Question

Can someone plz help me. How can you find the inequalities of 11/15 and 5/7. Next 5/9 and 7/13. Next 11/15 and 5/7. Lastly 5/9 and 7/13. PLZ HELP.

Answer 1

To make this a little clearer, let's give the pairs of inequalities the same denominator:

Question 1:

`(11)/(15)` ?
`(5)/(7)`
First, apply the common denominator to the first fraction:

`((11)/(15))7 \\ (11)/(15) * (7)/(7) \\ (11*7)/(15*7) \\ (77)/(105)`
Do the same for the second:
`15( (5)/(7)) \\ (5)/(7)* (15)/(15) \\ (5*15)/(7*15) \\ (75)/(105)`
Nest, compare the two fractions:

`(77)/(105) \ \textgreater \ (75)/(105)`
Therefore:

`(11)/(15)` >
`(5)/(7)`

Question Two:

`(5)/(9)` ?
`(7)/(13)`
Apply the common denominator to fraction one:

`13( (5)/(9)) \\ (5)/(9) * (13)/(13) \\ (5*13)/(9*13) \\ (65)/(117)`
Fraction two:

`9((7)/(13)) \\ (7)/(13) * (9)/(9) \\ (7*9)/(13*9) \\ (63)/(117)`
Evaluate:

`(65)/(117)` >
`<span>(63)/(117)`
Therefore:

`(5)/(9)` >
`(7)/(13)`

Hope this helps!