Dividing an integer by a number with a fraction

Question

There is a way regular people use to multiply a number with a number with a fraction. For example, multiply 6*2.5. They multiply 6*2=12 then 6*.5=3 then they add 12+3 to get the final result 15. I am trying to use the same way but with dividing not multiplying but I get a result that I was not expecting. I divided 6/2=3 then 6/.5=12 then subtracted 3 from 12 to get 9. When the actual result should be 2.4. My question is, can it be done the same way with multiplying, working with the integer then working with the fraction?

Answer 1

Short answer, no.

$2.5$ means $2+.5$, so $6\times2.5 = 6\times(2+.5)$. Then, by the distributive law of multiplication over addition, it equals $6\times2+6\times.5$.

However, there is no distributive law of division over addition, so there's no way in general to rewrite $6\div2.5 = 6\div(2+.5)$ in a similar way.

Answer 2

It cannot be done. Although $a(b+c) =ab +ac$, $\frac{a}{b+c} \ne \frac{a}{b} \pm \frac{a}{c}$ in general.