3-Digit Addition with Carry-over

Here we will learn numbers having 3-digit addition with carry-over. The additions are solved in three different ways.


Worked-out examples on 3-digit addition with carry-over:

1. Add together 248, 489 and 222 using expanded method in words.

Solution:

By expanding the numbers;

              248 = 2 hundreds + 4 tens + 8 ones                             

              489 = 4 hundreds + 8 tens + 9 ones  

          +  222 = 2 hundreds + 2 tens + 2 ones                             

  Sum            = 8 hundreds + 14 tens + 19 ones

                    = 8 hundreds + 14 tens + (1 ten) 9 ones            

                    = 8 hundreds + 15 tens + 9 ones   

                    = 8 hundreds + (1 hundred) 5 tens + 9 ones

                    = 9 hundreds + 5 tens + 9 ones                                  

                    = 959

Therefore, sum = 959

Steps to understand better:

(i) Adding one’s column = 8 + 9 + 2 = 19 ones = 1 tens 9 ones

(ii) Adding ten’s column = 4 + 8 + 2 = 14 tens = 1 hundred 4 tens

(iii) Adding hundred’s column = 2 + 4 + 2 = 8 hundreds

(iv) Carrying over 1 ten to ten’s column, 14 tens + 1 ten = 15 tens

                                                                            = 1 hundred + 5 tens

(v) Carrying over 1 hundred to hundred column, 8 hundred + 1 hundred = 9 hundred

(vi) We get as sum, 9 hundreds + 5 tens + 9 ones = 959.


2. Add together 375, 167 and 253 using expanded method in figures.

Solution:

By expanding the numbers;

               375 = 300 + 70 + 5                                

               167 = 100 + 60 + 7                                                  

           +  253 = 200 + 50 + 3                               

           Sum    = 600 + 180 + 15

                     = 600 + (100 + 80) + (10 + 5)

                     = 600 + (100 + 90) + 5                                          

                     = 700 + 90 + 5

                     = 795

Therefore, sum = 795

Steps to understand better:

(i) Adding one’s column = 5 + 7 + 3 = 15 ones = 10 + 5

(ii) Adding ten’s column = 70 + 60 + 50 = 180 = 100 + 80

(iii) Adding hundred’s column = 300 + 100 + 200 = 600

(iv) 600 + (100 + 80) + (10 + 5)

(v) 700 + 90 + 5

(vi) We get as sum = 795.


3. Add together 315, 432 and 197 in short method.

Solution:

By short method;

                                             3                  1                   5 

                                +           4                  3                   2

                                +           1                  9                   7

                 Sum       =              8                 13               14

                              =              8                 13  ← 1 T +    4

                              =              8           +    14           +    4

                              =              8  ← 1 H +     4            +   4

                              =             9 H         +    4 T          +    4

Therefore, sum = 944

Steps to understand 3-digit addition with carry-over using short method:

(i) Adding one’s column = 5 + 2 + 7 = 14 = 1 tens 4 ones

(ii) Adding ten’s column = 1 + 3 + 9 = 13 tens = 1 hundred 3 tens

(iii) Adding hundred’s column = 3 + 4 + 1 = 8 hundreds

(iv) Carrying over 1 ten to ten’s column from one’s column 13 + 1 = 14 T = 1 H 4 T

(v) Carrying over 1 hundred to hundred column from ten’s column 8 + 1 = 9

(vi) We get as sum = 944.





2nd Grade Math Practice

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