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?

2 Answers
Sep 20, 2016

#$208.44#

#color(green)("Showed a sort of cheat")#

Explanation:

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#

Sep 20, 2016

Another approach!

#$208.44#

Explanation:

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#