Addition of 5, 6 and 7 digit numbers (without regrouping)
Addition without regrouping : Arrange the numbers in different groups like ones, tens, hundreds, thousands, ten thousands, lakhs and ten lakhs and then add each group separately.
Example 1: Add the following:
Step 1 : add ones, 8 ones + 1 one = 9 ones.
Step 2 : add tens, 2 tens + 5 tens = 7 tens.
Step 3 : add hundreds, 3 hundreds + 3 hundreds = 6 hundreds.
Step 4 : add thousands, 6 thousands + 3 thousands = 9 thousands.
Step 5 : add ten thousands, 1 ten thousand + 7 ten thousands = 8 ten thousands.
Step 6 : add lakhs, 3 lakhs + 4 lakhs = 7 lakhs.
Step 7 : add ten lakhs, 2 ten lakhs + 6 ten lakhs = 8 ten lakhs.
Example 2:
Step 1 : add ones, 5 ones + 1 one = 6 ones.
Step 2 : add tens, 6 tens + 3 tens = 9 tens.
Step 3 : add hundreds, 8 hundreds + 1 hundred = 9 hundreds.
Step 4 : add thousands, 3 thousands + 3 thousands = 6 thousands.
Step 5 : add ten thousands, 2 ten thousands + 7 ten thousands = 9 ten thousands.
Step 6 : add lakhs, 5 lakhs + 1 lakh = 6 lakhs.
Example 3:
Step 1 : add ones, 6 ones + 1 one = 7 ones.
Step 2 : add tens, 4 tens + 5 tens = 9 tens.
Step 3 : add hundreds, 4 hundreds + 4 hundreds = 8 hundreds.
Step 4 : add thousands, 3 thousands + 1 thousand = 4 thousands.
Step 5 : add ten thousands, 2 ten thousands + 7 ten thousands = 9 ten thousands.
Addition of 5, 6 and 7 digit numbers (with regrouping)
Addition with regrouping : Group the numbers into columns like ones, tens, hundreds, thousands, ten thousands, lakhs and ten lakhs. Add the numbers in each column separately. If any number in a column is more than 9, carry it over to the next digit
Example 1: Addition of Seven Digit Numbers
Step 1 : add ones, 8 ones + 2 ones = 10 , Ones sum exceed 9, so carry left digit of the sum i.e 1 to the tens column and write down the 0.
Step 2 : add tens, 4 tens + 5 tens + 1 ten (carry) = 10. Tens sum exceed 9, so carry left digit of the sum i.e 1 to the hundreds column and write down the 0.
Step 3 : add hundreds, 5 hundreds + 2 hundreds + 1 hundred (carry) = 8 hundreds.
Step 4 : add thousands, 6 thousands + 3 thousands = 9 thousands.
Step 5 : add ten thousands, 1 ten thousand + 7 ten thousands = 8 ten thousands.
Step 6 : add lakhs, 3 lakhs + 4 lakhs = 7 lakhs.
Step 7 : add ten lakhs, 2 ten lakhs + 6 ten lakhs = 8 ten lakhs.
Example 3: Addition of Six Digit Numbers
Step 1 : add ones, 8 ones + 2 ones = 10, Ones sum exceed 9, so carry left digit of the sum i.e 1 to the tens column and write down the 0.
Step 2 : add tens, 4 tens + 5 tens + 1 ten (carry) = 10. Tens sum exceed 9, so carry left digit of the sum i.e 1 to the hundreds column and write down the 0.
Step 3 : add hundreds, 5 hundreds + 2 hundreds + 1 hundred (carry) = 8 hundreds.
Step 4 : add thousands, 6 thousands + 3 thousands = 9 thousands.
Step 5 : add ten thousands, 1 ten thousand + 7 ten thousands = 8 ten thousands.
Step 6 : add lakhs, 3 lakhs + 4 lakhs = 7 lakhs.
Example 3: Addition of Five Digit Numbers
Step 1 : add ones, 8 ones + 5 ones = 13, Ones sum exceed 9, so carry left digit of the sum i.e 1 to the tens column and write down the 3.
Step 2 : add tens, 4 tens + 4 tens + ten (carry) = 9 tens.
Step 3 : add hundreds, 5 hundreds + 3 hundreds = 8 hundreds.
Step 4 : add thousands, 6 thousands + 8 thousands = 14, Thousands sum exceed 9, so carry left digit of the sum i.e 1 to the tens thousands column and write down the 4.
Step 5 : add ten thousands, 1 ten thousand + 7 ten thousands + 1 ten thousand (carry) = 9 ten thousands.
Properties of Addition
Property 1 : Commutative : The answer will be the same even if you change the order of addition.
Example : Solve : 34,142 + 58,776 and 58,776 + 34,142
So, 34,142 + 58,776 = 92918 = 58,776 + 34,142
Property 2 : Associative : The Associative Property of Addition states that when adding three or more numbers, it doesn’t matter how the numbers are grouped. The sum of the numbers will be the same regardless of the grouping.
Example : Solve : (14,142 + 58,326) + 23,786 and 14,142 + (58,326 + 23,786)
So, (14,142 + 58,326) + 23,786 = 96254 = 14,142 + (58,326 + 23,786)
Property 3 : Additive Identity : This property states that the sum of any number and 0 is the number itself.
Example : Solve : 14,142 + 0
So, 14,142 + 0 = 14,142
Example 2 : Let’s find the sum of 43 and 56
Step 1: Add 40 + 50 hold, 3 and 6 in mind, 4 + 5 = 9 means 40 + 50 = 90.
Step 2: Add 3 + 6 = 9.
Step 3: Add 90 + 9 = 99, So 43 + 56 = 99.
Mental addition
Example 1 : Let’s find the sum of 28 and 44
Step 1: Add 20 + 40 hold, 8 and 4 in mind, 2 + 4 = 6 means 20 + 40 = 60.
Step 2: Add 8 + 4 = 12.
Step 3: Add 60 + 10 hold, 2 in mind, 60 + 10 = 70.
Step 4: Finally Add 70 + 2 which is 72, So 28 + 44 = 72
Example 2 : Let’s find the sum of 43 and 56
Step 1: Add 40 + 50 hold, 3 and 6 in mind, 4 + 5 = 9 means 40 + 50 = 90.
Step 2: Add 3 + 6 = 9.
Step 3: Add 90 + 9 = 99, So 43 + 56 = 99.