Properties of Subtraction

Definition and Notation

• Subtraction is a mathematical operation that represents the act of finding the difference between two numbers or quantities.
• It is denoted by the minus sign (-).

Properties of Subtraction

• Non-Commutative: The order of the numbers in a subtraction operation matters. a - b ≠ b - a
• Non-Associative: The order in which subtraction operations are performed matters. (a - b) - c ≠ a - (b - c)
• Distributive: Subtraction can be distributed over addition. a - (b + c) = (a - b) - c

Subtraction Facts

• Subtraction by Addition: Subtraction can be thought of as adding the opposite (additive inverse) of the subtrahend to the minuend.
• Zero Property: Subtracting 0 from a number does not change the number. a - 0 = a
• Identity Property: Subtracting a number from itself results in 0. a - a = 0

Subtracting Negative Numbers

• Subtracting a Negative Number: Subtracting a negative number is equivalent to adding its opposite (positive number).
• Example: 5 - (-3) = 5 + 3 = 8

Real-World Applications

• Measuring Length: Subtraction can be used to find the difference in length between two objects.
• Money: Subtraction can be used to calculate the change owed when making a purchase.
• Temperature: Subtraction can be used to find the difference in temperature between two days.

Definition and Notation

• Subtraction is a mathematical operation that represents finding the difference between two numbers or quantities.
• It is denoted by the minus sign (-).

Properties of Subtraction

• Subtraction is non-commutative, meaning the order of numbers matters.
• Subtraction is non-associative, meaning the order of operations matters.
• Subtraction is distributive over addition, meaning a - (b + c) = (a - b) - c.

Subtraction Facts

• Subtraction can be thought of as adding the opposite (additive inverse) of the subtrahend to the minuend.
• Subtracting 0 from a number does not change the number.
• Subtracting a number from itself results in 0.

Subtracting Negative Numbers

• Subtracting a negative number is equivalent to adding its opposite (positive number).
• For example, 5 - (-3) = 5 + 3 = 8.

Real-World Applications

• Subtraction can be used to find the difference in length between two objects.
• Subtraction can be used to calculate the change owed when making a purchase.
• Subtraction can be used to find the difference in temperature between two days.