Is 4/5 Greater than 6/7 ?

$${\frac{{\mathtt{4}}}{{\mathtt{5}}}} = {\mathtt{0.8}}$$

$${\frac{{\mathtt{6}}}{{\mathtt{7}}}} = {\mathtt{0.857\: \!1}}$$ (4 d.c.p.)

0.8 < 0.8571 

 

We can also solve this by making the denominators the same. 

$${\frac{\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{7}}\right)}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{7}}\right)}} = {\frac{{\mathtt{28}}}{{\mathtt{35}}}}$$

$${\frac{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{5}}\right)}{\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{5}}\right)}} = {\frac{{\mathtt{30}}}{{\mathtt{35}}}}$$

28<30