What is a Subtrahend?
A subtrahend is the number that is subtracted from another number. It comes from the Latin word “subtrahendus” which means “to be taken away”. The number that the subtrahend is subtracted from is called the minuend.
Expressions that have subtrahends subtracted from minuends are called differences. The answer to a subtraction problem is also called the difference because it is a simplified version of the expression.
Examples
Identify the parts of the equation:
\[6-2=4\]
\[{\red 6}-{\yellow 2}={\green 4}\]
\(\red 6\) is the minuend.
\(\yellow 2\) is the subtrahend.
\(\green 4\) is the fully simplified difference of \(\red 6\) and \(\yellow 2\).
Identify the parts of the expression:
\[8x-4y\]
\[{\red 8x}-{\yellow 4y}\]
\(\red 8x\) is the minuend.
\(\yellow 4y\) is the subtrahend.
The expression is not set equal to anything, so there is no simplified difference.
However, the entire expression is a difference, so I can say that \(\green {8x-4y}\) is the difference of \(\red 8x\) and \(\yellow 4y\).
Identify the parts of the equation:
\[7a+4b-5c=3\]
\[{\red 7a+4b}-{\yellow 5c}={\green 3d}\]
\(\red 7a+4b\) is the minuend.
\(\yellow 5c\) is the subtrahend.
\(\green 3\) is the difference of \(\red 7a+4b\) and \(\yellow 5c\).
Subtrahends and Variables
When we work with variables, we usually don’t differentiate between augends, addends, subtrahends, and minuends.
Instead, we just call all of them “terms” and then we interpret any subtraction as adding a negative so the entire expression can be called a sum.
So, in the purple example above, we could describe the expression \({\purple 7a}+{\red 4b}-{\yellow 5c}\) as the “sum of \(\purple 7a\), \(\red 4b\), and \(\yellow -5c\)” instead of saying that it is “the difference of the sum \({\red 7a+4b}\) and \({\yellow 5c}\)”.
Both descriptions are accurate, but it is easier to understand the first one. So, I recommend using the “sum” of “terms” to describe expressions with variables.
This will be a lot easier than trying to describe them as “sums” and “differences” of “augends”, “addends”, “subtrahends”, and “minuends”.
