..that is correct! The answer wouldn't be (in units of) time:

It would be 1000 meters, a distance. Just look at the units, and at which units cancel and what is remaining.

If it were 2 seconds * 1000 m/s, you'd get 2000 meters, right?

So, about these units.... Here's where I'm hoping you'll humor me a bit.

Here is my "test" for you: Are these two lines below the same? In other words:

Is the second line equal to the first line, but just stated differently?

50 meters/second (divided by) 200 meters/second =

50 meters/second (multiplied by) 1 second/200 meters ?

Im not sure what you expect to gain from this but here we go.

1 second * 1000 m/s is not equal to 1000 seconds

....

the result is not an amount of time.

the reason that the result is 1000 meters in the above equation

is because there is an amount of 1000 meters distance in 1000 m/s

meters PER second

If it were 2 seconds * 1000 m/s, you'd get 2000 meters, right?

right!

the purpose of the equation is to solve for the distance that would

be traveled over a time period of 2 seconds at a velcity of 1000 m/s

now for your equation and the line of text below it.

the equation itself

50 meters/second (divided by) 200 meters/second =

the equation has 3 elements on each side of the division symbol.

these are the number of meters (50 and 200)

these numbers are given in units of (meters for distance) and (seconds for time)

written as meters / second (meters per second)

the two units meters and seconds represent the two elements of distance and time.

both sides of the equation have these elements attached to the number that represents the amount of distance.

in order to show what the numbers represent.

(50 meters per second) and (200 meters per second)

the purpose of the equation is to solve for the difference in the rate of change

of position over an amount of time between the two sides of the equation and

by solving the equation you can find the difference in the rate of change of position over

an amount of time!!!

as in the below solved equation.

we know that in the equation we are discussing

t'=t*sqrt(1-(v2)/(c2)

the division that you are questioning and the result that I have given

is between v2 and c2 and by dividing v2 by c2 we get the ratio between

the two (v2/c2) so to stay closer to the OP I will

emphasize the ratio through an explaination of the result of the below equation.

50 meters/second (divided by) 200 meters/second = a ratio of .25 to 1 of 200 meters/second.

meaning that there is a .25 to 1 ratio between 50 m/s and 200 m/s

you can check this by multiplying 200 m/s times the .25 to 1 ratio between 50 m/s and 200 m/s.

so the difference in the rate of change or the ratio between the rate of change between 50 meters and 200 meters in a time period of 1 second is a ratio of .25 to 1 of 200 meters /second

the next line of text is a line of text and is not a proper equation.

50 meters/second (multiplied by) 1 second/200 meters ?

however were I to correct your error in assembling the equation by

inserting a (EQUAL) or (IS EQUAL TO) or (EQUALITY) symbol (=)

then the two sides of the equation have the same meaning

meters per second is the same as seconds per meter

ie ...

200 meters/second (meters per second) means that an objects rate of change

of position over a distance of 200 meters occurrs in a time peroid of 1 second.

200 meters per second = 1 second per 200 meters

1 second/200 meters (seconds per 200 meters) means that in a time period of 1 second

an object experiences a rate of change of position of 200 meters.

1 second per 200 meters = 200 meters per second

therefore to solve the line of text or the improper equation that you posted

through making it a proper equation by inserting the equals sign (=)

50 meters/second (multiplied by) 1 second/200 meters =

for example:

suppose you needed to know the total board length produced in meters and total production time in seconds for 250 machines 50 of the machines produce (50) 1 meter long boards each second and the other 200 machines produce (200) 1 meter long boards each second.

LOL^2

50 meters/second (multiplied by) 1 second/200 meters = 10,000 meters per second.

if we simply cancel out meters and seconds on both sides of the equation

we get 50 * 200 = 10,000 and thats it ... no units attached.

it has no value other than being a number that is derived through the

multiplication of 2 other numbers that have no units attached to them.

it is a number of unknown origin unless you associate it with the units

that it was formed from.

Im not certain why this seemed to be important to you however.

but your question was is it true...

if you were talking about the line of text then yes it is true

that the line of text is truly a line of text.