김연성
When you multiply a negative number twice, why you get a positive number?
I'll explain it to you in an easy way.
-1+1=0.
It means that if you multiply any number x by A number that is the product of -1 and x, you get 0.
To generalize, if any number is x, x+(-1)*x=0.
Now define x as -1. (x = -1)
x=-1, and the equation is x+(-1)*x=0.
To add a number to -1 and get 0, you need to add 1.
x+(-1)*x=0 can be expressed as -1+(-1)*(-1)=0.
If you add any number to -1 to get 0, that number is 1. Since x=-1 before, this equation becomes (-1)*(-1)=(-1)*x=1.
-> (-1)*(-1)=1
So you learn that if you multiply a negative by a negative, you get a positive.
2024年11月21日 14:22
訂正 · 7
1
When you multiply a negative number twice, why you get a positive number?
I'll explain it to you in an easy way.
-1+1=0.
It means that if you multiply any number x by A number that is the product of -1 and x, you get 0.
To generalize, if any number is x, x+(-1)*x=0.
Now define x as -1. (x = -1)
x=-1, and the equation is x+(-1)*x=0.
To add a number to -1 and get 0, you need to add 1.
x+(-1)*x=0 can be expressed as -1+(-1)*(-1)=0.
If you add any number to -1 to get 0, that number is 1. Since x=-1 before, this equation becomes (-1)*(-1)=(-1)*x=1.
-> (-1)*(-1)=1
So you learn that if you multiply a negative by a negative, you get a positive.
I am not convinced. You take for granted the existence of multiplication of integers. But how is it defined? What is meant by a*b if a and be are negative integers? Since you haven't said what it means, you can't come to any conclusion about it.
2024年11月21日 17:20
1
When you multiply a negative number twice, why DO you get a positive number? I'll
explain it to you in an easy way. -1+1=0. It means that if you multiply any
number x by A number that is the product of -1 and x, you get 0. To generalize,
if any number is x, x+(-1)*x=0. Now define x as -1. (x = -1) x=-1, and the
equation is x+(-1)*x=0. To add a number to -1 and get 0, you need to add 1.
x+(-1)*x=0 can be expressed as -1+(-1)*(-1)=0. If you add any number to -1 to
get 0, that number is 1. Since x=-1 before, this equation becomes
(-1)*(-1)=(-1)*x=1. -> (-1)*(-1)=1 So you learn that if you multiply a negative
by a negative, you get a positive.
2024年11月21日 16:17
When you multiply a negative number twice, why you get a positive number? I'll
explain it to you in an easy way. -1+1=0. It means that if you multiply any
number x by A number that is the product of -1 and x, you get 0. To generalize,
if any number is x, x+(-1)*x=0. Now define x as -1. (x = -1) x=-1, and the
equation is x+(-1)*x=0. To add a number to -1 and get 0, you need to add 1.
x+(-1)*x=0 can be expressed as -1+(-1)*(-1)=0. If you add any number to -1 to
get 0, that number is 1. Since x=-1 before, this equation becomes
(-1)*(-1)=(-1)*x=1. -> (-1)*(-1)=1 So you learn that if you multiply a negative
by a negative, you get a positive.
This explanation is insightful, and I appreciate how you’re trying to break it down! Let me simplify and clarify the reasoning even further for better understanding:
1. Why does multiplying two negatives give a positive?
Mathematically, it ensures the rules of arithmetic are consistent. The explanation revolves around how addition, subtraction, and multiplication work together.
2. Breaking it down with your example:
• You start with the equation x + (-1) \cdot x = 0 , which means adding x and (-1) \cdot x gives zero.
• Substituting x = -1 :
-1 + (-1) \cdot (-1) = 0 .
To balance the equation, the term (-1) \cdot (-1) must equal 1 . This keeps the math consistent and logical.
3. Intuitive explanation:
• Think of multiplying negatives as flipping directions:
A negative flips the sign of a number, and flipping twice (negative × negative) returns it to the original positive direction.
4. Conclusion:
Your explanation using -1 + (-1) \cdot (-1) = 0 is a good way to show how the rule holds! Multiplying negatives gives a positive because it aligns with how numbers behave in arithmetic.
2024年11月22日 08:19
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