Negative × Negative = Positive

Why does negative times negative give positive? Let's find out. Imagine a number line with zero in the middle. Positive means right, negative means left on the line.

• Right = positive, Left = negative

Now, three times two means three groups of two.

We jump right twice, three times. We land at six. What about three times negative two?

Three groups, but now we jump left twice each time. We land at negative six. Good. Now the key part. What does negative three times negative two mean?

• Jump left three times: land at -6
• Negative times = flip direction

Negative three means: do the opposite of three groups. Opposite of three groups jumping left is three groups jumping right.

• Negative three = opposite of three

Two negatives cancel out and flip us back to positive. If negative two times three is negative six, what is negative two times negative three? Negative times negative is positive because two flips return you forward.

• Flip twice = back to start