Addends
When we put things together, we do
addition.
‘+’ is
the sign of addition.
Numbers that are added are called addends.
The result
that we get is called the sum or total.
Example:
Thus, in the above example, the numbers 3 and 5 are addends.
We can have more than two addends in
an addition sum.
For example:
2 + 4 + 7 = 13
Addend Addend Addend
Here, 2, 4 and 7 are three addends.
Similarly, in the addition sum 5 + 6 +
2 + 3 = 16, there are four addends.
They are 5, 6, 2 and 3.
What is an Addend in Maths?
As we have just discussed, the numbers
being added together to get a sum are called the addends. Thus, in an addition
sentence, all the numbers which are added together to get a total are called
the addends.
For example:
145 ← Addend
+
235 ← Addend
-------------
380 ← Sum
-------------
Addend Definition
Addends are the numbers or terms in an
addition equation that are added to form the sum or total.
For example:
a.
321 ← Addend
+
417 ← Addend
-------------
738 ← Sum
-------------
b.
231 ← Addend
142 ← Addend
+
316 ← Addend
-------------
689 ← Sum
-------------
Properties of Addition
Properties
of addition define the different ways in which we can add the given numbers. Let’s
discuss a few properties of addition.
1. Closure
Property of Addition
If the sum of two natural numbers is a
natural number, then this property of addition is called the closure property
of addition for natural numbers.
Similarly, the closure property holds
true for whole numbers, integers, fraction, decimal, rational numbers, etc.
For Example:
(i)
5 + 8 = 13
Natural number + Natural number =
Natural number
(ii) –7 + (–4) = –11
Integer + Integer = Integer
2. Commutative
Property of Addition
There will be no change in the sum,
even if we change the order of the addends.
For example:
22 + 12 = 34
and 12
+ 22 = 34
You can
illustrate it by the following figure.
In general, if A and B are two numbers, then A + B = B + A.
3. Associative
Property of Addition
When we
add three or more numbers, the sum remains the same, even if the grouping of
addends is changed. So, the grouping of numbers does not change the
result.
For Example:
(i) (4 + 5) + 8 = 4 + (5 + 8)
Here, (4 + 5) + 8 = 9 + 8 = 17
And 4 + (5 + 8) = 4 + 13 = 17
Thus, the result does not change.
In general, if A, B and C are three
numbers, then A + (B + C) = (A + B) + C.
4. Zero Property
of Addition (Additive Identity Property of Addition)
If any number is added
to zero, or zero is added to any number, the result is the number itself.
For example:
(i) 8 + 0 = 8
(ii) 0 + 17 = 17
Solved Examples
Example 1: In the addition sentence, 1 + 3 + 7 = 11, write
the numbers which are addends.
Solution: Here, the numbers being added are 1, 3 and 7.
Thus, 1, 3 and 7 are the addends in
this addition sentence.
Example 2: Find the missing addend in the addition
equation 8 + ____ = 15.
Solution: The missing addend in the given addition equation
= 15 – 8 = 7.
Example 3: Given 6 + 10 = 10 + 6. Which property of
addition is used here.
Solution: We know that by commutative property of
addition, A + B = B + A.
Thus, the addition sentence 6 + 10 =
10 + 6 holds true by commutative property of addition.
Example 4: Which property is used in the addition sentence:
7 + (3 + 5) = (7 + 3) + 5?
Solution: We know that by associative property of addition,
A + (B + C) = (A + B) + C.
Thus, the addition sentence 7 + (3 + 5)
= (7 + 3) + 5 holds true by associative property of addition.
Example 5: Find the missing addend in 15 + ____ + 25 =
60.
Solution: Missing addend = 60 – (15 + 25)
= 60 – 40 = 20