The higher the denominator, the smaller the parts. For example, the following five fractions are in order from least to greatest:
\(\frac{1}{5} \frac{1}{4} \frac{1}{3} \frac{1}{2} \frac{1}{1}\)
However, when ordering \(\frac{1}{6} and \frac{3}{7}\) , you may notice that the second of those two has a higher numerator. In this particular case, that means that \(\frac{1}{6}\) is the smallest of the fractions given.
Since there are only two different denominators left now, it is easiest to make the demoninators the same.
2 X 7 = 14
5 X 7 = 35
3 X 7 = 21
3 X 5 = 15
7 X 5 = 35
The remaining fractions are \(\frac{14}{35} \frac{21}{35} \frac{15}{35}\)
Those three fractions are actually \(\frac{2}{5} \frac{3}{5} \frac{3}{7}\)
Therefore, in order of smallest to largest, the fractions are \(\frac{1}{6} \frac{2}{5} \frac{3}{7} \frac{3}{5}\)
