Subtraction
Subtraction is the arithmetic operation for finding the difference between two numbers, though it can also be generalized to other mathematical objects such as vectors and matrices.[1] The special names of the numbers in a subtraction expression are, minuend - subtrahend = difference.[2][3] For example, the expression [math]\displaystyle{ 7-4=3 }[/math] can be read as "seven minus four equals three," "seven take away four leaves three," or "four from seven leaves three."
If the minuend is less than the subtrahend, the difference will be a negative number. For example, 17 - 25 = -8 . This can be read as "Seventeen minus twenty-five equals negative eight."
Subtraction is how cash registers determine the change a buyer receives, when the buyer pays with more money than the purchase cost.
Properties
Anti-commutativity
Subtraction is anti-commutative, meaning that if swapping the numbers around the minus sign will change the difference:
- "a - b ≠ b - a"
Non-associativity
Subtraction is non-associative, which comes up when one tries to define repeated subtraction. In general, the expression
- "a − b − c"
can be defined to mean either (a − b) − c or a − (b − c), but these two possibilities lead to different answers. To resolve this issue, one must establish an order of operations, with different orders yielding different results.
Predecessor
In the context of integers, subtraction of one also plays a special role: for any integer a, the integer (a − 1) is the largest integer that is smaller than a, also known as the predecessor of a.
Subtraction Media
"5 − 2 = 3" (verbally, "five minus two equals three")
Placard outside a shop in Bordeaux advertising subtraction of 20% from the price of the second perfume purchased.
Subtraction of numbers 0–10. Line labels = minuend. X axis = subtrahend. Y axis = difference.
Labeled line segment
Subtraction on a line segment.
Vertical Subtraction, Austrian method
The difference is written under the line.
9 + ... = 5The required sum (5) is too small.
So, we add 10 to it and put a 1 under the next higher place in the subtrahend.
9 + ... = 15Now we can find the difference as before.
Related pages
References
- ↑ "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-26.
- ↑ Weisstein, Eric W. "Subtraction". mathworld.wolfram.com. Retrieved 2020-08-26.
- ↑ "Subtraction". www.mathsisfun.com. Retrieved 2020-08-26.