Addition and Subtraction
In the previous classes, we have learnt the basics of addition and subtraction. Here we will learn the addition and subtraction of bigger numbers.
- Addition Without Regrouping
- Addition With Regrouping
- Subtraction Without Regrouping
- Subtraction With Regrouping
- Addition and Subtraction Together
- Estimating Sums and Differences
Addition Without Regrouping
Add 14526 and 42432
Step 1: Arrange the numbers in columns.
1 4 5 2 6
+ 4 2 4 3 2
Step 2: Add the digits in ones column. 6 + 2 = 8, We write 8 in the ones place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
8
Step 3: Add the digits in tens column. 2 + 3 = 5, We write 5 in the tens place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
5 8
Step 4: Add the digits in hundreds column. 5 + 4 = 9, We write 9 in the hundreds place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
9 5 8
Step 5: Add the digits in thousands column. 4 + 2 = 6, We write 6 in the thousands place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
6 9 5 8
Step 6: Add the digits in ten-thousands column. 1 + 4 = 5, We write 5 in the ten-thousands place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
5 6 9 5 8
14526 + 42432 = 56958
1 4 5 2 6
+ 4 2 4 3 2
Step 2: Add the digits in ones column. 6 + 2 = 8, We write 8 in the ones place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
8
Step 3: Add the digits in tens column. 2 + 3 = 5, We write 5 in the tens place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
5 8
Step 4: Add the digits in hundreds column. 5 + 4 = 9, We write 9 in the hundreds place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
9 5 8
Step 5: Add the digits in thousands column. 4 + 2 = 6, We write 6 in the thousands place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
6 9 5 8
Step 6: Add the digits in ten-thousands column. 1 + 4 = 5, We write 5 in the ten-thousands place of the answer.
1 4 5 2 6
+ 4 2 4 3 2
5 6 9 5 8
14526 + 42432 = 56958
Addition With Regrouping
Add 4586 and 2827
We will regroup the digits where ever there is a carried over digit.
Step 1: Arrange the numbers in columns.
4 5 8 6
+ 2 8 2 7
Step 2: Add the digits in ones column. 6 + 7 = 13, We write 3 in the ones place of the answer and 1 in the tens place as a carry over.
1
4 5 8 6
+ 2 8 2 7
3
Step 3: Add the digits in tens column. 1 + 8 + 2 = 11, We write 1 in the tens place of the answer and 1 in the hundreds place as a carry over.
1
4 5 8 6
+ 2 8 2 7
1 3
Step 4: Add the digits in hundreds column. 1 + 5 + 8 = 14, We write 4 in the hundreds place of the answer and 1 in the thousands place as a carry over.
1
4 5 8 6
+ 2 8 2 7
4 1 3
Step 5: Add the digits in thousands column. 1 + 4 + 2 = 7, We write 7 in the thousands.
4 5 8 6
+ 2 8 2 7
7 4 1 3
4586 + 2827 = 7413
Step 1: Arrange the numbers in columns.
4 5 8 6
+ 2 8 2 7
Step 2: Add the digits in ones column. 6 + 7 = 13, We write 3 in the ones place of the answer and 1 in the tens place as a carry over.
1
4 5 8 6
+ 2 8 2 7
3
Step 3: Add the digits in tens column. 1 + 8 + 2 = 11, We write 1 in the tens place of the answer and 1 in the hundreds place as a carry over.
1
4 5 8 6
+ 2 8 2 7
1 3
Step 4: Add the digits in hundreds column. 1 + 5 + 8 = 14, We write 4 in the hundreds place of the answer and 1 in the thousands place as a carry over.
1
4 5 8 6
+ 2 8 2 7
4 1 3
Step 5: Add the digits in thousands column. 1 + 4 + 2 = 7, We write 7 in the thousands.
4 5 8 6
+ 2 8 2 7
7 4 1 3
4586 + 2827 = 7413
Subtraction Without Regrouping
Subtract 15423 from 56458
Step 1: Arrange the numbers in columns. Write the greater number above the smaller one
5 6 4 5 8
- 1 5 4 2 3
Step 2: Subtract the digits in ones column. 8 - 3 = 5, We write 5 in the ones place of the answer.
5 6 4 5 8
- 1 5 4 2 3
5
Step 3: Subtract the digits in tens column. 5 - 2 = 3, We write 3 in the tens place of the answer.
5 6 4 5 8
- 1 5 4 2 3
3 5
Step 4: Subtract the digits in hundreds column. 4 - 4 = 0, We write 0 in the hundreds place of the answer.
5 6 4 5 8
- 1 5 4 2 3
0 3 5
Step 5: Subtract the digits in thousands column. 6 - 5 = 1, We write 1 in the thousands place of the answer.
5 6 4 5 8
- 1 5 4 2 3
1 0 3 5
Step 6: Subtract the digits in ten-thousands column. 5 - 1 = 4, We write 4 in the ten-thousands place of the answer.
5 6 4 5 8
- 1 5 4 2 3
4 1 0 3 5
56458 - 15423 = 41035
5 6 4 5 8
- 1 5 4 2 3
Step 2: Subtract the digits in ones column. 8 - 3 = 5, We write 5 in the ones place of the answer.
