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I am not sure if this is possible. But I want to know if there is a formula to provide all possible combinations to any $a$ and $b$ in this example or any similar equation where the divider and number after the point is different:

$$a / 5 = b.8 $$ 1. A correct answer would be $a=9$, $b=1$. So $9 / 5 = 1.8$

Is there a calculation or formula to do this thanks

3 Answers 3

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Hint:

$\frac{a}{5}=b.8$

$\Rightarrow\frac{a}{5}=b + \frac{8}{10}$

$\Rightarrow a=5b+4$

For $b=0,1,2,3...$, you can find corresponding $a$.

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    Thanks Wicked-Its looks like I should loop through "b" to provide the "a". What if "b" was more complicated and I wanted to get a exact number rather than multiple. Is it possible? example a / 33 =b.333333333333333333333333333333 (I want the 1859 or 56) This does not seem possible unless I go through 56 attempts at "b" if I'm making sense. – 2017-01-03
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    Every rational number can be written in form $\frac{p}{q}$. Write $b.333$ as $b+\frac{1}{3}$ then you get $a=33b+11$. For given $a$, substitute $a$ in the equation to find $b$. – 2017-01-03
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The question is similar to the following; $$\frac{a}{5}=b+0.8\\a=5b+4\\a-5b=4$$Like all linear Diophantine equations if you have one solution you can determine all solutions;$$a=9,b=1\\a=9+5k,\ b=1+k\\9+5k-5(1+k)=9-5=4$$You can write it in a nicer way;$$a=4+5k\ \ ,b=k$$

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$a/5=b.8\iff$

$a/5=b+0.8\iff$

$a=5b+4$

This is a system of $1$ equation in $2$ variables.

So you can choose one variable freely and then compute the other variable.

For example:

  • Choose $b=0$ then compute $a=5\cdot0+4=4$
  • Choose $b=1$ then compute $a=5\cdot1+4=9$
  • Choose $a=19$ then compute $b=(19-4)/5=3$
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    Could you explain the use of 4 and how it would change in another equation. Thanks – 2017-01-05