Addition
By addition of two or more numbers, we mean putting together the objects of all the collections and counting the objects of the combined collection
- Alternative Methods of addition
- Adding 3-Digit Numbers With Regrouping
- Adding 4-Digit Numbers Without Regrouping
To add 5 and 7, we write it as 5 + 7 = 12.
Here 12 is called the sum of 5 and 7
5 + 7 = 7 + 5 = 12
The order of the numbers to be added does not change the sum.
When we add 1 to a number, we get its successor
Successor of 9 is 9 + 1 = 10
When 0 is added to a number, the number remains unchanged.
Examples:
Alternative methods of addition
1. By breaking one number.
Add 45 and 32.
45 + 32
= 45 + 30 + 2 (Break 32 as 30 + 2)
= 75 + 2
= 77
45 + 32
= 45 + 30 + 2 (Break 32 as 30 + 2)
= 75 + 2
= 77
Add 124 and 64.
124 + 64
= 124 + 60 + 4 (Break 64 as 60 + 4)
= 184 + 4
= 188
124 + 64
= 124 + 60 + 4 (Break 64 as 60 + 4)
= 184 + 4
= 188
2. By breaking both the numbers.
Add 56 and 23.
56 + 23
= 50 + 6 + 20 + 3 (Break 56 as 50 + 6 and 23 as 20 + 3)
= 50 + 20 + 6 + 3 (change the order to keep the ONES together)
= 70 + 9 (Add TENS and ONES separately)
= 79
56 + 23
= 50 + 6 + 20 + 3 (Break 56 as 50 + 6 and 23 as 20 + 3)
= 50 + 20 + 6 + 3 (change the order to keep the ONES together)
= 70 + 9 (Add TENS and ONES separately)
= 79
Add 256 and 38.
256 + 38
= 250 + 6 + 30 + 8 (Break 256 as 250 + 6 and 38 as 30 + 8)
= 250 + 30 + 6 + 8 (change the order to keep the ONES together)
= 280 + 14
= 280 + 10 + 4
= 290 + 4
= 294
256 + 38
= 250 + 6 + 30 + 8 (Break 256 as 250 + 6 and 38 as 30 + 8)
= 250 + 30 + 6 + 8 (change the order to keep the ONES together)
= 280 + 14
= 280 + 10 + 4
= 290 + 4
= 294
3. By counting in TENS.
Add 41 and 34.
41 + 34
= 41 + 10 + 10 + 10 + 4 (Break 34 as the sum of three 10s and 4)
= 71 + 4 (Adding the TENS)
= 75
41 + 34
= 41 + 10 + 10 + 10 + 4 (Break 34 as the sum of three 10s and 4)
= 71 + 4 (Adding the TENS)
= 75
Add 538 and 33.
538 + 33
= 538 + 10 + 10 + 10 + 3 (Break 33 as the sum of three 10s and 3)
= 568 + 3 (Adding the TENS to 538)
= 571
538 + 33
= 538 + 10 + 10 + 10 + 3 (Break 33 as the sum of three 10s and 3)
= 568 + 3 (Adding the TENS to 538)
= 571
Adding 3-Digit numbers with regrouping
1. Regrouping ONES only.
Do you remember how to regroup numbers from ONES to TENS?
