Enter The Correct 4-digit Code (no Spaces) By Solving The Following Expressions:1. \[$(5 - 2 + 8 \div 4) \times 5\$\]2. \[$(9 + 4 - 2) \times 10 - 4\$\]3. \[$2(3 + 4) + 32 \div 8\$\]4. \[$3(3 + 5) + 4 \times 4 -

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**Solving Math Expressions: A Step-by-Step Guide** =====================================================

Introduction

Math expressions can be a challenging and daunting task for many of us. However, with a clear understanding of the order of operations and a step-by-step approach, we can solve even the most complex expressions with ease. In this article, we will explore four math expressions and provide a detailed solution to each one.

Expression 1: (5−2+8÷4)×5(5 - 2 + 8 \div 4) \times 5

What is the solution to Expression 1?

To solve Expression 1, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: None in this expression.
  3. Multiplication and Division: Evaluate the division first, then the multiplication.
  4. Addition and Subtraction: Finally, evaluate the addition and subtraction.

Step-by-Step Solution

  1. Evaluate the expression inside the parentheses: 5−2+8÷45 - 2 + 8 \div 4
    • Division: 8÷4=28 \div 4 = 2
    • Addition and Subtraction: 5−2+2=55 - 2 + 2 = 5
  2. Multiply the result by 5: 5×5=255 \times 5 = 25

Answer: The solution to Expression 1 is 25.

Expression 2: (9+4−2)×10−4(9 + 4 - 2) \times 10 - 4

What is the solution to Expression 2?

To solve Expression 2, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: None in this expression.
  3. Multiplication and Division: Evaluate the multiplication first, then the subtraction.
  4. Addition and Subtraction: Finally, evaluate the addition and subtraction.

Step-by-Step Solution

  1. Evaluate the expression inside the parentheses: 9+4−29 + 4 - 2
    • Addition and Subtraction: 9+4=139 + 4 = 13, then 13−2=1113 - 2 = 11
  2. Multiply the result by 10: 11×10=11011 \times 10 = 110
  3. Subtract 4 from the result: 110−4=106110 - 4 = 106

Answer: The solution to Expression 2 is 106.

Expression 3: 2(3+4)+32÷82(3 + 4) + 32 \div 8

What is the solution to Expression 3?

To solve Expression 3, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: None in this expression.
  3. Multiplication and Division: Evaluate the multiplication first, then the division.
  4. Addition and Subtraction: Finally, evaluate the addition and subtraction.

Step-by-Step Solution

  1. Evaluate the expression inside the parentheses: 3+43 + 4
    • Addition: 3+4=73 + 4 = 7
  2. Multiply 2 by the result: 2×7=142 \times 7 = 14
  3. Divide 32 by 8: 32÷8=432 \div 8 = 4
  4. Add the results: 14+4=1814 + 4 = 18

Answer: The solution to Expression 3 is 18.

Expression 4: 3(3+5)+4×4−23(3 + 5) + 4 \times 4 - 2

What is the solution to Expression 4?

To solve Expression 4, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: None in this expression.
  3. Multiplication and Division: Evaluate the multiplication first, then the division.
  4. Addition and Subtraction: Finally, evaluate the addition and subtraction.

Step-by-Step Solution

  1. Evaluate the expression inside the parentheses: 3+53 + 5
    • Addition: 3+5=83 + 5 = 8
  2. Multiply 3 by the result: 3×8=243 \times 8 = 24
  3. Multiply 4 by 4: 4×4=164 \times 4 = 16
  4. Add the results: 24+16=4024 + 16 = 40
  5. Subtract 2 from the result: 40−2=3840 - 2 = 38

Answer: The solution to Expression 4 is 38.

Conclusion

Solving math expressions can be a challenging task, but with a clear understanding of the order of operations and a step-by-step approach, we can solve even the most complex expressions with ease. By following the order of operations (PEMDAS) and evaluating the expressions inside the parentheses first, we can simplify the expressions and arrive at the final solution.

Frequently Asked Questions

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 we evaluate mathematical expressions. The acronym PEMDAS stands for:

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

Q: How do I evaluate expressions inside the parentheses?

A: To evaluate expressions inside the parentheses, we need to follow the order of operations (PEMDAS). We start by evaluating any exponential expressions, then any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve numbers. However, multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Q: How do I add and subtract numbers?

A: To add and subtract numbers, we need to follow the order of operations (PEMDAS). We start by evaluating any expressions inside the parentheses, then any multiplication and division operations, and finally any addition and subtraction operations.

Q: What is the final answer to Expression 1?

A: The final answer to Expression 1 is 25.

Q: What is the final answer to Expression 2?

A: The final answer to Expression 2 is 106.

Q: What is the final answer to Expression 3?

A: The final answer to Expression 3 is 18.

Q: What is the final answer to Expression 4?

A: The final answer to Expression 4 is 38.