There are 1379 children signed up to play in a baseball
league. If exactly 9 players are to be placed on each
team, will any team be short of players?
b. A forester has 43,682 seedlings to be planted. Can these
be planted in an equal number of rows with 11 seedlings
in each row?
c. There are 261 students to be assigned to 9 teachers so
that each teacher has the same number of students. Is
this possible?
d. Six friends win with a lottery ticket. The payoff is
$242,800. Can the money be divided evenly?
a. 1379 is not evenly divisible by 9. You get 153 teams of nine, with two left over.
b. Divide 43,682 by 11. You will see a remainder of 1.
c. What is 261/9?
d. What is $242,800/6 ?
Do the calculations and see if you get remainders.
To determine if any team will be short of players in the baseball league, we can divide the total number of children signed up (1379) by the number of players on each team (9):
1379 ÷ 9 = 153 remainder 2
Since we have a remainder of 2, this means that there will be two leftover players who cannot be evenly distributed among the teams. Therefore, one team will be short of players.
To check if the forester's 43,682 seedlings can be planted in an equal number of rows with 11 seedlings in each row, we can divide the total number of seedlings by the number of seedlings per row:
43,682 ÷ 11 = 3,980 remainder 2
Since we have a remainder of 2, this means that the seedlings cannot be evenly distributed into an equal number of rows with 11 seedlings in each row. Therefore, it is not possible to plant the seedlings in this way.
To determine if the 261 students can be assigned to 9 teachers so that each teacher has the same number of students, we can divide the total number of students by the number of teachers:
261 ÷ 9 = 29 remainder 0
Since we have a remainder of 0, this means that the students can be evenly distributed among the 9 teachers, with each teacher having 29 students.
To check if the $242,800 lottery prize can be divided evenly among the 6 friends, we can divide the total amount of money by the number of friends:
$242,800 ÷ 6 = $40,466.67
Since the result is not an even number, the money cannot be divided evenly among the 6 friends.
a. To determine if any team will be short of players, we need to divide the total number of children (1379) by the number of players per team (9).
Using long division, we divide 1379 by 9:
-----------
9 | 1379
- 9
-----
47
- 45
-----
29
We find that 9 divides into 1379, with a remainder of 2. This means that after forming teams of 9 players, there will be 2 extra players that cannot be evenly distributed. So yes, one team will be short of players.
b. To determine if the seedlings can be planted in an equal number of rows with 11 seedlings in each row, we need to divide the total number of seedlings (43,682) by the number of seedlings per row (11).
Using long division, we divide 43,682 by 11:
------------
11 | 43,682
- 44
-----
362
- 352
-----
102
- 99
------
33
We find that 11 does not divide into 43,682 evenly, as there is a remainder of 33. Therefore, these seedlings cannot be planted in an equal number of rows with 11 seedlings in each row.
c. To determine if the students can be assigned to the teachers so that each teacher has the same number of students, we need to divide the total number of students (261) by the number of teachers (9).
Using long division, we divide 261 by 9:
---
9 | 261
- 27
---
18
- 18
---
0
We find that 9 divides into 261 evenly, resulting in 0 remainder. Therefore, these students can be assigned to the 9 teachers in a way that each of them will have the same number of students.
d. To determine if the lottery money can be divided evenly among the six friends, we need to check if the total amount of money ($242,800) is divisible by the number of friends (6).
We divide 242,800 by 6:
-----------
6 | 242,800
- 24,000
-----
22,800
- 21,000
-----
1,800
- 1,800
-----
0
We find that 6 divides into 242,800 with no remainder. Therefore, the money can be evenly divided among the six friends. Each friend would receive $242,800/6 = $40,466.67.