Which is cheaper to operate.An oven at 350 degrees running on 240V or a toaster oven at 350 degrees running on 120V for the same amount of time to cook something ?
Keep in mind you always have to pre heat the range oven first.

That's not a good comparison because in reality unless it's a really tiny item... its going to take longer in the toaster oven to achieve the same level of being done.

SO otherwise this is completely theoretical and in all actuality a homework question you haven't attempted first as site rules for homework require.

If you can cook something in a toaster oven, do so. The reason to use the bigger one is for evenly distributed heat, and consistent temperature, something toaster ovens are terrible at. Plus they have no insulation and let a lot of heat out around the door. They are just a toaster on it's side with a door. So just going by voltage is not meaningful.

There are a few brands of very expensive 'counter top ovens' that work about as well as a built in standard oven that use a standard 20A outlet,

The question was, "which is cheaper?"...
(sounds like homework!)

My answer is, the question has been left vague. The "pre-heat" time is undefined and therefore you cannot prove an answer...

To me, this sounds like a debate between a cook and a bill payer. The bill payer should concede for the sake of harmony in the kitchen.

I am thinking about buying a toaster oven.this is not homework... the range uses twice the voltage but half the amperage.. same temp... same amount of time.. this is a comparison between the appliances and energy consumed.. Which would use more KWH of electricity?. any electrical engineers out there? This is to find out which is more efficient to do the same job.I know there is the initial investment of the toaster oven.

The same item will not cook in the same time in the real world in both for the reasons stated above. And anyone that has actually used both for very long can back me up on that. Yes I'm old enough to remember the days everyone had one of these and not a microwave for small tasks.

Every one of us answering this understand Ohms law... and the real answer to this is NOT as simplistic as you think it is... I'm an Electronic Engineer and a few of the others are experienced people in the Electrical field. Meaning Electricians or Electrical Engineers... we all understand this really well.

That's why we were asking if this is a homework question because a lot of wrong assumptions have to be made if you look at only ONE aspect of this.

The real world and the theoretical world rarely overlap by much.

Outside of the math, the comment about pre-heat is undefined...
The answer is simple if you define the pre-heat setting and duration.

(assuming of course that both appliances have an equal resistance... )

I will simplify the question.. I just looked at a pizza box in my freezer.. it says cook at 450 degrees for 10 minutes in the range oven or 14 minutes in a toaster oven.. which would use the least energy to cook the food? The toaster oven is 1500 watts running 120V the oven is 4000 watts using the bottom element at 240V

Based on your explanation, assuming all pre-heat times are equal, assuming all duty cycles are also equal... the range = $.08, toaster = $.042
The cost is relative but does indicate that most nearly the range for this question is almost twice as expensive as the toaster...

(by the way the voltage in this question is irrelevant)