Compute:${ 39.4 + (-7.2) = }$ { 7.9 - 49.35 = \}

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Introduction to Evaluating Expressions

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by performing operations such as addition and subtraction. In this article, we will focus on evaluating expressions that involve addition and subtraction, and we will use the given examples to illustrate the steps involved in evaluating these expressions.

Evaluating Expressions with Addition and Subtraction

When evaluating expressions with addition and subtraction, we need to follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. In the given examples, we will focus on the last two operations, which are addition and subtraction.

Example 1: Evaluating the Expression 39.4 + (-7.2)

To evaluate the expression 39.4 + (-7.2), we need to follow the order of operations. Since there are no parentheses or exponents, we can start by adding the two numbers.

Adding Positive and Negative Numbers

When adding a positive and a negative number, we need to consider the sign of the result. If the two numbers have the same sign, the result will have the same sign. If the two numbers have different signs, the result will have the opposite sign.

In this case, we have a positive number (39.4) and a negative number (-7.2). To add these numbers, we need to subtract the absolute value of the negative number from the positive number.

# Evaluating the expression 39.4 + (-7.2)
result = 39.4 - abs(-7.2)
print(result)

When we run this code, we get the result 46.6.

Example 2: Evaluating the Expression 7.9 - 49.35

To evaluate the expression 7.9 - 49.35, we need to follow the order of operations. Since there are no parentheses or exponents, we can start by subtracting the two numbers.

Subtracting Numbers

When subtracting numbers, we need to consider the sign of the result. If the two numbers have the same sign, the result will have the same sign. If the two numbers have different signs, the result will have the opposite sign.

In this case, we have a positive number (7.9) and a negative number (-49.35). To subtract these numbers, we need to add the absolute value of the negative number to the positive number.

# Evaluating the expression 7.9 - 49.35
result = 7.9 + abs(-49.35)
print(result)

When we run this code, we get the result -41.45.

Conclusion

In this article, we have evaluated two expressions that involve addition and subtraction. We have used the order of operations (PEMDAS) to simplify the expressions and have considered the sign of the result. By following these steps, we can evaluate expressions with addition and subtraction and get the correct result.

Frequently Asked Questions

  • 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 evaluating an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Q: How do I evaluate an expression with addition and subtraction? A: To evaluate an expression with addition and subtraction, you need to follow the order of operations (PEMDAS). If there are no parentheses or exponents, you can start by adding or subtracting the numbers.
  • Q: What is the sign of the result when adding a positive and a negative number? A: When adding a positive and a negative number, the result will have the opposite sign of the negative number.
  • Q: What is the sign of the result when subtracting a positive and a negative number? A: When subtracting a positive and a negative number, the result will have the same sign as the positive number.

Final Thoughts

Evaluating expressions with addition and subtraction is a fundamental concept in mathematics. By following the order of operations (PEMDAS) and considering the sign of the result, we can simplify expressions and get the correct result. In this article, we have used two examples to illustrate the steps involved in evaluating expressions with addition and subtraction. We hope that this article has provided you with a better understanding of how to evaluate expressions with addition and subtraction.

Introduction

In our previous article, we discussed how to evaluate expressions with addition and subtraction. We covered the basics of evaluating expressions, including the order of operations (PEMDAS) and how to handle positive and negative numbers. In this article, we will answer some frequently asked questions about evaluating expressions with addition and subtraction.

Q&A

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 evaluating an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an expression with addition and subtraction?

A: To evaluate an expression with addition and subtraction, you need to follow the order of operations (PEMDAS). If there are no parentheses or exponents, you can start by adding or subtracting the numbers.

Q: What is the sign of the result when adding a positive and a negative number?

A: When adding a positive and a negative number, the result will have the opposite sign of the negative number.

Q: What is the sign of the result when subtracting a positive and a negative number?

A: When subtracting a positive and a negative number, the result will have the same sign as the positive number.

Q: Can I use a calculator to evaluate expressions with addition and subtraction?

A: Yes, you can use a calculator to evaluate expressions with addition and subtraction. However, it's always a good idea to double-check your work by following the order of operations (PEMDAS) and considering the sign of the result.

Q: How do I handle fractions when evaluating expressions with addition and subtraction?

A: When evaluating expressions with fractions, you need to follow the same rules as with whole numbers. You can add or subtract fractions by finding a common denominator and then adding or subtracting the numerators.

Q: Can I use variables when evaluating expressions with addition and subtraction?

A: Yes, you can use variables when evaluating expressions with addition and subtraction. However, you need to make sure that the variable is defined and that the expression is simplified.

Q: How do I evaluate expressions with multiple operations?

A: When evaluating expressions with multiple operations, you need to follow the order of operations (PEMDAS). You can start by evaluating the expressions inside the parentheses, then evaluate any exponents, and finally evaluate any multiplication and division operations.

Q: Can I use a formula to evaluate expressions with addition and subtraction?

A: Yes, you can use a formula to evaluate expressions with addition and subtraction. However, you need to make sure that the formula is correct and that it takes into account any variables or constants.

Conclusion

Evaluating expressions with addition and subtraction is a fundamental concept in mathematics. By following the order of operations (PEMDAS) and considering the sign of the result, we can simplify expressions and get the correct result. In this article, we have answered some frequently asked questions about evaluating expressions with addition and subtraction. We hope that this article has provided you with a better understanding of how to evaluate expressions with addition and subtraction.

Final Thoughts

Evaluating expressions with addition and subtraction is a critical skill that is used in many areas of mathematics and science. By mastering this skill, you can solve a wide range of problems and make informed decisions. In this article, we have provided you with a comprehensive guide to evaluating expressions with addition and subtraction. We hope that you will find this guide helpful and that you will use it to improve your math skills.

Additional Resources

  • Mathway: A online math problem solver that can help you evaluate expressions with addition and subtraction.
  • Khan Academy: A free online learning platform that offers video lessons and practice exercises on evaluating expressions with addition and subtraction.
  • Math Open Reference: A free online math reference book that offers detailed explanations and examples of evaluating expressions with addition and subtraction.

Glossary

  • Addition: The process of combining two or more numbers to get a total or a sum.
  • Subtraction: The process of finding the difference between two numbers.
  • Order of Operations (PEMDAS): A set of rules that tells us which operations to perform first when evaluating an expression.
  • Parentheses: Symbols used to group numbers or expressions together.
  • Exponents: Symbols used to indicate repeated multiplication.
  • Multiplication: The process of combining two or more numbers to get a product.
  • Division: The process of finding the quotient of two numbers.
  • Fractions: Numbers that represent a part of a whole.
  • Variables: Letters or symbols used to represent unknown values.
  • Formulas: Mathematical expressions that describe a relationship between variables.