a basketball tournament starts with 64 teams. after one loss the team is out. how many games does the team that wins the tournament have to play?
64/2=32
32/2=16
16/2=8
8/2=4
4/2=2
2/2=1
The answer is 6 games.
How would I write the number sentence?
since half the teams are out after n rounds, you want
64 * 2^-n = 1
You can write the number sentence as follows:
64 ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 = 1
So, the team that wins the tournament has to play a total of 6 games.
To write the number sentence for this, you can express the steps of elimination as divisions by 2. Starting with 64 teams:
64 ÷ 2 = 32 (remaining teams after the first round)
32 ÷ 2 = 16 (remaining teams after the second round)
16 ÷ 2 = 8 (remaining teams after the third round)
8 ÷ 2 = 4 (remaining teams after the fourth round)
4 ÷ 2 = 2 (remaining teams after the fifth round)
2 ÷ 2 = 1 (remaining team after the sixth round, the winner)
Alternatively, you can express it using exponential notation:
64 ÷ 2^6 = 1
So, the number sentence is: 64 ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 = 1