\color{cyan}{\textnormal{Subtraction}} is the act of separating numbers.
Subtraction answers: “What happens when I take away a certain amount of things from another group?”
For instance, if I have 20 watermelons at a party, and the partygoers eat 12 watermelons, how many will I have left?
To model this situation, you would write the following:
20 - 12
This is spoken as “Twenty minus twelve.”
Because you start with 20 watermelons, you write that first. Then, 12 are eaten, so you would subtract 12 from 20. This would result in 8 watermelons, which can be written as:
20 - 12 = 8
This is spoken as “Twenty minus twelve equals eight.”
Subtraction is the \color{cyan}{\textnormal{inverse operation}} to addition. That is, the following is true:
20 + 12 - 12 = 20
By adding 12, then subtracting twelve, you end up back where you started! That is, inverse operations perform the opposite task. Addition and subtraction are inverse operations, which means they can be “cancelled out” if the quantities are the same, as shown in the equation above.
Inverse operations are critical for simplifications and other work, which will be explored in later sections.
Subtraction refers to their terms in a particular order, since the order of the terms is more important for subtraction. The first term is known as the \color{cyan}{\textnormal{subtrahend}} or \color{cyan}{\textnormal{minuend}}, while the second term is known as the \color{cyan}{\textnormal{subtrahere}}. It is extremely unlikely that you will come across these names (I had to look them up myself) but come trivia night you may have the upper hand. The result of subtraction is known as the \color{cyan}{\textnormal{difference}}, which is a much more common term to know.
\text{subtrahend} + \text{subtrahere} = \text{difference}
\color{cyan}{\textnormal{Long Subtraction}} is similar to long addition, except instead of a carry, you may require what is called a borrow!
\color{cyan}{\textnormal{Borrows}} work how you probably think they do. Rather than carrying the overflow over to the next column, you instead may take away from the next column (hence, borrow).
For example, if you take the addition step and instead execute it as subtraction, you may see how this could happen.
\begin{aligned} \phantom{00}_{-1}\phantom{0}\\ \phantom{-}852 \\ \underline{-\phantom{0}299} \\ \phantom{-055}3 \\ \end{aligned} \\ \\ 2-9 \text{ is negative, so you need to borrow from the tens place to change the 2 into a 12:} \\ 12-9=3\\ \text{Notice the borrow is marked as negative; this indicates a borrow.}\\ \phantom{\n} \\ \begin{aligned} \phantom{0}_{-1}\phantom{00}\\ \phantom{-}852 \\ \underline{-\phantom{0}299} \\ \phantom{-05}53 \\ \end{aligned} \\ \\ -1 - 5 - 9 \text{ also requires a borrow:}\\ 15 - 1 - 9 = 14-9=5 \\ \\ \begin{aligned} \phantom{-}852 \\ \underline{-\phantom{0}299} \\ \phantom{-0}553 \\ \end{aligned} \\ 8 - 2 - 1 = 5 \\ \\ \text{ This requires no borrow!}\\
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