An addend is a number that is added to another number. It comes from the Latin word “addendus” which means “to be added”.
The number it is added to is called the augend. However, this word is not very well-known. So, most people just call the augend an “addend”. Both words will work, but augend is more precise and accurate.
You can also use the word “summand” to describe augends and addends.
Expressions that have an augend and addend(s) added together are called sums. The answer to an addition problem is also called the sum because it is a simplified version of the expression.
Examples with Numbers
In this example, 4 is the augend, 3 is the addend, and 7 is the sum.
4 + 3 = 7
Here, 12 is the augend, 6 and 1 are addends, and the sum is 19.
12 + 6 + 1 = 19
The numbers 12 and 4 can also be called addends. It is just more precise to call them augends. 12, 6, 1, 4, and 3 can all be called summands.
Examples with Variables
5x + 7y + 6z
In this example, 5x , 7y, and 6z are addends.
And 5x + 7y + 6z is the sum.
If this expression was equal to a number, that number would also be the sum. The sum can either be the entire expression OR the number that the expression is equal to.
2a + 8b – 3
In this example, 2a and 8b are addends and 3 is a subtrahend.
2a + 8b – 3 is the difference of 2a + 8b (which is a sum) and 3.
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 2a + 8b – 3 as the “sum of 2a, 8b, and -3” 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”.