Question

How do you divide rational numbers in decimal form?

Answer 1

By example: This is one method of many.

Explanation:

Just picking values at random, suppose we had: `2.35/2.65`
`color(blue)("Making the numbers more straight forward")`

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)( [2.35/2.65color(red)(xx1)] color(white)("ddd") -> color(white)("ddd")[2.35/2.65color(red)(xx100/100)] )`

`color(green)(color(white)("dddddddddddd")->color(white)("ddddddd")235/265 = 47/53)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Conducting the division")`

What follows is one method of many.

Note that `47` is the same as `470xx1/10`

I will use this adjustment approach to make division itself more straight forward. We will need to apply the appropriate adjustment at the end.

So for `47-:53` we have `470-:53color(magenta)(xx1/10)`

`color(white)("ddddddd")470 color(magenta)(xx1/10)`
`color(magenta)(8)(53) ->ul( 424 larr" Subtract")`
`color(white)("dddddddd")46 larr" less than 53 so we adjust again"`
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`color(white)("ddddddd")460 color(magenta)(xx1/10)`
`color(magenta)(8)(53)->ul(424larr" Subtract")`
`color(white)("dddddddd") 36larr" less than 53 so we adjust again"`
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`color(white)("ddddddd")360 color(magenta)(xx1/10)`
`color(magenta)(6)(53)->ul(318larr" Subtract")`
`color(white)("dddddddd")42larr" less than 53 so we adjust again"`
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`color(magenta)("AND SO THE CYCLE CONTINUES:")`

So far we have:

`color(magenta)(886xx1/10xx1/10xx1/10 = 0.886)`

The full printout from my calculator is: 0.88679245283