Method 1:
Look at the picture.
[tex]\dfrac{1}{7}[/tex] is greater than [tex]\dfrac{1}{9}[/tex]
[tex]\boxed{\dfrac{1}{7}>\dfrac{1}{9}}[/tex]
Method 2:
Find the common denominator:
multiples of 7: 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, ...
multiples of 9: 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
63 = 7 · 9
[tex]\dfrac{1}{7}=\dfrac{1\cdot9}{7\cdot9}=\dfrac{9}{63}\\\\\dfrac{1}{9}=\dfrac{1\cdot7}{9\cdot7}=\dfrac{7}{63}[/tex]
[tex]\dfrac{9}{63} > \dfrac{7}{63}[/tex]
therefore
[tex]\dfrac{1}{7} > \dfrac{1}{9}[/tex]
