Understanding the Concept of Adding and Subtracting Negative Numbers

Oct 13, 2025 by miodeya.com 11 views

When dealing with arithmetic operations involving negative numbers, it's essential to understand the concept of adding and subtracting negative numbers. In this article, we will explore the concept of equivalent expressions in arithmetic operations, specifically focusing on the expression $$63.56 + (-81.47)$$.

What are Negative Numbers?

A negative number is a real number that is less than zero. It is denoted by a minus sign (-) preceding the number. For example, -5 is a negative number, as it is less than zero.

Understanding the Concept of Adding and Subtracting Negative Numbers

When adding or subtracting negative numbers, we need to follow the rules of arithmetic operations. The rules are as follows:

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 value of the negative number from the positive number.
When subtracting a positive number and a negative number, we add the absolute value of the negative number to the positive number.

Evaluating the Expression $$63.56 + (-81.47)$$

To evaluate the expression $$63.56 + (-81.47)$$, we need to follow the rules of arithmetic operations. Since we are adding a positive number and a negative number, we will subtract the absolute value of the negative number from the positive number.

The absolute value of -81.47 is 81.47. Therefore, we will subtract 81.47 from 63.56.

63.56 + (-81.47) = 63.56 - 81.47

Which Expression is Equivalent to $$63.56 + (-81.47)$$?

Now that we have evaluated the expression $$63.56 + (-81.47)$$, we need to determine which expression is equivalent to it. The options are:

A. $$63.56 - 81.47$$ B. $$63.56 + 81.47$$ C. $$-63.56 - 81.47$$ D. $$-63.56 + 81.47$$

Based on our evaluation, we can see that the expression $$63.56 - 81.47$$ is equivalent to $$63.56 + (-81.47)$$.

Conclusion

In conclusion, when dealing with arithmetic operations involving negative numbers, it's essential to understand the concept of adding and subtracting negative numbers. By following the rules of arithmetic operations, we can evaluate expressions involving negative numbers and determine which expressions are equivalent to them.

Key Takeaways

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 value of the negative number from the positive number.
When subtracting a positive number and a negative number, we add the absolute value of the negative number to the positive number.

Frequently Asked Questions

Q: What is the difference between adding and subtracting negative numbers?

A: 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.

Q: How do we evaluate the expression $$63.56 + (-81.47)$$?

A: To evaluate the expression $$63.56 + (-81.47)$$, we need to follow the rules of arithmetic operations. Since we are adding a positive number and a negative number, we will subtract the absolute value of the negative number from the positive number.

Q: Which expression is equivalent to $$63.56 + (-81.47)$$?

A: The expression $$63.56 - 81.47$$ is equivalent to $$63.56 + (-81.47)$$.

Q: What is the concept of absolute value?

In this section, we will address some of the most common questions related to the concept of negative numbers and arithmetic operations.

Q: What is the difference between adding and subtracting negative numbers?

A: 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.

Q: How do we evaluate the expression $$63.56 + (-81.47)$$?

Q: Which expression is equivalent to $$63.56 + (-81.47)$$?

A: The expression $$63.56 - 81.47$$ is equivalent to $$63.56 + (-81.47)$$.

Q: What is the concept of absolute value?

A: The absolute value of a number is its distance from zero on the number line. It is denoted by a vertical bar (|) preceding the number. For example, the absolute value of -5 is 5.

Q: How do we add and subtract fractions with negative numbers?

A: When adding or subtracting fractions with negative numbers, we need to follow the rules of arithmetic operations. We will add or subtract the numerators and keep the same denominator.

Q: Can we add or subtract a negative number and a fraction?

A: Yes, we can add or subtract a negative number and a fraction. We will follow the rules of arithmetic operations and add or subtract the numerators and keep the same denominator.

Q: How do we evaluate the expression $$-2.5 + 3.7 - 1.2$$?

A: To evaluate the expression $$-2.5 + 3.7 - 1.2$$, we need to follow the order of operations (PEMDAS). We will first add 3.7 and -2.5, then subtract 1.2.

Q: What is the difference between a negative number and a positive number?

A: A negative number is a real number that is less than zero. A positive number is a real number that is greater than zero.

Q: Can we compare two negative numbers?

A: Yes, we can compare two negative numbers. We will compare their absolute values and determine which one is greater.

Q: How do we order negative numbers?

A: We will order negative numbers by comparing their absolute values. The negative number with the smaller absolute value will come first.

Q: Can we add or subtract a negative number and a decimal?

