how to explain?

how to explain -1 x -1 = +1 (minus x minus equals plus). Is there any practical example (explanation) for this? I have read as a mathematical formula, but how it is true? Kindly enlighten me. Any guidance on this issue is welcome.

With advance thanks.

Re: how to explain?

Quote:

Originally Posted by arangu1508

how to explain -1 x -1 = +1 (minus x minus equals plus). Is there any practical example (explanation) for this? I have read as a mathematical formula, but how it is true? Kindly enlighten me. Any guidance on this issue is welcome.

With advance thanks.

Math Forum: Ask Dr. Math FAQ: Negative Times a Negative

Re: how to explain?

Quote:

Originally Posted by arangu1508

how to explain -1 x -1 = +1 (minus x minus equals plus). Is there any practical example (explanation) for this? I have read as a mathematical formula, but how it is true? Kindly enlighten me. Any guidance on this issue is welcome.

With advance thanks.

Do you know the distributive law? $\displaystyle \begin{align*} (a + b) \cdot (c + d) = a\cdot c + a\cdot d + b\cdot c + b\cdot d \end{align*}$ .

Let's look at, say, $\displaystyle \begin{align*} 9 \cdot 9 = 81 \end{align*}$

We could also write this as

$\displaystyle \begin{align*} 9 \cdot 9 &= (10 - 1) \cdot (10 - 1) \\ &= 10\cdot 10 + 10\cdot (-1) + (-1) \cdot 10 + (-1)\cdot (-1) \\ &= 100 - 10 - 10 + (-1) \cdot (-1) \\ &= 80 + (-1)\cdot (-1) \end{align*}$

But we know that $\displaystyle \begin{align*} 9\cdot 9 = 81 \end{align*}$ , so

$\displaystyle \begin{align*} 80 + (-1)\cdot (-1) &= 81 \\ (-1) \cdot (-1) &= 81 - 80 \\ (-1) \cdot (-1) &= 1 \end{align*}$

If we want to visualise this, just picture a 10 x 10 square, and picture evaluating 9 x 9 by removing one row of 10 and one column of 10. The problem is that by doing this, one of the unit squares has been removed twice, and so needs to be put back.