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Why does multiplying negative integers by negative integers result in positive integers?
Any negative integer can be factored to -1 times its positive value. Because negative one times itself is positive one, when multiplied by each other they cancel out.
So if you're multiplying a negative integer A by a negative integer B. Replace A and B with -1*|A| and -1*|B| (You can do this because you know A and B are negative), and use the distributive property to rearrange them. Now you can see the -1*-1 term and equate it to 1, leaving only the |A| and |B| behind. Because two positive numbers multiplied together are always positive, the result will always be positive.
Represented algebraically, as long as A and B are negative integers, the following is true:
AB = -1|A|*-1|B| = -1*-1|AB| = |AB|.
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What is multiplication of positive numbers?
Multiplying positive numbers will result in a positive number.
When you add 2 negatives numbers is the result a positive number?
Never, it will always be negative, regardless the numbers.
Why square root of negative 36 is not a real number?
When you multiply any number by itself, the result is always positive. You cannot take any real number and square it to get something negative. The square root of -36 is 6i.
What are the similarities between rational numbers and fractions?
All integers belong to the set {..., -2, -1, 0, 1, 2, ...}. The absolute value of any integer results in a whole number {0, 1, 2, ...}. Adding and subtracting integers always results in an integer. Multiplying integers always results in an integer. Dividing integers can sometimes not result in an integer.
Why are all American automotive electrical systems negative ground?
In a negative grounding system, current travels from positive to negative. In dc automotive power, the automobile chassis is utilized as a current return network for the negative to have a return path to the battery. It's much cheaper to produce a car with a negative ground system; because in a positive ground system, current flow is mastered with a switch that is wired in series through the automobiles positive power circuit instead of the negative power circuit such a case as switching on a dome light. The drawback to a negative ground system is that when a switch closes to complete a circuit (dome light coming on), the switch , at the exact moment of contact, incurs a slight spark, as current travels in a DC circuit from positive to negative. It's Basically a matter of production choice.#2There is no strict answer as to 'why' American cars are ground based systems. Rumors are that it was because of Benjamin Franklin's guess to the 'poles' of electricity as to which way current actually flowed, and degenerate into derogatory comments about American's ignoring the laws of physics. The convention for labeling batteries, despite physics, remains however.Despite any claim to the contrary DC Current ALWAYStravels from the ground (-) side of a battery to the positive (+) side; because electricity is made up of free electrons that accumulate on that side of the plate as a result of a chemical reaction.Also, all switches (except immersed switches - no arc switches used for explosive gas environments) will 'arc' when the contact is almost made.Also, production prices between positive and negative chassis systems are no different as electrical systems are the same in concept as well as production. There is no "requirement" that one system have a master switch (or any switch for that matter) because of its ground source. It is true however that most of these positive systems use better wiring, and relays for current load where American cars rely on the switch itself to handle the current load; which increases the cost and complexity of the system (Lucas prince of darkness, Jaguar comes to mind).Lastly, Ground based chassis systems have one inherent problem not normally seen on a Positive chassis system; known as a ground loop. A "ground Loop" is properly stated as an electron potential imbalance; where there are more electron's available in one point of the car as opposed to another point in the car / this is eliminated in positive based systems and compensated for in negative systems by running ground straps through the chassis.
