Adding Numbers in Expanded Form

Learn to arrange for adding numbers in expanded form (in short form and in long form). The numbers are written in column form; the digits are arranged in expanded form and then finally find the sum of the given numbers.

Solved examples on adding numbers in expanded form:

1. Add 32 and 25

Solution:

Numbers are written in column form        T      O

                                                            3       2

                                                       +   2       5

                                                            5       7

Adding ones:  2 ones + 5 ones = 7 ones 

This 7 is written in one’s column.

Adding tens: 3 tens + 2 tens = 5 tens

This 5 is written in tens column.

Thus, answer is 57


2. In other way, add the expanded form of the numbers 32 + 25

Solution:

                32     =  30 + 2       Expanded form of the numbers

            +  25     =  20 + 5

                        =  50 + 7

                        =  57

The numbers are written in expanded form as 32 = 30 + 2 and 25 = 20 + 5.

Now digits of one’s place are added, i.e., 2 + 5 = 7.

Again numbers of ten’s place are added, i.e., 30 + 20 = 50

Therefore, total sum = 50 + 7 = 57


3. Add 63 and 35 in long form.

Solution:

Numbers are placed in column

           63      Sum of digit of one’s place = 3 ones + 5 ones = 8 ones

       +  35     Sum of digit of ten’s place = 6 ten’s + 3 ten’s = 9 ten’s

Therefore, sum =        98      = 9 ten’s + 8 ones


4. Add 38 and 61 in short form.

Solution:            

                               38         Sum of digit of one’s place = 8 + 1 = 9

                          +   61        Sum of digit of ten’s place = 30 + 60 = 90

Therefore, sum =      99                                              = 90 + 9


5. Add 23, 31 and 44

Solution: 

                                23        Sum of digit of one’s place = 3 + 1 + 4 = 8

                             +  31       Sum of digit of ten’s place = 2 + 3 + 4 = 9

                             +  44

Therefore, sum =        98


More solved examples on 3-digits for adding numbers in expanded form.

6. Add 314 and 563

Solution:

First the digits are arranged in columns

Sum of digit of one’s place = 4 + 3 = 7

Sum of digit of ten’s place = 1 + 6 = 7

Sum of digit of hundred’s place = 3 + 5 = 8

                              314

                          +  563

Therefore, sum =     877


7. Add 361 and 527 by arranging the numbers in expanded form.

Solution:

    361 = 3 hundreds + 6 tens + 1 one

+  527 = 5 hundreds + 2 tens + 7 one

 Sum   = 8 hundreds + 8 tens + 8 one

          =888

or,        361 = 300 + 60 + 1

        +  527 = 500 + 20 + 7

       Sum     = 800 + 80 + 8

                  = 888


8. Add 231, 402 and 355

Solution:               

                    231        ones         = 1 + 2 + 5 = 8

                +  402        tens         = 3 + 0 + 5 = 8

                +  355        hundreds  = 2 + 4 + 3 = 9

Therefore, addition sum = 988

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2nd Grade Math Practice

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