Question

How do you evaluate `7517.4\div 1.34`?

Answer 1

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`

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`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`