What is an augend?
An augend is a number that other numbers are added to. It comes from the Latin word “augendus” which means “to be increased”.
I just learned this word today as I was doing research for this page about addends. So, if you’ve never heard of it, don’t feel bad. I’ve been a math teacher for 6 years and I’d never heard of it either 🙂
Because this word is not very well-known, most people use the word “addend” to describe the first number in an addition problem. So, you can use either word, but augend is more precise and accurate.
You can 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.
8 + 1 = 9
2 + 1 + 7 = 10
3x + 12y + 9z
In this example, 12y and 9z are addends, and 3x is the augend.
3x + 12y + 9z 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.
7a + 4b – 5
Here, 7a is the augend, 4b is an addend, and 5 is a 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”.