Adding 5-digit Numbers with Regrouping

We will learn adding 5-digit numbers with regrouping.

We have learnt the addition of 4-digit numbers with regrouping and now in the same way we will do addition of 5-digit numbers with regrouping. We arrange the numbers one below the other in place value columns and then we start adding from the ones place and regroup, if required as shown in the following examples.

Solved Examples on Adding 5-digit Numbers with Regrouping:

1. Add 34396 and 58124.

Solution:

Step I: Add the ones. 6 + 4 = 10 ones = 1 ten and 0 one. Write 0 in ones column and carry 1 to the tens column.

Step II: Add the tens. 9 + 2 + 1 (carry over) = 12 tens. 12 tens = 1 hundreds and 2 tens. Write 2 in tens column and carry 1 to the hundreds column.

Step III: Add the hundreds. 3 + 1 + 1 (carry over) = 5 hundreds. Write 5 in the hundreds column.

Step IV: Add the thousands column. 4 + 8 = 12 thousands. 12 thousands = 1 ten thousand and 2 thousands. Write 2 in the thousands column.

Step V: Add the ten thousands column. 3 + 5 + 1 (carry over) = 9 ten thousands. Write 9 in ten thousands column.




Adding 5-digit Numbers with Regrouping

Hence, 34396 + 58124 = 92520



2. Add 5182, 60924 and 10200.

Solution:

Step I: Add the ones. 2 + 4 + 0 = 6 ones. Write 6 in ones column.

Step II: Add the tens. 8 + 2 + 0 = 10 tens. 10 tens = 1 hundreds and 0 tens. Write 0 in tens column and carry 1 to the hundreds column.

Step III: Add the hundreds. 1 + 9 + 2 + 1 (carry over) = 13 hundreds. 13 hundreds = 1 thousand and 3 hundreds. Write 3 in the hundreds column and carry 1 to the thousands column.

Step IV: Add the thousands. 5 + 0 + 0 + 1 (carry over) = 6 thousands. Write 6 in the thousands column.

Step V: Add the ten thousands column. 6 + 1 = 7 ten thousands. Write 7 in ten thousands column.




Adding 5-digit Numbers

Hence, 5182 + 60924 + 10200 = 76306


3. Add: 25839, 43465 and 6829.

Solution:

Step I: Arrange the numbers in columns.

5-Digit Addition with Carrying


Step II: Adding ones, we have:

9 ones + 5 ones + 9 ones = 23 ones = 2 ten + 3 ones.

Carry over 2 to tens column and write 3 under ones column.

5-Digit Addition with Carrying - Adding Ones


Step III: Adding tens, we have:

2 ten (carried) + 3 tens + 6 tens + 2 tens = 13 tens = 1 hundred + 3 tens.

Carry over 1 to hundreds column and write 3 under tens column.

5-Digit Addition with Carrying - Adding Tens


Step IV: Adding hundreds, we have:

1 hundred (carried) + 8 hundreds + 4 hundreds + 8 hundreds 

                                      = 21 hundreds

                                      = 2 thousands + 1 hundred.

Carry over 2 to thousands column and write 1 under hundreds column.

5-Digit Addition with Carrying - Adding Hundreds


Step V: Adding thousands, we have

2 thousands (carried) + 5 thousands + 3 thousands + 6 thousands 

                                      = 16 thousands

                                      = 1 ten thousand + 6 thousands

Carry over 1 to ten thousands column and write 6 under thousands column.

5-Digit Addition with Carrying - Adding Thousands


Step VI: Adding ten thousands, we have

1 ten thousand (carried) + 2 ten thousands + 4 ten thousands

                                      = 7 ten thousands

Write 7 under ten thousands column.

5-Digit Addition with Carrying - Adding Ten Thousands

Hence, 25,839 + 43,465 + 6,829 = 76,133

(Seventy-six thousand, one hundred thirty-three).


Questions and Answers on Adding 5-digit Numbers with Regrouping:

I. Add the given numbers:

(i) 20129 and 58992

(ii) 38496 and 59837

(iii) 40128, 21397 and 22588

(iv) 1340, 21980 and 16748

(v) 25908, 256 and 9817

(vi) 44201, 32004 and 8173

(vii) 6415, 386 and 90281

(viii) 11028, 33015 and 48100


Answers:

I. (i) 79121

(ii) 98333

(iii) 84113

(iv) 40068

(v) 35981

(vi) 84378

(vii) 97082

(viii) 92143

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