Subtraction is a basic operation in mathematics that is used to find the difference between two numbers. It is represented using the symbol "-" and can be represented in equations, word problems, and other forms.
Definitions:
- Subtraction: Subtraction is the operation of finding the difference between two numbers. The symbol used to represent subtraction is the minus sign (-). The number being subtracted from is called the minuend, the number being subtracted is called the subtrahend, and the result of the subtraction is called the difference.
Examples:
- 8 - 3 = 5
- 10 - 5 = 5
- 12 - 8 - 2 = 2
- 20 - 15 = 5
- Minuend: The number being subtracted from in a subtraction problem is called the minuend.
Examples:
- 8 in the problem 8 - 3 = 5
- 10 in the problem 10 - 5 = 5
- 12 in the problem 12 - 8 - 2 = 2
- 20 in the problem 20 - 15 = 5
- Subtrahend: The number being subtracted in a subtraction problem is called the subtrahend.
Examples:
- 3 in the problem 8 - 3 = 5
- 5 in the problem 10 - 5 = 5
- 8 and 2 in the problem 12 - 8 - 2 = 2
- 15 in the problem 20 - 15 = 5
- Difference: The result of a subtraction problem is called the difference.
Examples:
- 5 in the problem 8 - 3 = 5
- 5 in the problem 10 - 5 = 5
- 2 in the problem 12 - 8 - 2 = 2
- 5 in the problem 20 - 15 = 5
Relation with other operations:
- Subtraction and addition: Subtraction and addition are inverse operations, meaning that the result of one operation can be undone by the other. For example, if we know that 8 - 3 = 5, we can also say that 5 + 3 = 8.
Examples:
- 8 - 3 = 5 and 5 + 3 = 8
- 10 - 5 = 5 and 5 + 5 = 10
- Subtraction and multiplication: Subtraction and multiplication are related through the distributive property, which states that for any numbers a, b, and c, a(b - c) = ab - ac.
Examples:
- 2(5 - 3) = 2(2) = 4
- 3(10 - 6) = 3(4) = 12
Relevant properties:
- Non-commutative property: The non-commutative property states that the order in which numbers are subtracted does change the result.
Examples:
- 8 - 3 = 5 and 3 - 8 = -5
- 10 - 5 = 5 and 5 - 10 = -5
- Subtraction identity: The subtraction identity is the number 0, which when subtracted from any number does not change the value of the number.
Examples:
- 8 - 0 = 8
- 5 - 0 = 5
Special cases:
- Subtractive inverse: The subtractive inverse of a number is the number that when subtracted from the original number, the result is 0.
Examples:
- 8 - 8 = 0
- 5 - 5 = 0
Notable differences:
Commutative and Non-Commutative: Addition is commutative, meaning that the order of the numbers doesn't matter, while subtraction is non-commutative, meaning that the order of the numbers does matter.
Additive identity and Subtractive identity: The additive identity is 0, while the subtractive identity is also 0.
Additive inverse and Subtractive inverse: Additive inverse is the opposite of a number, while subtractive inverse is the same number.
The use of symbols: Addition uses the symbol "+" while subtraction uses the symbol "-".
Exercises:
- Solve the following subtraction problem: 15 - 8 = 7
- Solve the following subtraction problem: 20 - 10 = 10
- Use the non-commutative property to solve the following problem: 8 - 3 = 5 (using the non-commutative property, we can also get 3 - 8 = -5)
- Use the subtraction identity to solve the following problem: 5 - 0 = 5
- Solve the following problem using the subtractive inverse: 8 - 8 = 0
Solutions:
- 15 - 8 = 7
- 20 - 10 = 10
- 8 - 3 = 5 (using the non-commutative property, we can also get 3 - 8 = -5)
- 5 - 0 = 5
- 8 - 8 = 0