Question 1199403
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This is the original fraction you started with
{{{(75.92)/(1.3)}}}


You then multiplied the numerator by 100, and the denominator by 10
{{{(75.92*100)/(1.3*10)}}}
to end up with
{{{7592/13}}}


You correctly found that
{{{7592/13 = 584}}}


The problem is that {{{(75.92)/(1.3)}}} is NOT the same as {{{7592/13}}}
The reason for that is because the factor (100/10) isn't 1, so you multiplied by some number larger than 1.
Meaning that {{{(75.92)/(1.3) < 7592/13}}}


Let's pull out those terms to form another fraction
{{{(75.92*100)/(1.3*10)}}} is equivalent to {{{((75.92)/(1.3))*(100/10)}}}


In order to cancel out the 100/10, we need to multiply by 10/100. 
This is the reciprocal.
{{{((75.92)/(1.3))*(100/10)}}}


{{{((75.92)/(1.3))*(100/10)*(10/100)}}}


Then notice how 10/100 = 1/10 = 0.1
This tells us to move the decimal point one spot to the left.
This effectively corrects what happened when applying the factor (100/10).


You'll go from the result you got, 584, to <font color=red>58.4</font> after moving the decimal point one spot to the left.


{{{(75.92)/(1.3) = highlight(58.4)}}}


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As the tutors have mentioned, it's best to move the decimal point the same number of spots for both numerator and denominator.
If you were to move each decimal point one spot to the right for instance, then you're multiplying top and bottom by 10.
This is the same as multiplying by 1 since 10/10 = 1.


In other words,
{{{(75.92)/(1.3) = ((75.92)/(1.3))*1 = ((75.92)/(1.3))*(10/10) = (75.92*10)/(1.3*10) = (759.2)/(13)}}}
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