Question

Starting from $\left(-1\right)\times 5$, write various products showing some pattern to show $\left(-1\right)\times \left(-1\right)=1$.

Answer 1

Starting from $\left(-1\right)\times 5$, write various products showing some pattern to show $\left(-1\right)\times \left(-1\right)=1$.

According to the pattern,

$$\begin{gathered} \left(-1\right)\times \left(5\right)=-5 \\ \left(-1\right)\times \left(4\right)=-4 \\ \left(-1\right)\times \left(3\right)=-3 \\ \left(-1\right)\times \left(2\right)=-2 \\ \left(-1\right)\times \left(1\right)=-1 \\ \left(-1\right)\times \left(0\right)=0 \\ \left(-1\right)\times \left(-1\right)=1 \end{gathered}$$

The product of two integers with similar sign numbers will always be positive. This means the product of two positive numbers or two negative numbers will always be positive. While the product of a positive number and a negative number (integers with different signs) will always be negative.