It is often more helpful to write the numbers in what I call column form:
To make adding up easier us the place holder method. For example instead of 209 I could write 00209. This does not change value.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Adding up the units column we have 29 so we have #color(red)(9)# #color(magenta)("carry 2")#
#" "0color(white)(.)3color(white)(.)8color(white)(.)4#
#" "2color(white)(.)9color(white)(.)1color(white)(.)2#
#" "2color(white)(.)0color(white)(.)0color(white)(.)8#
#" "0color(white)(.)2color(white)(.)0color(white)(.)9#
#" "ul(0color(white)(.)0color(white)(.)2color(white)(.)6) larr" Add up the columns"#
#" "ul(color(white)(..........)color(red)(9))#
#" "color(magenta)(color(white)(.......)^2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Adding the tens column we have 11 plus the carry of 2 makes 13
So we have #color(red)(3)# #color(magenta)("carry 1")#
#" "0color(white)(.)3color(white)(.)8color(white)(.)4#
#" "2color(white)(.)9color(white)(.)1color(white)(.)2#
#" "2color(white)(.)0color(white)(.)0color(white)(.)8#
#" "0color(white)(.)2color(white)(.)0color(white)(.)9#
#" "ul(0color(white)(.)0color(white)(.)2color(white)(.)6) larr" Add up the columns"#
#" "ul(color(white)(......)color(red)(3)color(white)(.)9)#
#" "color(white)(....)^(color(magenta)(1)color(white)(.)2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Adding the hundreds column we have 14 plus the carry of 1 makes 15. So we have #color(red)(5)# #color(magenta)("carry 1")#
#" "0color(white)(.)3color(white)(.)8color(white)(.)4#
#" "2color(white)(.)9color(white)(.)1color(white)(.)2#
#" "2color(white)(.)0color(white)(.)0color(white)(.)8#
#" "0color(white)(.)2color(white)(.)0color(white)(.)9#
#" "ul(0color(white)(.)0color(white)(.)2color(white)(.)6) larr" Add up the columns"#
#" "ul(color(white)(..)color(red)(5)color(white)(.)3color(white)(.)9)#
#""color(white)(....)^(color(magenta)(1)color(white)(.)1color(white)(.)2)#
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Adding the thousands column we have 4 plus the carry of 1 makes 5. So we have #color(red)(5)# no carry
#" "0color(white)(.)3color(white)(.)8color(white)(.)4#
#" "2color(white)(.)9color(white)(.)1color(white)(.)2#
#" "2color(white)(.)0color(white)(.)0color(white)(.)8#
#" "0color(white)(.)2color(white)(.)0color(white)(.)9#
#" "ul(0color(white)(.)0color(white)(.)2color(white)(.)6) larr" Add up the columns"#
#""color(white)(....)ul(color(red)(5)color(white)(.)5color(white)(.)3color(white)(.)9)#
#""color(white)(....)^(1color(white)(.)1color(white)(.)2)#
