Answer:
[tex]\frac{4}{6} < \frac{7}{9}[/tex] ; [tex]\frac{8}{10} > \frac{7}{9}[/tex] ; [tex]\frac{6}{4} < \frac{8}{5}[/tex] ; [tex]\frac{2}{12} < \frac{4}{8}[/tex] ; [tex]\frac{6}{9} > \frac{5}{12}[/tex] ; [tex]\frac{3}{8} < \frac{5}{6}[/tex] ; [tex]\frac{2}{9} < \frac{5}{7}[/tex] ; [tex]\frac{6}{10} < \frac{2}{3}[/tex] ; [tex]\frac{3}{6} > \frac{4}{11}[/tex] ; [tex]\frac{5}{11} < \frac{3}{6}[/tex]
Step-by-step explanation:
For each comparsion, simplify, find the common denominator, then compare.
(a)
Simplify [tex]\frac{4}{6}=\frac{2}{3}[/tex]
Then between 3 and 9, the lowest common denominator would be 9.
This gives: [tex]\frac{2}{3} = \frac{6}{9}[/tex] and [tex]\frac{7}{9}[/tex] stays the same.
Therefore [tex]\frac{6}{9} < \frac{7}{9}[/tex] and [tex]\frac{4}{6} < \frac{7}{9}[/tex]
(b)
Simplify [tex]\frac{8}{10}=\frac{4}{5}[/tex]
Then between 5 and 9, the lowest common denominator would be 45.
This gives: [tex]\frac{4}{5} = \frac{36}{45}[/tex] and [tex]\frac{7}{9} = \frac{35}{45}[/tex]
Therefore [tex]\frac{36}{45} > \frac{35}{45}[/tex] and [tex]\frac{8}{10} > \frac{7}{9}[/tex]
(c)
Simplify [tex]\frac{6}{4}=\frac{3}{2}[/tex]
Then between 2 and 5, the lowest common denominator would be 10.
This gives: [tex]\frac{3}{2} = \frac{15}{10}[/tex] and [tex]\frac{8}{5} =\frac{16}{10}[/tex]
Therefore [tex]\frac{15}{10} < \frac{16}{10}[/tex] and [tex]\frac{6}{4} < \frac{8}{5}[/tex]
(d)
Simplify [tex]\frac{2}{12}=\frac{1}{6}[/tex] and [tex]\frac{4}{8} = \frac{1}{2}[/tex]
Then between 2 and 6, the lowest common denominator would be 6.
This gives: [tex]\frac{1}{6}[/tex] stays the same and [tex]\frac{1}{2} =\frac{3}{6}[/tex]
Therefore [tex]\frac{1}{6} < \frac{3}{6}[/tex] and [tex]\frac{2}{12} < \frac{4}{8}[/tex]
It's a similar process for the rest and you can always verify your answer with a calculator. If you need more help with the rest just say so! Hope this helps.
Also, when in doubt of finding a common denominator just multiply the two denominators. For example in (b) the lowest common denominator between 5 and 9 = 5*9=45.
