If your weekly salary is $386.00, how much do you take home each week after deductions for taxes and retirement are made of $177.56?

Question

Luna Angel · Accepted Answer

#$208.44#

#color(green)("Showed a sort of cheat")# These become easier to calculate once you get used to them and do some practice. If it is the decimals that are throwing you this is a little trick you can use. #color(green)("Get rid of the decimal point!")# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(brown)("The next 2 lines have not changed the actual values but they have")# #color(brown)("made the numbers look different.")# #color(magenta)("Both numbers must be multiplied by the same adjustment value")# Write #" "$386.00" as " $38600 color(magenta)(xx1/100 )# Write #" "$177.56" as "$17756color(magenta)(xx1/100)# So the answer will be:#" the subtraction "color(magenta)(xx1/100)# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Forget about the $ sign for now. #38600# #ul(17756)" "larr" Subtract"# #ul(20844)" " larr" Part answer"# Final answer is #20844xx1/100 = $208.44#

Emery Allen · Answer

Another approach!

#$208.44# Shown in stages so that you can see what is going on. For the purposes of clarity I am going to space out the columns. #386.00# #ul(177.56) " "larr" Subtract"# ,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(brown)("The numbers are spread out for clarity")# #color(blue)("Making all the numerals in the top number greater than the bottom ")# #color(green)(ul("Column number "-> 5" "4" "3color(white)(.)" "2" "1)# #" "3" "8" "6." "0" "0# #" "ul(1" "7" "7." "5" "6) " "larr" Subtract"# For 386.00 remove 1 from column 3 and move it to column 2. Remembering that moving one column down changes it to 10. #color(green)(ul("Column number "-> 5" "4" "3color(white)(.)" "2" "1)# #" "3" "8" "cancel(6)^5." "cancel(0)^(10)" "0# #" "ul(1" "7" "7^(color(white)(4))." "5" "6) " "larr" Subt."# But we need a number at the top of column 1 so we move 1 of the 10 at the top of column 2 (making it 9) to the top of column 1. Remembering that moving one column down changes it to 10. #color(green)(ul("Column number "-> 5" "4" "3color(white)(.)" "2" "1)# #" "3" "8" "cancel(6)^5." "cancel(0)^(9)" "cancel(0)^(10)# #" "ul(1" "7" "7^(color(white)(4))." "5" "6) " "larr" Subt."# We still need to change something before we do the subtraction. Notice that in column 3 we have #5 - 7#. So we move 1 from the 8 in column 4 to column 3 remembering that this becomes 10. This will change the 5 in column 3 into 15 as #10+5=15#. #color(green)(ul("Column number "-> 5" "4" "3color(white)(.)" "2" "1)# #" "3" "cancel(8)^7" "cancel(6)^(15)." "cancel(0)^(9)" "cancel(0)^(10)# #" "ul(1" "7" "7^(color(white)(42))." "5" "6) # #color(darkviolet)("Note that "3cancel(8)^7cancel(6)^(15).cancel(0)^9cancel(0)^(10)" is the same value as 386")# #color(red)("Now all the numerals in the top number are greater than those")##color(red)("in the bottom we can carry out the subtraction")# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Applying the subtraction")# #color(green)(ul("Column number "-> 5" "4" "3color(white)(.)" "2" "1)# #" "3" "cancel(8)^7" "cancel(6)^(15)." "cancel(0)^(9)" "cancel(0)^10# #" "ul(1" "7" "7^(color(white)(14))." "5" "6) # #" "2" "0" "8^(color(white)(14))." "4" "4#