these numbers in order from least to greatest. \begin{tabular}{l}\( 8 \frac{9}{20} \) \\ Submit \\ \hline\( \frac{9}{25} \) \\ \hline\( \frac{10}{40} \) \\ \hline\end{tabular}

To compare the numbers \( 8 \frac{9}{20} \), \( \frac{9}{25} \), and \( \frac{10}{40} \), it's useful to convert them into a common fractional format or decimals. Starting with \( \frac{10}{40} \), simplifying it yields \( \frac{1}{4} \) or 0.25. The fraction \( \frac{9}{25} \) can be converted to decimal as 0.36. Lastly, the mixed number \( 8 \frac{9}{20} \) can be rewritten as \( 8 + 0.45 \), which equals 8.45. Now, ordering them gives us \( \frac{10}{40} < \frac{9}{25} < 8 \frac{9}{20} \). So, the order from least to greatest is: \[ \frac{10}{40}, \frac{9}{25}, 8 \frac{9}{20} \] Finding common ground between fractions can be fun! Did you know that representing fractions with different denominators usually boils down to getting them to “speak” the same numerical language? This approach makes it super easy to spot the smallest or largest values in a series! Don’t forget about the power of estimation! Sometimes it helps to round numbers off to the nearest whole number or simple fraction when comparing. For instance, instead of directly computing everything, rounding \( 8 \frac{9}{20} \) to 8.5 and comparing that with \( 0.36 \) or \( 0.25 \) can lead to quicker insights. Just make sure to refine back to the exact numbers when you want to finalize!