5 6 4 5 8
- 1 5 4 2 3
5
Step 3: Subtract the digits in tens column. 5 - 2 = 3, We write 3 in the tens place of the answer.
5 6 4 5 8
- 1 5 4 2 3
3 5
Step 4: Subtract the digits in hundreds column. 4 - 4 = 0, We write 0 in the hundreds place of the answer.
5 6 4 5 8
- 1 5 4 2 3
0 3 5
Step 5: Subtract the digits in thousands column. 6 - 5 = 1, We write 1 in the thousands place of the answer.
5 6 4 5 8
- 1 5 4 2 3
1 0 3 5
Step 6: Subtract the digits in ten-thousands column. 5 - 1 = 4, We write 4 in the ten-thousands place of the answer.
5 6 4 5 8
- 1 5 4 2 3
4 1 0 3 5
56458 - 15423 = 41035
Subtraction With Regrouping
Subtract 1789 from 5653
Step 1: Arrange the numbers in columns. Write the greater number above the smaller one
5 6 5 3
- 1 7 8 9
Step 2: Subtract the digits in ones column. 3 - 9 is not possible, 3 < 9. So we will regroup the digit at the tens place.
5 tens = 4 tens + 10 ones.
Now the digit at the tens place become 4 and the digit at the ones place become 13.
13 - 9 = 4, we write 4 in the ones place of the answer.
4 13
5 6 5 3
- 1 7 8 9
4
Step 3: Subtract the digits in tens column. 4 - 8 is not possible, 4 < 8. So we will regroup the digit at the hundreds place.
6 hundreds = 5 hundreds + 10 tens.
Now the digit at the hundreds place become 5 and the digit at the tens place become 14.
14 - 8 = 6, we write 6 in the tens place of the answer.
5 14
5 6 5 3
- 1 7 8 9
6 4
Step 4: Subtract the digits in hundreds column. 5 - 7 is not possible, 5 < 8. So we will regroup the digit at the thousands place.
5 thousands = 4 thousands + 10 hundreds.
Now the digit at the thousands place become 4 and the digit at the hundreds place become 15.
15 - 7 = 8, we write 8 in the hundreds place of the answer.
4 15
5 5 6 3
- 1 7 8 9
8 6 4
Step 5: Subtract the digits in thousands column. 4 - 1 = 3, we write 3 in the thousands place of the answer.
4
5 6 5 3
- 1 7 8 9
3 8 6 4
5653 - 1789 = 3864
5 6 5 3
- 1 7 8 9
Step 2: Subtract the digits in ones column. 3 - 9 is not possible, 3 < 9. So we will regroup the digit at the tens place.
5 tens = 4 tens + 10 ones.
Now the digit at the tens place become 4 and the digit at the ones place become 13.
13 - 9 = 4, we write 4 in the ones place of the answer.
4 13
5 6 5 3
- 1 7 8 9
4
Step 3: Subtract the digits in tens column. 4 - 8 is not possible, 4 < 8. So we will regroup the digit at the hundreds place.
6 hundreds = 5 hundreds + 10 tens.
Now the digit at the hundreds place become 5 and the digit at the tens place become 14.
14 - 8 = 6, we write 6 in the tens place of the answer.
5 14
5 6 5 3
- 1 7 8 9
6 4
Step 4: Subtract the digits in hundreds column. 5 - 7 is not possible, 5 < 8. So we will regroup the digit at the thousands place.
5 thousands = 4 thousands + 10 hundreds.
Now the digit at the thousands place become 4 and the digit at the hundreds place become 15.
15 - 7 = 8, we write 8 in the hundreds place of the answer.
4 15
5 5 6 3
- 1 7 8 9
8 6 4
Step 5: Subtract the digits in thousands column. 4 - 1 = 3, we write 3 in the thousands place of the answer.
4
5 6 5 3
- 1 7 8 9
3 8 6 4
5653 - 1789 = 3864
Addition and Subtraction Together
Let's simplify 5536 - 2504 + 1890
Step 1: Subtract 2504 from 5536 first.
(5536 - 2504) + 1890
= 3032 + 1890
Step 2: Now add 1890 to the sum obtained in the previous step.
3032 + 1890 = 4922
So, 5536 - 2504 + 1890 = 4922
(5536 - 2504) + 1890
= 3032 + 1890
Step 2: Now add 1890 to the sum obtained in the previous step.
3032 + 1890 = 4922
So, 5536 - 2504 + 1890 = 4922
Estimating Sums and Differences
To estimate the sum or difference of the given numbers, we round off the given numbers and then find their sum or difference.Usually we round off to the nearest ten
Let's estimate the sum and difference of the numbers 314 and 247
Step 1: Round down 314 to the nearest ten. 314 → 310
Step 2: Round up 247 to the nearest ten. 247 → 250
Estimated Sum: 310 + 250 = 560
Estimated Difference: 310 - 250 = 60
Actual Sum: 314 + 247 = 561
Actual Difference: 314 - 247 = 67
Step 1: Round down 314 to the nearest ten. 314 → 310
Step 2: Round up 247 to the nearest ten. 247 → 250
Estimated Sum: 310 + 250 = 560
Estimated Difference: 310 - 250 = 60
Actual Sum: 314 + 247 = 561
Actual Difference: 314 - 247 = 67