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# How do you solve $6.5n = 45.5$?

Last updated date: 20th Jun 2024
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Hint: Here first of all we will take the given expression and make the required unknown “n” as the subject moving all the terms on one side of the equations, remove decimal points and convert it in the form of simple fraction and then simplify the equation for the required resultant answer.

Complete step-by-step solution:
Take the given expression: $6.5n = 45.5$
Remove the decimal point from both the sides of the equation by placing the number ten since both the terms have one digit after decimal point.
$\Rightarrow \dfrac{{65}}{{10}}n = \dfrac{{455}}{{10}}$
Common factors in the denominator of both the sides are the same, so they cancel each other and therefore remove from the denominator of both the sides of the equation.
$\Rightarrow 65n = 455$
Now, the term multiplicative on one side of the equation if moved to the opposite side then it goes to the denominator.
$\Rightarrow n = \dfrac{{455}}{{65}}$
Find factors of the above expression for both the numbers in the numerator and the denominator.
$\Rightarrow n = \dfrac{{13 \times 7 \times 5}}{{13 \times 5}}$
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator of the above equation.
This is the required solution.

Note: Be good in multiples and always remember that common factor from the numerator and the denominator cancel each other. Also be careful while removing the decimal point. Always count the number of digits after the decimal point and then put zeros under it or ten for one digit, hundred for two digits and so on. Be good in finding the factors of the numbers and then remove common factors from the numerator and the denominator.