The greatest ratio among the ratios 2 : 3, 5 : 8, 75 : 121 and 40 : 25 is
2 : 3
5 : 8
75 : 121
40 : 25
Write each ratio as a fraction.
(displaystyle 2:3 ;Rightarrow; rac{2}{3})
(displaystyle 5:8 ;Rightarrow; rac{5}{8})
(displaystyle 75:121 ;Rightarrow; rac{75}{121})
(displaystyle 40:25 ;Rightarrow; rac{40}{25})
Decide whether each fraction is less than 1 or greater than 1.
If the numerator is smaller than the denominator, the value is less than 1.
If the numerator is larger than the denominator, the value is greater than 1.
(displaystyle rac{2}{3}): (2 < 3) → less than 1
(displaystyle rac{5}{8}): (5 < 8) → less than 1
(displaystyle rac{75}{121}): (75 < 121) → less than 1
(displaystyle rac{40}{25}): (40 > 25) → greater than 1
Compare.
Any number greater than 1 is bigger than any number less than 1.
Therefore, (displaystyle rac{40}{25}) is the greatest among the four.
(Optional) Simplify to see it clearly.
(displaystyle rac{40}{25} ;=; rac{8}{5})
(displaystyle rac{8}{5} ;=; 1.6)