Question

If the numbers 4, 5 and 6 are each used exactly once to replace the letters in the expression A ( B − C ), what is the least possible result?

Answer 1

-10

Explanation:

you want to multiply by the smallest number, so the parantheses should be (smallest number-largest number)

(4-6)5=-2*5=-10

Answer 2

The least possible result is -10.

Explanation:

Given the numbers 4, 5 and 6 are to be chosen one of the letters A, B or C.

First of all,

Let A = 4, B = 5 and C = 6

`A(B-C) = 4 * (5-6) = 4 * -1 = -4`

Let A = 4, B = 6 and C = 5

`A(B-C) = 4 * (6-5) = 4 * 1 = 4`

Let A = 5, B =4 and C = 6

`A(B-C) = 5 * (4-6) = 5 * -2 = -10`

Let A = 5, B = 6 and C = 4

`A(B-C) = 4 * (6-4) = 4 * 2 = 8`

Let A = 6, B = 4 and C = 5

`A(B-C) = 6 * (4-5) = 6 * -1 = -6`

Let A = 6, B = 5 and C = 4

`A(B-C) = 6 * (6-5) = 6 * 1 = 6`

Summarizing the above values in the form of a table:

`\begin{center}\begin{tabular}{ c c c c}A & B & C & A(B-C)\\ 4 & 5 & 6 & -4\\ 4 & 6 & 5 & 4\\ 5 & 4 & 6 & -10\\ 5 & 6 & 4 & 10\\ 6 & 4 & 5 & -6\\ 6 & 5 & 4 & 6\end{tabular}\end{center}`

So, the least possible result is -10.