In subtraction, the difference is found by subtracting the subtrahend from the minuend. The minuend is the value in which is subtracted, and the subtrahend is the value subtracted by.
The difference between a and b is negative if b (the subtrahend) is greater than a (the minuend).
Any value subtracted by zero is equal to the value itself. Any value that zero is subtracted by is equal to the value times negative one.
Any terms that are negative in an addition are to be subtracted instead of added.
Subtracting by a negative reverses the operation upon itself and changes the operation into addition.
Subtracting a value by itself equals to zero.
Multiplying a subtraction by negative one effectively flips the terms of the subtraction, and vice versa.
Order does matter when subtracting, and equality cannot be assumed when order is changed.
Grouping matters in subtraction, and equality cannot be assumed when groupings are changed.
Subtracting by zero is equivalent to subtracting by nothing, which has no effect on the value. Subtracting zero (or nothing) by a value is equivalent to a value which is less than nothing (or a negative).
Even more complex is the action subtracting a negative. The act of turning a double negative into a positive is best explained by the phrase, "The loss of a loss is a gain."
Negative are important in subtraction. When subtracting two terms, we must know whether the minuend or the subtrahend is larger to determine the sign of the difference.
Recall that subtracting a value from itself will always equal zero.
Also recall that any value added or subtracted by zero is equal to the value itself
When we combine these two properties, we end up with 'cancellation' (a+(b-b)=a). Cancelling values from addition equations allows us to rid the equation of those values, simplifying the equation. This action is demonstrated in the solution below, we simplify the equation by cancelling (or removing) the 4.
The act of cancellation can be achieved not only through the reordering of added terms, but through multiplication and division.
When we multiply a group by a negative (or subtract by a group), we have the option to distribute that negative (which is equals to a negative one) to every term in that group.
For a quick written example, when we distribute a negative over a basic subtraction operation -(a-b), we get: (-1)a-(-1)b. Applying fundamental properties we find that this equals the reverse of the original subtraction: -a--b = b-a.
The action of distributing negatives to each term in a grouping can be applied no matter how large or complex the group, you simply multiply each term (or added value) by a negative one.
Click to reveal answers
admin@sophisticatedprimate.com
bug@sophisticatedprimate.com