Question

Q2 Identify the rule of the game. Enter your response here Matt and his friend Joe make up their own game and decide to play it. Player 1 starts the game. He announces a ratio, and player 2 has to respond according to a rule. Matt and Joe take turns to be Player 1. Look at the following table and figure out the rule of the game. Game number Player 1 says Player 2 says 1 1:3 9:27 2 81:9 9:1 3 4:16 1:4 4 30:6 5:1 5 2:7 8:28

Answer 1

`\begin{gathered} 1\colon3=(1)/(3) \\ 9\colon27=(9)/(27) \\ so\colon \\ (9)/(27)=(3)/(3)*((1)/(3)) \end{gathered}`
`\begin{gathered} 81\colon9=(81)/(9) \\ 9\colon1=(9)/(1) \\ so\colon \\ (81)/(9)=(9)/(9)*((9)/(1)) \end{gathered}`

According to the above, we can conclude that when one player names a ratio, the other must answer with an equivalent ratio. Therefore, for a given ratio:

`\begin{gathered} a\colon b=(a)/(b) \\ b\\e0 \end{gathered}`

The answer from the other player must be given by:

`\begin{gathered} ka\colon kb=(k)/(k)*(a)/(b)=(ka)/(kb) \\ k\in N \end{gathered}`