2 tens + 15 ones = 3 tens + 5 ones
6 tens + 23 ones = 8 tens + 3 ones
4 tens + 36 ones = 7 tens + 6 ones
7 tens + 20 ones = 9 tens + 0 ones
6 tens + 23 ones = 8 tens + 3 ones
4 tens + 36 ones = 7 tens + 6 ones
7 tens + 20 ones = 9 tens + 0 ones
Add 526 and 247
526 = 5 hundreds + 2 tens + 6 ones
247 = 2 hundreds + 4 tens + 7 ones
526 + 247 = 5 hundreds + 2 tens + 6 ones + 2 hundreds + 4 tens + 7 ones
526 + 247 = 5 hundreds + 2 hundreds + 2 tens + 4 tens + 6 ones + 7 ones
526 + 247 = 7 hundreds + 6 tens + 13 ones
526 + 247 = 7 hundreds + 6 tens + 1 tens + 3 ones
526 + 247 = 7 hundreds + 7 tens + 3 ones
526 + 247 = 773
247 = 2 hundreds + 4 tens + 7 ones
526 + 247 = 5 hundreds + 2 tens + 6 ones + 2 hundreds + 4 tens + 7 ones
526 + 247 = 5 hundreds + 2 hundreds + 2 tens + 4 tens + 6 ones + 7 ones
526 + 247 = 7 hundreds + 6 tens + 13 ones
526 + 247 = 7 hundreds + 6 tens + 1 tens + 3 ones
526 + 247 = 7 hundreds + 7 tens + 3 ones
526 + 247 = 773
2. Regrouping TENS only.
Let us recall the regrouping of numbers from TENS to HUNDREDS
15 tens = 1 hundred + 5 tens
3 hundreds + 18 tens = 4 hundreds + 8 tens
5 hundreds + 24 tens = 7 hundreds + 4 tens
2 hundreds + 35 tens = 5 hundreds + 5 tens
4 hundreds + 12 tens + 8 ones = 5 hundreds + 2 tens + 8 ones
3 hundreds + 18 tens = 4 hundreds + 8 tens
5 hundreds + 24 tens = 7 hundreds + 4 tens
2 hundreds + 35 tens = 5 hundreds + 5 tens
4 hundreds + 12 tens + 8 ones = 5 hundreds + 2 tens + 8 ones
Add 463 and 271
463 = 4 hundreds + 6 tens + 3 ones
271 = 2 hundreds + 7 tens + 1 ones
463 + 271 = 4 hundreds + 6 tens + 3 ones + 2 hundreds + 7 tens + 1 ones
463 + 271 = 4 hundreds + 2 hundreds + 6 tens + 7 tens + 3 ones + 1 ones
463 + 271 = 6 hundreds + 13 tens + 4 ones
463 + 271 = 6 hundreds + 1 hundred + 3 tens + 4 ones
463 + 271 = 7 hundreds + 3 tens + 4 ones
463 + 271 = 734
271 = 2 hundreds + 7 tens + 1 ones
463 + 271 = 4 hundreds + 6 tens + 3 ones + 2 hundreds + 7 tens + 1 ones
463 + 271 = 4 hundreds + 2 hundreds + 6 tens + 7 tens + 3 ones + 1 ones
463 + 271 = 6 hundreds + 13 tens + 4 ones
463 + 271 = 6 hundreds + 1 hundred + 3 tens + 4 ones
463 + 271 = 7 hundreds + 3 tens + 4 ones
463 + 271 = 734
3. Regrouping TENS and ONES.
Add 375 and 468
375 = 3 hundreds + 7 tens + 5 ones
468 = 4 hundreds + 6 tens + 8 ones
375 + 468 = 3 hundreds + 7 tens + 5 ones + 4 hundreds + 6 tens + 8 ones
375 + 468 = 3 hundreds + 4 hundreds + 7 tens + 6 tens + 5 ones + 8 ones
375 + 468 = 7 hundreds + 13 tens + 13 ones
375 + 468 = 7 hundreds + 1 hundred + 3 tens + 1 ten + 3 ones
375 + 468 = 8 hundreds + 4 tens + 3 ones
375 + 468 = 843
468 = 4 hundreds + 6 tens + 8 ones
375 + 468 = 3 hundreds + 7 tens + 5 ones + 4 hundreds + 6 tens + 8 ones
375 + 468 = 3 hundreds + 4 hundreds + 7 tens + 6 tens + 5 ones + 8 ones
375 + 468 = 7 hundreds + 13 tens + 13 ones
375 + 468 = 7 hundreds + 1 hundred + 3 tens + 1 ten + 3 ones
375 + 468 = 8 hundreds + 4 tens + 3 ones
375 + 468 = 843
Adding 4-Digit Numbers Without Regrouping
Let's add 2510 and 3215Express these numbers in their expanded forms.
2510 = 2 Thousands + 5 Hundreds + 1 Tens + 0 Ones
3215 = 3 Thousands + 2 Hundreds + 1 Tens + 1 Ones
Let's add the values at the same place
2510 + 3215 = (2+3) Thousands + (5+2) Hundreds + (1+1) Tens + (0+5) Ones
= 5 Thousands + 7 Hundreds + 2 Tens + 5 Ones
2510 + 3215 = 5725
We got the sum through the addition of the expanded forms. Let's find the sum using the short forms.
Add 2510 and 3215
Step 1: Write the numbers in columns.
Th H T O
2 5 1 0
+ 3 2 1 5
Step 2: Add Ones and write in Ones place.
Th H T O
2 5 1 0
+ 3 2 1 5
5
Step 3: Add Tens and write in Tens place.
Th H T O
2 5 1 0
+ 3 2 1 5
2 5
Step 4: Add Hundreds and write in Hundreds place.
Th H T O
2 5 1 0
+ 3 2 1 5
7 2 5
Step 5: Add Thousands and write in Thousands place.
Th H T O
2 5 1 0
+ 3 2 1 5
5 7 2 5
Th H T O
2 5 1 0
+ 3 2 1 5
Step 2: Add Ones and write in Ones place.
Th H T O
2 5 1 0
+ 3 2 1 5
5
Step 3: Add Tens and write in Tens place.
Th H T O
2 5 1 0
+ 3 2 1 5
2 5
Step 4: Add Hundreds and write in Hundreds place.
Th H T O
2 5 1 0
+ 3 2 1 5
7 2 5
Step 5: Add Thousands and write in Thousands place.
Th H T O
2 5 1 0
+ 3 2 1 5
5 7 2 5