Simplify The Expression:$-10 + (-30$\]

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us to evaluate and solve equations efficiently. When dealing with negative numbers, it's essential to understand the rules of addition and subtraction to simplify expressions accurately. In this article, we will focus on simplifying the expression $-10 + (-30)$, exploring the concept of combining like terms and applying the rules of arithmetic operations.

Understanding Negative Numbers

Before we dive into simplifying the expression, let's take a moment to understand the concept of negative numbers. A negative number is a number that is less than zero. In the context of the expression $-10 + (-30)$, both $-10$ and $-30$ are negative numbers. When we add or subtract negative numbers, we need to follow specific rules to ensure that we get the correct result.

Rules of Addition and Subtraction

When adding or subtracting negative numbers, we need to remember the following rules:

• When adding two negative numbers, we add their absolute values and keep the negative sign.
• When subtracting two negative numbers, we subtract their absolute values and keep the negative sign.
• When adding a positive number and a negative number, we subtract the absolute values and determine the sign based on the original numbers.

Simplifying the Expression

Now that we have a solid understanding of negative numbers and the rules of addition and subtraction, let's simplify the expression $-10 + (-30)$.

To simplify this expression, we need to combine the two negative numbers. Since both numbers are negative, we add their absolute values and keep the negative sign.

|-10| = 10 |-30| = 30

Now, we add the absolute values:

10 + 30 = 40

Since both numbers are negative, we keep the negative sign:

-10 + (-30) = -40

Therefore, the simplified expression is $-40$.

Conclusion

Simplifying expressions is a fundamental skill in mathematics that helps us to evaluate and solve equations efficiently. By understanding the rules of addition and subtraction, we can combine like terms and simplify expressions accurately. In this article, we focused on simplifying the expression $-10 + (-30)$, exploring the concept of combining like terms and applying the rules of arithmetic operations. We learned that when adding two negative numbers, we add their absolute values and keep the negative sign. By following these rules, we can simplify expressions and arrive at the correct result.

Frequently Asked Questions

• What is the simplified expression of $-10 + (-30)$?
• How do we simplify expressions with negative numbers?
• What are the rules of addition and subtraction for negative numbers?

Answers

• The simplified expression of $-10 + (-30)$ is $-40$.
• To simplify expressions with negative numbers, we need to combine like terms and apply the rules of arithmetic operations.
• The rules of addition and subtraction for negative numbers are:
  • When adding two negative numbers, we add their absolute values and keep the negative sign.
  • When subtracting two negative numbers, we subtract their absolute values and keep the negative sign.
  • When adding a positive number and a negative number, we subtract the absolute values and determine the sign based on the original numbers.

Final Thoughts

Simplifying expressions is a crucial skill in mathematics that helps us to evaluate and solve equations efficiently. By understanding the rules of addition and subtraction, we can combine like terms and simplify expressions accurately. In this article, we focused on simplifying the expression $-10 + (-30)$, exploring the concept of combining like terms and applying the rules of arithmetic operations. We learned that when adding two negative numbers, we add their absolute values and keep the negative sign. By following these rules, we can simplify expressions and arrive at the correct result.

Introduction

In our previous article, we explored the concept of simplifying expressions with negative numbers. We focused on the expression $-10 + (-30)$ and learned how to combine like terms and apply the rules of arithmetic operations. In this article, we will continue to answer some of the most frequently asked questions related to simplifying expressions with negative numbers.

Q&A

Q1: What is the simplified expression of $-10 + (-30)$?

A1: The simplified expression of $-10 + (-30)$ is $-40$.

Q2: How do we simplify expressions with negative numbers?

A2: To simplify expressions with negative numbers, we need to combine like terms and apply the rules of arithmetic operations. When adding two negative numbers, we add their absolute values and keep the negative sign. When subtracting two negative numbers, we subtract their absolute values and keep the negative sign.

Q3: What are the rules of addition and subtraction for negative numbers?

A3: The rules of addition and subtraction for negative numbers are:

• When adding two negative numbers, we add their absolute values and keep the negative sign.
• When subtracting two negative numbers, we subtract their absolute values and keep the negative sign.
• When adding a positive number and a negative number, we subtract the absolute values and determine the sign based on the original numbers.

Q4: Can we simplify expressions with multiple negative numbers?

A4: Yes, we can simplify expressions with multiple negative numbers. We need to combine like terms and apply the rules of arithmetic operations. For example, if we have the expression $-10 + (-30) + (-20)$, we can simplify it by combining the like terms: $-10 + (-30) = -40$, and then $-40 + (-20) = -60$.

Q5: How do we handle negative numbers with decimals?

A5: When working with negative numbers with decimals, we need to follow the same rules as before. For example, if we have the expression $-10.5 + (-30.2)$, we can simplify it by combining the like terms: $-10.5 + (-30.2) = -40.7$.

Q6: Can we simplify expressions with negative numbers and fractions?

A6: Yes, we can simplify expressions with negative numbers and fractions. We need to follow the same rules as before and also apply the rules of fractions. For example, if we have the expression $-\frac{1}{2} + (-\frac{3}{4})$, we can simplify it by finding a common denominator and then combining the like terms.

Q7: How do we simplify expressions with negative numbers and exponents?

A7: When working with negative numbers and exponents, we need to follow the same rules as before and also apply the rules of exponents. For example, if we have the expression $-2^3 + (-3^2)$, we can simplify it by evaluating the exponents and then combining the like terms.

Conclusion

Simplifying expressions with negative numbers is a crucial skill in mathematics that helps us to evaluate and solve equations efficiently. By understanding the rules of addition and subtraction, we can combine like terms and simplify expressions accurately. In this article, we answered some of the most frequently asked questions related to simplifying expressions with negative numbers. We learned that we can simplify expressions with multiple negative numbers, negative numbers with decimals, negative numbers and fractions, and negative numbers and exponents.

Final Thoughts

Simplifying expressions with negative numbers is a fundamental concept in mathematics that helps us to evaluate and solve equations efficiently. By understanding the rules of addition and subtraction, we can combine like terms and simplify expressions accurately. In this article, we continued to explore the concept of simplifying expressions with negative numbers and answered some of the most frequently asked questions. We learned that we can simplify expressions with multiple negative numbers, negative numbers with decimals, negative numbers and fractions, and negative numbers and exponents. By following these rules, we can simplify expressions and arrive at the correct result.