Question

There are 80 Students in the marching band.

Can they match in 2,5, and /or 10 equal rows? Explain.

Answer 1

Step-by-step explanation: Yes, they can match in 2, 5, and/or 10 equal rows. This is because the number of items in the set can be divided evenly by 2, 5, and 10. For example, if there are 20 items in the set, it can be divided into 2 rows of 10, 5 rows of 4, or 10 rows of 2.

Answer 2

No, the 80 students in the marching band cannot match in 2, 5, or 10 equal rows.

Step-by-step explanation:

It is not possible for the 80 students in the marching band to match in 2, 5, or 10 equal rows because the number 80 is not evenly divisible by 2, 5, or 10. In order for the students to match in equal rows, the total number of students must be divisible by the number of rows.

To understand this concept better, we can use the mathematical operation of division to calculate the number of students that will be in each row for 2, 5, and 10 equal rows.

For 2 equal rows: If we divide 80 by 2, we get 40. This means that there will be 40 students in each row. However, 40 is not equal to 80, so the rows will not be equal.

For 5 equal rows: If we divide 80 by 5, we get 16. This means that there will be 16 students in each row. Again, 16 is not equal to 80, so the rows will not be equal.

For 10 equal rows: If we divide 80 by 10, we get 8. This means that there will be 8 students in each row. Once again, 8 is not equal to 80, so the rows will not be equal.

In order for the students to match in equal rows, the total number of students must be divisible by the number of rows. This means that the number of students in each row must be a whole number, not a decimal or fraction. Since 80 cannot be divided evenly by 2, 5, or 10, it is not possible for the students to match in equal rows.

Furthermore, even if we were to rearrange the students in different ways, the total number of students would still not change. For example, if we rearrange the students into 4 rows instead of 2, there will be 20 students in each row. Again, 20 is not equal to 80, so the rows will not be equal. The same applies for 8 rows (10 students in each row) and any other number of rows.

In conclusion, the 80 students in the marching band cannot match in 2, 5, or 10 equal rows because the number 80 is not evenly divisible by these numbers. In order for the students to match in equal rows, the total number of students must be divisible by the number of rows.