2. Using divisibility tests, answer each of the following:
a. 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?e. Jack owes $7812 on a new car. Can this amount be paid
in 12 equal monthly installments?
We'll be glad to check your answers.
Six friends win with a lottery ticket. The payoff is
$242,800. Can the money be divided evenly?e. Jack owes $7812 on a new car. Can this amount be paid
in 12 equal monthly installments?
To answer each of these questions using divisibility tests, we need to determine if the given quantities can be divided equally by the specified numbers. Here's how you can apply divisibility tests to find the answers:
a. To check if 1379 children can be divided equally among teams of 9 players, we divide 1379 by 9. If the quotient is an integer and the remainder is 0, then the division is possible without any team being short of players. In this case, 1379 ÷ 9 = 153 remainder 2. Since the remainder is not 0, there will be some teams that will have fewer players.
b. To check if 43,682 seedlings can be divided equally into rows of 11 seedlings, we divide 43,682 by 11. If the quotient is an integer and the remainder is 0, then the division is possible. In this case, 43,682 ÷ 11 = 3970 remainder 2. Since the remainder is not 0, the seedlings cannot be planted in an equal number of rows.
c. To check if 261 students can be divided equally among 9 teachers, we divide 261 by 9. If the quotient is an integer and the remainder is 0, then the division is possible. In this case, 261 ÷ 9 = 29 remainder 0. Since the remainder is 0, each teacher can have an equal number of students.
d. To check if $242,800 can be divided evenly among the six friends, we divide $242,800 by 6. If the quotient is an integer and the remainder is 0, then the division is possible. In this case, $242,800 ÷ 6 = $40,466.67. Since the quotient is not an integer, the money cannot be divided evenly among the friends.
e. To check if $7812 can be paid in 12 equal monthly installments, we divide $7812 by 12. If the quotient is an integer and the remainder is 0, then the division is possible. In this case, $7812 ÷ 12 = $651. Since the quotient is an integer, the amount can be paid in 12 equal monthly installments.
Using divisibility tests allows you to determine if a quantity can be divided evenly by another number.