Question

Using integers -9 to 9 at most one time each, fill in the boxes to create a quotient with the greatest possible value.

A. -3 ÷ 1
B. 9 ÷ (-1)
C. -9 ÷ (-3)
D. 2 ÷ 2

Answer 1

The quotient with the greatest possible value is obtained by choosing the division
`\(B. 9 ÷ (-1)\)`, which equals -9.

Step-by-step explanation:

To maximize the quotient, we want to divide a large positive number by a small negative number. Among the given options,
`\(B. 9 ÷ (-1)\)` provides the highest result. Dividing 9 by -1 yields -9. The negative sign indicates that the quotient is less than zero, but among the options, this is the largest possible value.

Choosing other options would result in smaller magnitudes or positive values, which do not maximize the quotient. For example,
`\(A. -3 ÷ 1\)` gives -3,
`\(C. -9 ÷ (-3)\)` gives 3, and
`\(D. 2 ÷ 2\)` gives 1. In each case, the magnitude of the quotient is smaller than -9.

In summary, the choice of
`\(B. 9 ÷ (-1)\)` maximizes the quotient by dividing a large positive number by a small negative number, resulting in the greatest possible value of -9.

The strategy involves understanding the impact of the sign of the divisor on the magnitude of the quotient. In this case, selecting a large positive dividend and a small negative divisor leads to the highest magnitude for the quotient. The negative sign in the result is crucial for achieving the maximum value among the given options.