Question

How to simplify these fractions 0.25/0.75 and 6.25/12.5

Answer 1

One of the easier ways of simplifying 0.25/0.75 would be to recognice that 0.25 goes into 0.75 3 times.  Thus, 0.25/0.75 = 1/3.

Similary, 6.25/12.5 = 6.25/12.50 = 1/2.

Answer 2

You can always convert any decimal to a fraction by "using as many zeros in the denominator as there are decimals and lose the dot atop", let's do so with these, and then simplify them,

$\bf 0.\underline{25}\implies \cfrac{025}{1\underline{00}}\implies \cfrac{25}{100}\implies \stackrel{simplified}{\cfrac{1}{4}} \\\\\\ 0.\underline{75}\implies \cfrac{075}{1\underline{00}}\implies \cfrac{75}{100}\implies \stackrel{simplified}{\cfrac{3}{4}} \\\\\\ \cfrac{0.25}{0.75}\implies \cfrac{\quad \frac{1}{4}\quad }{\frac{3}{4}}\implies \cfrac{1}{4}\cdot \cfrac{4}{3}\implies \cfrac{1}{3}\\\\ -------------------------------$

$\bf 6.\underline{25}\implies \cfrac{625}{1\underline{00}}\implies \cfrac{625}{100}\implies \stackrel{simplified}{\cfrac{25}{4}} \\\\\\ 12.\underline{5}\implies \cfrac{125}{1\underline{0}}\implies \cfrac{125}{10}\implies \stackrel{simplified}{\cfrac{25}{2}} \\\\\\ \cfrac{6.25}{12.5}\implies \cfrac{\quad \frac{25}{4}\quad }{\frac{25}{2}}\implies \cfrac{25}{4}\cdot \cfrac{2}{25}\implies \cfrac{2}{4}\implies \stackrel{simplified}{\cfrac{1}{2}}$