Match Each Expression On The Left With An Equivalent Expression On The Right. Some Answer Choices On The Right Will Not Be Used.Left Side:1. \[$(2 \cdot 3) \cdot 7\$\]2. \[$3 + 12 + 79\$\]3. \[$2 + 7 + 3\$\]4. \[$5 - 1 =

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Introduction

Mathematical expressions are a fundamental aspect of mathematics, and understanding how to manipulate and simplify them is crucial for problem-solving. In this article, we will explore the concept of equivalent expressions and provide a comprehensive guide to matching each expression on the left with an equivalent expression on the right.

What are Equivalent Expressions?

Equivalent expressions are mathematical expressions that have the same value or result, even if they are written differently. They can be obtained by applying various mathematical operations, such as addition, subtraction, multiplication, and division, in a specific order. Understanding equivalent expressions is essential for simplifying complex mathematical expressions and solving problems efficiently.

Left Side Expressions

1. {(2 \cdot 3) \cdot 7$}$

This expression involves the multiplication of two numbers, 2 and 3, and then multiplying the result by 7. To simplify this expression, we can follow the order of operations (PEMDAS):

  1. Multiply 2 and 3: 2 × 3 = 6
  2. Multiply 6 by 7: 6 × 7 = 42

Therefore, the equivalent expression on the right is:

2. ${42\$}

2. ${3 + 12 + 79\$}

This expression involves the addition of three numbers, 3, 12, and 79. To simplify this expression, we can add the numbers in any order:

  1. Add 3 and 12: 3 + 12 = 15
  2. Add 15 and 79: 15 + 79 = 94

Therefore, the equivalent expression on the right is:

3. ${94\$}

3. ${2 + 7 + 3\$}

This expression involves the addition of three numbers, 2, 7, and 3. To simplify this expression, we can add the numbers in any order:

  1. Add 2 and 7: 2 + 7 = 9
  2. Add 9 and 3: 9 + 3 = 12

Therefore, the equivalent expression on the right is:

4. ${12\$}

4. ${5 - 1 = 4\$}

This expression involves the subtraction of 1 from 5. To simplify this expression, we can perform the subtraction:

5 - 1 = 4

Therefore, the equivalent expression on the right is:

5. ${4\$}

Conclusion

In this article, we have explored the concept of equivalent expressions and provided a comprehensive guide to matching each expression on the left with an equivalent expression on the right. We have seen how to simplify complex mathematical expressions by applying various mathematical operations in a specific order. Understanding equivalent expressions is essential for problem-solving and simplifying complex mathematical expressions.

Key Takeaways

  • Equivalent expressions are mathematical expressions that have the same value or result.
  • Understanding equivalent expressions is essential for simplifying complex mathematical expressions and solving problems efficiently.
  • The order of operations (PEMDAS) is crucial for simplifying mathematical expressions.
  • Adding and subtracting numbers in any order can simplify complex mathematical expressions.

Further Reading

For further reading on mathematical expressions and equivalent expressions, we recommend the following resources:

  • Khan Academy: Mathematical Expressions
  • Mathway: Equivalent Expressions
  • Wolfram MathWorld: Equivalent Expressions

References

  • "Mathematical Expressions" by Khan Academy
  • "Equivalent Expressions" by Mathway
  • "Equivalent Expressions" by Wolfram MathWorld
    Mathematical Expression Matching: A Comprehensive Guide ===========================================================

Q&A: 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 mathematical operations should be performed when there are multiple operations in an expression. PEMDAS stands for:

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

Q: How do I simplify a mathematical expression?

A: To simplify a mathematical expression, 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 an expression and an equation?

A: An expression is a mathematical statement that contains variables, constants, and mathematical operations, but does not contain an equal sign (=). An equation, on the other hand, is a mathematical statement that contains an equal sign (=) and is used to solve for a variable.

Q: How do I determine if two expressions are equivalent?

A: To determine if two expressions are equivalent, follow these steps:

  1. Simplify each expression using the order of operations (PEMDAS).
  2. Compare the simplified expressions to see if they are the same.

Q: What is the concept of equivalent expressions?

A: Equivalent expressions are mathematical expressions that have the same value or result, even if they are written differently. They can be obtained by applying various mathematical operations, such as addition, subtraction, multiplication, and division, in a specific order.

Q: How do I match each expression on the left with an equivalent expression on the right?

A: To match each expression on the left with an equivalent expression on the right, follow these steps:

  1. Simplify each expression on the left using the order of operations (PEMDAS).
  2. Compare the simplified expressions to see if they match any of the expressions on the right.

Q: What are some common types of equivalent expressions?

A: Some common types of equivalent expressions include:

  • Like terms: Expressions that contain the same variables and coefficients, but may have different constants.
  • Distributive property: Expressions that involve the multiplication of a single term by a sum or difference of terms.
  • Combining like terms: Expressions that involve the combination of like terms to simplify an expression.

Q: How do I use equivalent expressions in real-world applications?

A: Equivalent expressions are used in a variety of real-world applications, including:

  • Algebra: Equivalent expressions are used to solve equations and inequalities.
  • Geometry: Equivalent expressions are used to describe the properties of geometric shapes.
  • Physics: Equivalent expressions are used to describe the laws of motion and energy.

Conclusion

In this article, we have explored the concept of equivalent expressions and provided a comprehensive guide to matching each expression on the left with an equivalent expression on the right. We have seen how to simplify complex mathematical expressions by applying various mathematical operations in a specific order. Understanding equivalent expressions is essential for problem-solving and simplifying complex mathematical expressions.

Key Takeaways

  • Equivalent expressions are mathematical expressions that have the same value or result.
  • Understanding equivalent expressions is essential for simplifying complex mathematical expressions and solving problems efficiently.
  • The order of operations (PEMDAS) is crucial for simplifying mathematical expressions.
  • Adding and subtracting numbers in any order can simplify complex mathematical expressions.

Further Reading

For further reading on mathematical expressions and equivalent expressions, we recommend the following resources:

  • Khan Academy: Mathematical Expressions
  • Mathway: Equivalent Expressions
  • Wolfram MathWorld: Equivalent Expressions

References

  • "Mathematical Expressions" by Khan Academy
  • "Equivalent Expressions" by Mathway
  • "Equivalent Expressions" by Wolfram MathWorld