Question
Starting from $(–1)$ $\times$ $5$, write various products showing some pattern to show $(–1)$ $\times$ $(–1) = 1.$
✓
Answer
From the question, we obtain,
- $1$ $\times$ $5 = - 5$
- $1 $$\times$ $4 = - 4 = - 5 + 1$
- $1$ $\times$ $3 = - 3 = - 4 + 1$
- $1$ $\times$ $2 = - 2 = - 3 + 1$
- $1$ $\times$ $1 = - 1 = - 2 + 1$
- $1$ $\times$ $0 = 0 = - 1 + 1$
Therefore, - $1$ $\times$ $(-1) = 0 + 1 = 1$
- $1$ $\times$ $5 = - 5$
- $1 $$\times$ $4 = - 4 = - 5 + 1$
- $1$ $\times$ $3 = - 3 = - 4 + 1$
- $1$ $\times$ $2 = - 2 = - 3 + 1$
- $1$ $\times$ $1 = - 1 = - 2 + 1$
- $1$ $\times$ $0 = 0 = - 1 + 1$
Therefore, - $1$ $\times$ $(-1) = 0 + 1 = 1$
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