Sort the following fractions from greatest to smallest: $$\dfrac{4}{3}, \dfrac{7}{9}, \dfrac{11}{8}, \dfrac{5}{6}$$ and $$1.$$
See development and solution
Development:
We compare the fractions one by one.
- $$\dfrac{4}{3}=\dfrac{12}{9}$$ and then it $$\dfrac{4}{3}$$ is bigger than $$\dfrac{7}{9}$$.
- $$\dfrac{4}{3}=\dfrac{32}{24}$$ and $$\dfrac{11}{8}=\dfrac{33}{24}$$ then $$\dfrac{4}{3}$$ is less than $$\dfrac{11}{8}$$.
- $$\dfrac{4}{3}=\dfrac{8}{6}$$ and then $$\dfrac{4}{3}$$ is bigger than $$\dfrac{5}{6}$$.
- $$1=\dfrac{3}{3}$$ and then $$\dfrac{4}{3}$$ is bigger than $$1$$.
Then, the biggest is $$\dfrac{11}{8}$$ and the second biggest is $$\dfrac{4}{3}$$. We compare three remaining ones. $$\dfrac{5}{6}=\dfrac{15}{18}$$ and $$\dfrac{7}{9}=\dfrac{14}{18}$$, then $$\dfrac{5}{6}$$ is bigger than $$\dfrac{7}{9}.$$ $$1=\dfrac{9}{9}$$ and then $$\dfrac{7}{9}$$ is less than $$1$$.
In conclusion, sorted from greatest to smallest we have the fractions $$\dfrac{7}{9}, \dfrac{5}{6}, 1, \dfrac{4}{3}$$ and $$\dfrac{11}{8}.$$
Solution:
Sorted from smallest to greatest we have the fractions $$\dfrac{7}{9}, \dfrac{5}{6}, 1, \dfrac{4}{3}$$ and $$\dfrac{11}{8}.$$