Subtraction

Definition

Subtraction is a fundamental mathematical operation that involves removing or taking away a quantity from another quantity. It is one of the four basic arithmetic operations, along with addition, multiplication, and division. Subtraction is essential in various mathematical contexts, including algebra, integers, and real numbers.

5 Must Know Facts For Your Next Test

1. Subtraction can be used to find the difference between two quantities, such as the difference between two integers or the difference between two real numbers.
2. When subtracting a negative number, the operation is equivalent to adding the additive inverse of that number.
3. Subtraction of integers follows specific rules, such as subtracting a positive integer results in a smaller value, while subtracting a negative integer results in a larger value.
4. The properties of real numbers, such as the commutative, associative, and distributive properties, can be applied to subtraction operations.
5. Subtraction is often used in algebraic expressions to represent the removal or reduction of a quantity, and it plays a crucial role in simplifying and solving algebraic equations.

Review Questions

• Explain how subtraction is used in the context of adding and subtracting integers.
  • Subtraction of integers is closely related to addition of integers. When subtracting a positive integer, the result is a smaller value, while subtracting a negative integer results in a larger value. This is because subtracting a negative number is equivalent to adding the additive inverse of that number. For example, 5 - (-3) = 5 + 3 = 8, as the additive inverse of -3 is 3. Understanding the relationship between subtraction and addition of integers is essential for performing operations with integers.
• Describe how the properties of real numbers, such as the commutative, associative, and distributive properties, can be applied to subtraction.
  • The properties of real numbers, which include the commutative, associative, and distributive properties, can be applied to subtraction operations. The commutative property states that the order of subtraction does not affect the result, so $a - b = b - a$. The associative property allows for grouping of subtraction operations, so $(a - b) - c = a - (b - c)$. The distributive property connects subtraction to multiplication, so $a - (b + c) = (a - b) - c$. Applying these properties can help simplify and manipulate algebraic expressions involving subtraction, which is crucial in the context of using the language of algebra.
• Analyze how subtraction is used in the properties of real numbers and how it relates to the concept of the additive inverse.
  • The concept of subtraction is deeply intertwined with the properties of real numbers and the idea of the additive inverse. Subtraction can be viewed as the inverse operation of addition, as the difference between two numbers is the value that, when added to the subtrahend, results in the minuend. This relationship is captured in the additive inverse property, where $a - b = a + (-b)$. The properties of real numbers, such as the commutative, associative, and distributive properties, can be applied to subtraction operations, allowing for the manipulation and simplification of algebraic expressions involving subtraction. Understanding how subtraction relates to the properties of real numbers and the additive inverse is crucial for mastering the language of algebra and performing operations with real numbers.

Related terms

Additive Inverse: The additive inverse of a number is the number that, when added to the original number, results in a sum of zero.

Difference: The result of subtracting one number from another is called the difference.

Negative Number: A negative number is a number that is less than zero and is often represented with a minus sign (-) in front of the number.