A: Yes, we can add or subtract a negative number and a decimal. We will follow the rules of arithmetic operations and add or subtract the numerators and keep the same denominator.

Q: How do we evaluate the expression $$-4.2 + 2.5 - 1.8$$?

A: To evaluate the expression $$-4.2 + 2.5 - 1.8$$, we need to follow the order of operations (PEMDAS). We will first add 2.5 and -4.2, then subtract 1.8.

Q: What is the concept of negative exponents?

A: A negative exponent is a power of a number that is less than zero. It is denoted by a negative sign preceding the exponent. For example, $$2^{-3}$$ is equal to $$\frac{1}{2^3}$$.

Q: How do we evaluate the expression $$2^{-3}$$?

A: To evaluate the expression $$2^{-3}$$, we need to follow the rules of exponents. We will divide 1 by $$2^3$$.

Q: Can we add or subtract a negative exponent and a positive exponent?

A: Yes, we can add or subtract a negative exponent and a positive exponent. We will follow the rules of exponents and add or subtract the exponents.

Q: How do we evaluate the expression $$2^{-3} + 2^3$$?

A: To evaluate the expression $$2^{-3} + 2^3$$, we need to follow the rules of exponents. We will add the exponents and keep the same base.

Q: What is the concept of scientific notation?

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It is denoted by a number between 1 and 10, multiplied by a power of 10.

Q: How do we convert a number to scientific notation?

A: To convert a number to scientific notation, we need to move the decimal point to the left or right until we have a number between 1 and 10. We will then multiply the number by a power of 10.

Q: Can we add or subtract numbers in scientific notation?

A: Yes, we can add or subtract numbers in scientific notation. We will follow the rules of arithmetic operations and add or subtract the numbers.

Q: How do we evaluate the expression $$2.5 \times 10^3 + 3.2 \times 10^2$$?

A: To evaluate the expression $$2.5 \times 10^3 + 3.2 \times 10^2$$, we need to follow the rules of arithmetic operations. We will add the numbers and keep the same exponent.

Q: What is the concept of order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

Q: How do we evaluate an expression using the order of operations?

A: To evaluate an expression using the order of operations, we need to follow the rules of PEMDAS. We will perform the operations in the correct order and simplify the expression.

Q: Can we add or subtract expressions with multiple operations?

A: Yes, we can add or subtract expressions with multiple operations. We will follow the rules of arithmetic operations and add or subtract the expressions.

Q: How do we evaluate the expression $$2(3 + 4) - 5$$?

A: To evaluate the expression $$2(3 + 4) - 5$$, we need to follow the order of operations (PEMDAS). We will first evaluate the expression inside the parentheses, then multiply 2 by the result, and finally subtract 5.

Q: What is the concept of algebraic expressions?

A: An algebraic expression is a mathematical expression that contains variables and constants. It is used to represent a value or a relationship between values.

Q: How do we evaluate an algebraic expression?

A: To evaluate an algebraic expression, we need to follow the rules of arithmetic operations and substitute the values of the variables.

Q: Can we add or subtract algebraic expressions?

A: Yes, we can add or subtract algebraic expressions. We will follow the rules of arithmetic operations and add or subtract the expressions.

Q: How do we evaluate the expression $$2x + 3y - 4z$$?

A: To evaluate the expression $$2x + 3y - 4z$$, we need to follow the rules of arithmetic operations and substitute the values of the variables.

Q: What is the concept of functions?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). It is used to describe a relationship between variables.

Q: How do we evaluate a function?

A: To evaluate a function, we need to follow the rules of arithmetic operations and substitute the values of the variables.

Q: Can we add or subtract functions?

A: Yes, we can add or subtract functions. We will follow the rules of arithmetic operations and add or subtract the functions.

Q: How do we evaluate the expression $$f(x) = 2x + 3$$?

A: To evaluate the expression $$f(x) = 2x + 3$$, we need to follow the rules of arithmetic operations and substitute the values of the variable.

Q: What is the concept of graphing?

A: Graphing is the process of representing a function or an equation on a coordinate plane. It is used to visualize the relationship between variables.

Q: How do we graph a function?

A: To graph a function, we need to follow the rules of graphing and plot the points on the coordinate plane.

Q: Can we add or subtract graphs?

A: Yes, we can add or subtract graphs. We will follow the rules of graphing and add or subtract the graphs.

Q: How do we evaluate the expression $$y = 2x + 3$$?

A: To evaluate the expression $$y = 2x + 3$$, we need to follow the rules of arithmetic operations and substitute the values of the variable.

**Q: What is the concept of systems of