How do you evaluate 7517.4\div 1.34?

1 Answer
Jan 29, 2017

This is two sort of cheats for manual calculation method

Explanation:

color(blue)("Step 1 - making the numbers easier to handle")

I am guessing that the decimals are giving you trouble. This is a way round that.

Note that:
7517.4 is the same as 75174xx1/10
1.34 is the same as 134xx1/10^2

So we have: 75174/134xx1/10-:1/10^2

75174/134xx1/10xx10^2

75174/134xx10

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Step 2 - determine the start value for division")

10xx134=1340 larr" not big enough"
100xx134=13400 larr" correct count of digits but too small"
700xx134=93800larr" too big"
500xx134=6" something" larr" start with this one"

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Step 3 - applying the division. This is a different format of long division")

" "75174larr" numerator value"
color(red)(500)xx134 ->ul(67000) larr" subtract"
" "8174
color(red)(60)xx134" "->ul(8040) larr" subtract"
" "134
color(red)(1)xx134" "->ul(134) larr" sibtract"
" "0

so 75174/134 = color(red)(500+60+1) = 561

But we still need to deal with the adjustment of xx10

So 7517.4/1.34=561xx10 = 5610
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check by calculator -> 7517.4/1.34 = 5610