Minus times minus makes a plus. Most students learn the rule. Here's a way to actually see why it's true.
Imagine a video of someone walking
Two things can each be positive or negative:
- The walking: forwards is positive, backwards is negative.
- The video: playing is positive, rewinding is negative.
What you see on screen is the answer.
The four cases
- Positive × positive: walk forwards, play the video. They go forwards.
- Negative × positive: walk backwards, play it. They go backwards.
- Positive × negative: walk forwards, but rewind. On screen, they go backwards.
- Negative × negative: walk backwards, and rewind. On screen, they walk forwards.
Two negatives make a positive.
Worked example: −3 × −4
Someone walking backwards at 3 steps a second, rewound for 4 seconds. On screen, that's 12 steps forwards. So −3 × −4 = +12.
The formal reason
The video is a picture that makes the rule believable. The proof uses the distributive law: −3 × (4 + −4) = −3 × 0 = 0. That's −12 plus −3 × −4, so −3 × −4 must be +12 to cancel the −12 out.
What's −5 × −6?
Show the answer
Two negatives make a positive, so it's +30.
Save this for your next test
- A negative flips the direction.
- Two flips bring you back the way you started.
- So negative × negative = positive.
- Negative × positive = negative.
Read the video transcript
- Why does minus times minus make a plus? Here's a way you can actually see it.
- Imagine a video of someone walking.
- Walking forwards is positive. Walking backwards is negative.
- Playing the video is positive. Rewinding it is negative.
- Positive times positive: walk forwards, play the video. They go forwards.
- Negative times positive: walk backwards, play it. They go backwards.
- Positive times negative: walk forwards, but rewind. On screen, they go backwards.
- Now negative times negative: walk backwards, and rewind the video.
- On screen, they walk forwards! Two negatives make a positive.
- Let's try one: minus 3 times minus 4. Walking backwards 3 steps a second, rewound for 4 seconds.
- On screen, that's 12 steps forwards. So minus 3 times minus 4 is plus 12.
- Now you: what's minus 5 times minus 6? Tell me in the comments.
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