What is a minuend?
A minuend is a number that other numbers are subtracted from. It comes from the Latin word “minuendus” which means “to be diminished”. The number that is subtracted is called the subtrahend.
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.
12 – 5 = 7
In this example, 12 is the minuend and 5 is the subtrahend.
The difference is 7.
102 – 78 = 24
Here, 102 is the minuend and 78 is the subtrahend.
The difference is 24.
8x – 15y
In this example, 8x is the minuend and 15y is the subtrahend.
8x – 15y is the difference.
If this expression was equal to a number, that number would also be the difference. The difference can either be the entire expression OR the number that the expression is equal to.
7a + 4b – 5
Here, 7a + 4b is the minuend and 5 is the subtrahend.
7a + 4b – 5 is the difference of 7a + 4b (which is a sum) and 5.
Variables and Terms
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 example above, it is actually more likely that we would describe 7a + 4b – 5 as the “sum of 7a, 4b, and -5” instead of saying that it is “the difference of a sum and a number”.
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”.