Match Each Expression With Its Simplified Answer.1. $100 \times 2 \div 5$2. $89 + 43 - 10$3. $100 \div 2 \times 5$4. $ 4 × 8 − 14 4 \times 8 - 14 4 × 8 − 14 [/tex]5. $15 + 8 - 6$Answers:A. 18B. 17C. 40D. 250E. 122

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Simplifying expressions is an essential skill that helps us evaluate and solve mathematical problems efficiently. In this article, we will focus on simplifying five different expressions using the order of operations (PEMDAS) and provide step-by-step solutions.

Expression 1: 100 × 2 ÷ 5

To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Multiply 100 and 2: 100 × 2 = 200
  2. Divide 200 by 5: 200 ÷ 5 = 40

Therefore, the simplified answer for expression 1 is 40.

Expression 2: 89 + 43 - 10

To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Add 89 and 43: 89 + 43 = 132
  2. Subtract 10 from 132: 132 - 10 = 122

Therefore, the simplified answer for expression 2 is 122.

Expression 3: 100 ÷ 2 × 5

To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Divide 100 by 2: 100 ÷ 2 = 50
  2. Multiply 50 by 5: 50 × 5 = 250

Therefore, the simplified answer for expression 3 is 250.

Expression 4: 4 × 8 - 14

To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Multiply 4 and 8: 4 × 8 = 32
  2. Subtract 14 from 32: 32 - 14 = 18

Therefore, the simplified answer for expression 4 is 18.

Expression 5: 15 + 8 - 6

To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Add 15 and 8: 15 + 8 = 23
  2. Subtract 6 from 23: 23 - 6 = 17

Therefore, the simplified answer for expression 5 is 17.

Conclusion

In this article, we have simplified five different expressions using the order of operations (PEMDAS). By following the correct order of operations, we can evaluate and solve mathematical problems efficiently. Remember to always follow the order of operations (PEMDAS) when simplifying expressions:

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

Introduction

In our previous article, we explored the concept of simplifying expressions using the order of operations (PEMDAS). In this article, we will provide a Q&A guide to help you better understand and apply the concepts of simplifying expressions.

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying expressions. The acronym PEMDAS stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. 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 (PEMDAS)?

A: Following the order of operations (PEMDAS) is crucial to ensure that mathematical expressions are evaluated correctly. If we don't follow the correct order, we may get incorrect results. For example, consider the expression 3 × 2 + 10. If we don't follow the order of operations, we might evaluate the expression as 3 + 2 × 10, which would give us an incorrect result.

Q: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, follow the order of operations (PEMDAS):

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

Q: What if I have an expression with multiple parentheses?

A: If you have an expression with multiple parentheses, evaluate the innermost parentheses first, and then work your way outwards. For example, consider the expression (2 + 3) × (4 - 2). To simplify this expression, we would first evaluate the innermost parentheses: (2 + 3) = 5 and (4 - 2) = 2. Then, we would multiply the results: 5 × 2 = 10.

Q: Can I simplify expressions with variables?

A: Yes, you can simplify expressions with variables. To simplify an expression with variables, follow the same order of operations (PEMDAS) as you would with numerical expressions. For example, consider the expression 2x + 3y - 4. To simplify this expression, we would first evaluate any expressions inside parentheses (if any), and then follow the order of operations.

Q: What if I have an expression with a negative sign?

A: If you have an expression with a negative sign, treat the negative sign as a separate operation. For example, consider the expression -2 × 3. To simplify this expression, we would first multiply 2 and 3, and then apply the negative sign: -2 × 3 = -6.

Conclusion

In this Q&A guide, we have covered some common questions and scenarios related to simplifying expressions. By following the order of operations (PEMDAS) and understanding the rules for simplifying expressions, you will become more confident and proficient in solving mathematical problems. Remember to always follow the order of operations (PEMDAS) and to evaluate expressions carefully to ensure accurate results.