Struggling on How to Find the Sum using Addition Property? Don’t bother with the different Addition properties available in mathematics makes it quite simple for you to find the sum. All the additional properties along with examples are given in this article. Check out the different properties of addition such as identity, commutative, associative, etc. in this article. Find the sum with the help of these addition properties and learn the complete concept in no time.
Also, Check
- Adding with Zero or Additive Identity Property of Addition
- Find the Difference using Subtraction Property
Properties of Addition
There are four different properties available to find the sum of the numbers. The four Addition Properties are
- Commutative Property of Addition
- Associative Property of Addition
- Additive Identity Property of Addition
- Distributive Property of Addition
1. Commutative Property of Addition
Commutative Property of Addition means if you add two numbers or integers, then the sum of the numbers are remaining the same. Even if you change the order of the numbers while adding the result remains the same. If you take two integers A and B, then adding A with B or Adding B with A remains the same.
- A + B = B + A
Examples of Commutative Property of Addition
Example 1.
Add 5 and 8 using Commutative Property of Addition
Solution:
Given numbers are 5 and 8.
Add number 5 with 8. 5 + 8 = 13.
Add number 8 with 5. 8 + 5 = 13
The result is 13 for both 5 + 8 and 8 + 5.
Therefore, 5 + 8 = 8 + 5.
Example 2.
Add 24 and 46 using Commutative Property of Addition?
Solution:
Given numbers are 24 and 46.
Add number 24 with 46. 24 + 46 = 70.
Add number 46 with 24. 46 + 24 = 70
The result is 70 for both 24 + 46 and 46 + 24.
Therefore, 24 + 46 = 46 + 24.
Example 3.
Add 314 and 287 using Commutative Property of Addition?
Solution:
Given numbers are 314 and 287.
Add number 314 with 287. 314 + 287 = 601.
Add number 287 with 314. 287 + 314 = 601
The result is 601 for both 314 + 287 and 287 + 314.
Therefore, 314 + 287 = 287 + 314.
2. Associative Property of Addition
Associative Property of Addition means when you add three numbers with different patterns does not change the output. The sum of the three numbers will be the same if you add those three numbers by changing the addends. If you take three integers A, B, and C, then adding A with B then with C or Adding B with C and then with A remains the same.
- A + (B + C) = (A + B) + C
How to find the Sum using the Associative Property of Addition?
If the A, B and C are three integers, then Associative Property of Addition will be A + (B + C) = (A + B) + C. The following procedure will prove the given A, B, and C follow the Associative Property of Addition.
Step 1: Write the left-hand side of equation i.e. (A + B) + C
Step 2: Add the numbers in parentheses to obtain one number i.e. A + B
Step 3: Add the resultant number of A + B to the left-out numbers and obtain the answer for it.
Step 4: Now, write the right-hand side of the equation i.e. A + (B + C)
Step 5: Add the numbers in parentheses i.e. B + C
Step 6: Add the resultant number of B + C to the left-out numbers and obtain the answer for it.
Step 7: Now, compare the results of A + (B + C) and (A + B) + C.
Associative Property of Addition Examples
Example 1.
Find the sum 4, 3, and 7 using Associative Property of Addition?
Solution:
The given numbers are 4, 3, and 7.
The Associative Property of Addition is A + (B + C) = (A + B) + C.
A = 4, B = 3, and C = 7.
A + (B + C) = 4 + (3 + 7) = 4 + (10) = 14.
(A + B) + C = (4 + 3) + 7 = (7) + 7 = 14.
14 = 14.
Therefore, A + (B + C) = (A + B) + C.
Example 2.
Find the sum using addition property of 21 + 36 + 17?
Solution:
The given numbers are 21, 36, and 17.
The Associative Property of Addition is A + (B + C) = (A + B) + C.
A = 21, B = 36, and C = 17.
A + (B + C) = 21 + (36 + 17) = 21 + (53) = 74.
(A + B) + C = (21 + 36) + 17 = (57) + 17 = 74.
