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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

Respuesta :

[tex]\begin{gathered} 1\colon3=\frac{1}{3} \\ 9\colon27=\frac{9}{27} \\ so\colon \\ \frac{9}{27}=\frac{3}{3}\times(\frac{1}{3}) \end{gathered}[/tex][tex]\begin{gathered} 81\colon9=\frac{81}{9} \\ 9\colon1=\frac{9}{1} \\ so\colon \\ \frac{81}{9}=\frac{9}{9}\times(\frac{9}{1}) \end{gathered}[/tex]

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:

[tex]\begin{gathered} a\colon b=\frac{a}{b} \\ b\ne0 \end{gathered}[/tex]

The answer from the other player must be given by:

[tex]\begin{gathered} ka\colon kb=\frac{k}{k}\times\frac{a}{b}=\frac{ka}{kb} \\ k\in N \end{gathered}[/tex]