Question

Which of the following is true?5/6 > 11/123/4 < 2/39/15 < 4/518/27 = 1/3

Answer 1

To determine which of the following comparisms is true, we will have to convert each of the fractions into whole number using the denominators lowest common multiple (LCM) and then decide on which of the comparisms is true.

Statement 1

`\begin{gathered} (5)/(6)>(11)/(12) \\ \text{LCM}\Rightarrow12 \\ 12*(5)/(6)=(60)/(6)=10 \\ 12*(11)/(12)=(132)/(12)=11 \\ \text{ Since 10 is not greater than 11},\text{ then} \\ (5)/(6)>(11)/(12)\Rightarrow\text{false} \end{gathered}`

Statement 2

`\begin{gathered} (3)/(4)<(2)/(3) \\ \text{LCM}\Rightarrow12 \\ 12*(3)/(4)=3*3=9 \\ 12*(2)/(3)=4*2=8 \\ \text{ Since 9 is not less than 8, then} \\ (3)/(4)<(2)/(3)\Rightarrow\text{false} \end{gathered}`

Statement 3

`\begin{gathered} (9)/(15)<(4)/(5) \\ \text{LCM}\Rightarrow15 \\ 15*(9)/(15)=1*9=9 \\ 15*(4)/(5)=3*4=12 \\ \text{ Since 9 is less than 12, then} \\ (9)/(15)<(4)/(5)\Rightarrow\text{true} \end{gathered}`

Statement 4

`\begin{gathered} (18)/(27)=(1)/(3) \\ \text{LCM}\Rightarrow27 \\ 27*(18)/(27)=1*18=18 \\ 27*(1)/(3)=9*1=9 \\ \text{ Since 18 is not equal to 9, then} \\ (18)/(27)=(1)/(3)\Rightarrow\text{false} \end{gathered}`

Hence, the statement that is true in all the statements is

`(9)/(15)<(4)/(5)`