74 = 74.
Therefore, A + (B + C) = (A + B) + C.
Example 3.
Find the sum using addition property of 236 + 421 + 257?
Solution:
The given numbers are 236, 421, and 257.
The Associative Property of Addition is A + (B + C) = (A + B) + C.
A = 236, B = 421, and C = 257.
A + (B + C) = 236 + (421 + 257) = 236 + (678) = 914.
(A + B) + C = (236 + 421) + 257 = (57) + 17 = 914.
914 = 914.
Therefore, A + (B + C) = (A + B) + C.
3. Additive Identity Property of Addition
Additive Identity Property of Addition means every number that added to a unique real number (zero) gives the number itself as an output. If you take one number and added to zero gives the same number as output. If you take an integer A and added it to the 0, then the output will be A.
- A + 0 = A or 0 + A = A
Additive Identity Property of Addition Examples
Example 1.
Add 6 and 0 using Additive Identity Property of Addition
Solution:
6 + 0 = 6.
0 + 6 = 6.
The final answer is 6.
Example 2.
Add 21 and 0 using Additive Identity Property of Addition
Solution:
21 + 0 = 21.
0 + 21 = 21.
The final answer is 21.
Example 3.
Add 487 and 0 using Additive Identity Property of Addition
Solution:
487 + 0 = 487.
0 + 487 = 487.
The final answer is 487.
4. Distributive Property of Addition
Distributive Property of Addition means the sum of two numbers multiplied by the third number is equal to the each of those two numbers is multiplied to the third number. If A, B, and C are three integers, then the Distributive Property of Addition becomes
- A × (B + C) = A × B + A × C
Distributive Property of Addition Examples
Example 1.
Find the sum using Distributive Property of Addition for 3, 5, 2 numbers?
Solution:
The given numbers are 3, 5, and 2.
The Distributive Property of Addition is A × (B + C) = A × B + A × C.
A = 3, B = 5, and C = 2.
A × (B + C) = 3 × (5 + 2) = 3 × (7) = 21.
A × B + A × C = (3 × 5) + (3 × 2) = 15 + 6 = 21.
21 = 21.
Therefore, A × (B + C) = A × B + A × C.
Example 2.
Find the sum using Distributive Property of Addition for 21, 48, and 13 numbers?
Solution:
The given numbers are 21, 48, and 13.
The Distributive Property of Addition is A × (B + C) = A × B + A × C.
A = 21, B = 48, and C = 13.
A × (B + C) = 21 × (48 + 13) = 21 × (61) = 1281.
A × B + A × C = (21 × 48) + (21 × 13) = 1008 + 273 = 1281.
1281 = 1281.
Therefore, A × (B + C) = A × B + A × C.
Example 3.
Find the sum using Distributive Property of Addition for 154, 112, and 313 numbers?
Solution:
The given numbers are 154, 112, and 313.
The Distributive Property of Addition is A × (B + C) = A × B + A × C.
A = 154, B = 112, and C = 313.
A × (B + C) = 154 × (112 + 313) = 154 × (425) = 65450.
A × B + A × C = (154 × 112) + (154 × 313) = 17248 + 48202 = 65450.
65450 = 65450.
Therefore, A × (B + C) = A × B + A × C.
FAQs on Finding the Sum using Addition Property
1. What are the 4 important properties of addition?
The four important properties of addition are
(i) Commutative property
(ii) Identity Property
(iii) Associative property
(iv) Distributive property
2. What is the additive identity of 24?
As per the Additive Identity Property of Addition, any number that added to a unique real number (zero) gives the number itself as an output. Therefore, the additive identity of 24 is 24.
3. What is the commutative property of addition?
The commutative property of addition explains that Even the order of addends is changed the sum never changes.
4. What is the use of properties of addition?
The properties of addition help us to find the complex addition problems simply.
5. Which property uses both addition and multiplication operations?
The distributive property uses both addition and multiplication operations.