Question

How can we prove that a negative number multiplied/divided/subtracted by a negative gives positive result?

Answer 1

Hint: In this question we have been asked to prove that a negative number multiplied/divided/subtracted by a negative gives positive result. We will do that by assuming some numbers and verifying if these operations result in positive or negative numbers.

Complete step by step solution:
Here we have been asked to prove that a negative number multiplied/divided/subtracted by a negative gives positive result.
Now we will assume $-3$ and $-4$, perform the given basic arithmetic operations on them and verify the result we get is positive or negative.
When we multiply $-3$ and $-4$ we get $-3\times -4=12$ . We have noticed that we have a positive result in this case.
When we subtract $-4$ from $-3$ then we will have $ -3-\left( -4 \right)=-3+4\Rightarrow 1$ . We have noticed that we have a positive result in this case.
When we subtract $-3$ from $-4$ then we will have $ -4-\left( -3 \right)=-4+3\Rightarrow -1$ . We have noticed that we have a negative result in this case.
When we multiply $-3$ , $-5$ and $-4$ we get $-3\times -4\times -5=-60$ . We have noticed that we have a negative result in this case.
When we divide $-12$ and $-3$ we will get $ \dfrac{-12}{-3}=4$ . We have noticed that we have a positive result in this case.
When we divide $-24$ and $-3$ we will get $ \dfrac{-24}{-3}=8$ . We have noticed that we have a positive result in this case.
Hence we can conclude that when we multiply an even number of negative numbers then we will have a positive result otherwise we will have a negative result. Similarly in the case of subtraction it depends on the numbers but in the case of division the operation performed between two negative numbers always results positive.

Note: While answering questions of this type we should be sure with our concepts that we apply because these are very simple and tricky questions. Similarly we can evaluate in the case of addition if we add $-3$ and $-4$ then we will get $-3+-4=-7$ therefore we can conclude that in the case of addition when we perform between two negative numbers it always results in a negative number.