What is an Addend in Maths

# What is an Addend in Maths

When we put things together, we do addition.

‘+’ is the sign of addition.

The result that we get is called the sum or total.

Example:

Thus, in the above example, the numbers 3 and 5 are addends.

For example:

2             +             4              +              7                =                13

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:

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380   ← Sum

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Addends are the numbers or terms in an addition equation that are added to form the sum or total.

For example:

a.

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738   ← Sum

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b.

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689   ← Sum

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Properties of addition define the different ways in which we can add the given numbers. Let’s discuss a few properties 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

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.

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.

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

Related Topics:

What is an Addend in Maths

Minuend and subtrahend

Multiplicand and multiplier

Dividend, divisor, quotient and remainder

Natural numbers

Whole numbers

Properties of rational numbers

Are all integers rational numbers?

Find five rational numbers between 3/5 and 4/5