Not sure where to begin, so let's start at the top
3(-5) is the same written as 3 x -5
When spoken, this expresion is "Three times negative five" or "Three multiplied by negative five"
Now when we deal with multipling or dividing negative and positive numbers there are a few rules to remember.
1. A positive number muliplied or divided by a positive number equals a POSITIVE
2. A negative number muliplied or divided by a negative number equals a POSITIVE
3. A positive number muliplied or divided by a negative number equals a NEGATIVE
OR A negative number muliplied or divided by a positive number equals a NEGATIVE
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Now with the problem 3(-5)
We can pull the negative symbol from -5 to be;
3(-5) = -(3)(5)
We easily know what (3)(5) or 3*5 (Three times Five)
(3)(5) = 15
So plug (3)(5) = 15 into -(3)(5)
-(15)
The minus sign in -(15) also can be (-1)
So
-(15) = (-1)(15)
(-1)(15) = -15 because a negative multiplied by a positive equals a negative
Thus;
3(-5) = -(3)(5) = -(15) = (-1)(15) = -15
3(-5) = -15