Evaluate The Expression:$(-13) + (+21) =$

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression means finding the value of the expression by performing the operations in the correct order. In this article, we will evaluate the expression (−13)+(+21)=(-13) + (+21) = and understand the concept of positive and negative numbers.

Understanding Positive and Negative Numbers

Positive numbers are numbers that are greater than zero, while negative numbers are numbers that are less than zero. In the given expression, (−13)(-13) is a negative number, and (+21)(+21) is a positive number. When we add a negative number and a positive number, we need to consider the sign of the result.

Adding Negative and Positive Numbers

When we add a negative number and a positive number, we need to subtract the absolute value of the negative number from the positive number. The absolute value of a number is its distance from zero, without considering the sign. In this case, the absolute value of (−13)(-13) is 1313, and the absolute value of (+21)(+21) is also 2121.

Evaluating the Expression

To evaluate the expression (−13)+(+21)=(-13) + (+21) =, we need to subtract the absolute value of the negative number from the positive number. So, we have:

(−13)+(+21)=−13+21(-13) + (+21) = -13 + 21

Applying the Rule of Signs

When we add a negative number and a positive number, we need to apply the rule of signs. The rule of signs states that when we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value. In this case, the absolute value of (−13)(-13) is 1313, and the absolute value of (+21)(+21) is 2121. Since 2121 is greater than 1313, the result will have the same sign as (+21)(+21), which is positive.

Evaluating the Expression with the Rule of Signs

Now that we have applied the rule of signs, we can evaluate the expression (−13)+(+21)=(-13) + (+21) =:

(−13)+(+21)=−13+21=8(-13) + (+21) = -13 + 21 = 8

Conclusion

In conclusion, the expression (−13)+(+21)=(-13) + (+21) = evaluates to 88. We learned that when we add a negative number and a positive number, we need to subtract the absolute value of the negative number from the positive number and apply the rule of signs. The rule of signs states that when we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value.

Frequently Asked Questions

  • Q: What is the value of (−13)+(+21)=(-13) + (+21) =? A: The value of (−13)+(+21)=(-13) + (+21) = is 88.
  • Q: Why do we need to apply the rule of signs when adding a negative number and a positive number? A: We need to apply the rule of signs because it helps us determine the sign of the result.
  • Q: What is the rule of signs? A: The rule of signs states that when we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value.

Examples

  • Evaluate the expression (−25)+(+30)=(-25) + (+30) =.
  • Evaluate the expression (−10)+(+20)=(-10) + (+20) =.
  • Evaluate the expression (−5)+(+15)=(-5) + (+15) =.

Step-by-Step Solution

  1. Identify the negative and positive numbers in the expression.
  2. Find the absolute value of the negative number.
  3. Find the absolute value of the positive number.
  4. Subtract the absolute value of the negative number from the positive number.
  5. Apply the rule of signs to determine the sign of the result.

Tips and Tricks

  • When adding a negative number and a positive number, always apply the rule of signs.
  • The rule of signs states that when we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value.
  • To evaluate an expression with negative and positive numbers, follow the steps outlined above.

Summary

In this article, we evaluated the expression (−13)+(+21)=(-13) + (+21) = and learned about the concept of positive and negative numbers. We also learned how to apply the rule of signs when adding a negative number and a positive number. The rule of signs states that when we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value. We also provided examples and a step-by-step solution to help you evaluate expressions with negative and positive numbers.

Introduction

In our previous article, we evaluated the expression (−13)+(+21)=(-13) + (+21) = and learned about the concept of positive and negative numbers. We also learned how to apply the rule of signs when adding a negative number and a positive number. In this article, we will answer some frequently asked questions about evaluating expressions with negative and positive numbers.

Q&A

Q: What is the value of (−25)+(+30)=(-25) + (+30) =?

A: To evaluate this expression, we need to apply the rule of signs. The absolute value of (−25)(-25) is 2525, and the absolute value of (+30)(+30) is 3030. Since 3030 is greater than 2525, the result will have the same sign as (+30)(+30), which is positive. Therefore, the value of (−25)+(+30)=(-25) + (+30) = is 55.

Q: Why do we need to apply the rule of signs when adding a negative number and a positive number?

A: We need to apply the rule of signs because it helps us determine the sign of the result. When we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value.

Q: What is the rule of signs?

A: The rule of signs states that when we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value.

Q: How do we evaluate an expression with multiple negative and positive numbers?

A: To evaluate an expression with multiple negative and positive numbers, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate any expressions inside 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.

Q: What is the value of (−10)+(+20)+(−15)=(-10) + (+20) + (-15) =?

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

  1. Parentheses: There are no expressions inside parentheses.
  2. Exponents: There are no exponential expressions.
  3. Multiplication and Division: There are no multiplication and division operations.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

First, we need to add (−10)(-10) and (+20)(+20):

(−10)+(+20)=10(-10) + (+20) = 10

Then, we need to add 1010 and (−15)(-15):

10+(−15)=−510 + (-15) = -5

Therefore, the value of (−10)+(+20)+(−15)=(-10) + (+20) + (-15) = is −5-5.

Q: What is the value of (−5)+(+15)+(−10)=(-5) + (+15) + (-10) =?

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

  1. Parentheses: There are no expressions inside parentheses.
  2. Exponents: There are no exponential expressions.
  3. Multiplication and Division: There are no multiplication and division operations.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

First, we need to add (−5)(-5) and (+15)(+15):

(−5)+(+15)=10(-5) + (+15) = 10

Then, we need to add 1010 and (−10)(-10):

10+(−10)=010 + (-10) = 0

Therefore, the value of (−5)+(+15)+(−10)=(-5) + (+15) + (-10) = is 00.

Conclusion

In this article, we answered some frequently asked questions about evaluating expressions with negative and positive numbers. We learned how to apply the rule of signs when adding a negative number and a positive number, and how to evaluate expressions with multiple negative and positive numbers. We also provided examples to help you understand the concept.

Frequently Asked Questions

  • Q: What is the value of (−25)+(+30)=(-25) + (+30) =? A: The value of (−25)+(+30)=(-25) + (+30) = is 55.
  • Q: Why do we need to apply the rule of signs when adding a negative number and a positive number? A: We need to apply the rule of signs because it helps us determine the sign of the result.
  • Q: What is the rule of signs? A: The rule of signs states that when we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value.

Examples

  • Evaluate the expression (−10)+(+20)+(−15)=(-10) + (+20) + (-15) =.
  • Evaluate the expression (−5)+(+15)+(−10)=(-5) + (+15) + (-10) =.
  • Evaluate the expression (−25)+(+30)+(−20)=(-25) + (+30) + (-20) =.

Step-by-Step Solution

  1. Identify the negative and positive numbers in the expression.
  2. Find the absolute value of the negative number.
  3. Find the absolute value of the positive number.
  4. Apply the rule of signs to determine the sign of the result.
  5. Follow the order of operations (PEMDAS) to evaluate the expression.

Tips and Tricks

  • When adding a negative number and a positive number, always apply the rule of signs.
  • The rule of signs states that when we add a negative number and a positive number, the result will have the same sign as the number with the greater absolute value.
  • To evaluate an expression with multiple negative and positive numbers, follow the order of operations (PEMDAS).