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The product of three negative integers is:
- a)a positive integer
- b)either a positive integer or a negative integer
- c)a negative integer
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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The product of three negative integers is:a)a positive integerb)either...
If the number of negative integers in a product is odd, then the product is a negative integer.
Most Upvoted Answer
The product of three negative integers is:a)a positive integerb)either...
Explanation:
To find the product of three negative integers, we multiply three negative integers together. Let's consider the following examples:
- (-2) x (-3) x (-4) = -24 (product is negative)
- (-1) x (-1) x (-1) = -1 (product is negative)
- (-5) x (-10) x (-15) = -750 (product is negative)
As we can see from these examples, the product of three negative integers is always negative. Therefore, the correct answer is option C - a negative integer.
We can also prove this mathematically. Let's assume that we have three negative integers a, b, and c. Then:
a < />
b < />
c < />
Multiplying all three together, we get:
abc = (-1) x (-1) x (-1) x a x b x c
Since (-1) x (-1) x (-1) = -1, we can simplify this to:
abc = -a x -b x -c
Multiplying three negative integers together is the same as multiplying their absolute values together and then adding a negative sign. Since the absolute value of a negative integer is always positive, we have:
|a| x |b| x |c| = a x b x c
Therefore:
abc = -|a| x |b| x |c|
Since the product of three positive integers is always positive, we have:
|a| x |b| x |c| > 0
Therefore:
-|a| x |b| x |c| < />
So, the product of three negative integers is always negative.
To find the product of three negative integers, we multiply three negative integers together. Let's consider the following examples:
- (-2) x (-3) x (-4) = -24 (product is negative)
- (-1) x (-1) x (-1) = -1 (product is negative)
- (-5) x (-10) x (-15) = -750 (product is negative)
As we can see from these examples, the product of three negative integers is always negative. Therefore, the correct answer is option C - a negative integer.
We can also prove this mathematically. Let's assume that we have three negative integers a, b, and c. Then:
a < />
b < />
c < />
Multiplying all three together, we get:
abc = (-1) x (-1) x (-1) x a x b x c
Since (-1) x (-1) x (-1) = -1, we can simplify this to:
abc = -a x -b x -c
Multiplying three negative integers together is the same as multiplying their absolute values together and then adding a negative sign. Since the absolute value of a negative integer is always positive, we have:
|a| x |b| x |c| = a x b x c
Therefore:
abc = -|a| x |b| x |c|
Since the product of three positive integers is always positive, we have:
|a| x |b| x |c| > 0
Therefore:
-|a| x |b| x |c| < />
So, the product of three negative integers is always negative.
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Community Answer
The product of three negative integers is:a)a positive integerb)either...
Like this will be the equation
(-ve) ×(-ve) × (-ve) =negative integer
because (-) (-) =(+)
(+) (+) =(+)
(-) (+) =(-)
(+) (-) =(-)
so (-) ×(-) =(+) ×(-) =(-) means negative integers
that's why this is the answer
(-ve) ×(-ve) × (-ve) =negative integer
because (-) (-) =(+)
(+) (+) =(+)
(-) (+) =(-)
(+) (-) =(-)
so (-) ×(-) =(+) ×(-) =(-) means negative integers
that's why this is the answer
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