How Can I Calculate Negative Multiplication Without Following Traditional Rules?

[pyroclasticsoul]

TL;DR Summary

Negative times positive

Say I have 6 pencils. I want to times this by negative two. Now ignoring the rules that your teacher taught you work this out. 6 pencils negative 2 times. Negative one time would be 0 and another negative times would be -6 right? So 6 x - 2 = -6 according to simple logic. The calculator will say -12 but if I took 6 away from 6 3 times that would be -12.

 

[DaveC426913]

TL;DR Summary: Negative times positive

Say I have 6 pencils. I want to times this by negative two. Now ignoring the rules that your teacher taught you work this out. 6 pencils negative 2 times. Negative one time would be 0 and another negative times would be -6 right? So 6 x - 2 = -6 according to simple logic. The calculator will say -12 but if I took 6 away from 6 3 times that would be -12.

No. You started out with 6. "I have 6 pencils." You're describing 6 + -2x6 which equals -6.

If you had started out with zero, then the final answer would indeed be -12.

 

[pyroclasticsoul]

No. You started out with 6. "I have 6 pencils." You're describing 6 + -2x6 which equals -6.

If you had started out with zero, then the final answer would indeed be -12.

I thought about that but why do I start with 0 and not 6 since 6 is the number adjusted by -2.

 

[DaveC426913]

why do I start with 0

Read the problem statement you wrote.

"I have 6 pencils"

The problem starts at +6 pencils.

 

[berkeman]

Note -- the OP deleted their first post after getting help from Dave. This is not allowed. The OP text is restored and this thread is now closed.