splitting a number into equal parts.

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

A: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses, then evaluate any exponential expressions, followed by any multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right.

Q: What is the importance of following the order of operations?

A: Following the order of operations is crucial in mathematics because it ensures that expressions are evaluated consistently and accurately. Without following the order of operations, expressions may be evaluated incorrectly, leading to incorrect results.

Q: Can I use a calculator to evaluate expressions?

A: Yes, you can use a calculator to evaluate expressions. However, it's essential to understand the order of operations and how to evaluate expressions manually to ensure accuracy and build mathematical skills.

Q: How do I evaluate an expression with variables?

A: To evaluate an expression with variables, follow the same steps as evaluating an expression with numbers. However, you may need to substitute values for the variables to get a numerical result.

Q: What is the difference between an expression and an equation?

A: An expression is a mathematical statement that contains variables and constants, while an equation is a statement that says two expressions are equal. Equations often involve solving for a variable to find a solution.

Q: How do I solve an equation?

A: To solve an equation, follow these steps: 1. Simplify the equation by combining like terms. 2. Isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value. 3. Solve for the variable by evaluating the expression.

Q: What is the importance of solving equations?

A: Solving equations is crucial in mathematics because it allows you to find the value of a variable, which can be used to solve real-world problems. Solving equations also helps to build mathematical skills and understanding.

Related Topics

• Order of Operations (PEMDAS)
• Evaluating Expressions
• Algebra
• Equations
• Variables

References

• "Order of Operations" by Math Open Reference
• "Evaluating Expressions" by Khan Academy
• "Algebra" by Wikipedia
• "Equations" by Math Is Fun
• "Variables" by Math Goodies