
When you ask "What number is halfway between 45 and 420?" we assume you mean the number in the exact middle of the two numbers on a number line, as illustrated below, where X=45 and Y=420.

To find the number halfway between 45 and 420, we use the following formula:
(X + Y)/2 = Halfway Between
When we enter 45 and 420 into our formula, we get:
(45 + 420)/2 = 232.5
Thus, the number halfway between 45 and 420 is 232.5.
To check that our answer is correct, we subtract 45 from 232.5 and subtract 232.5 from 420 and compare the two numbers:
232.5 - 45 = 187.5
420 - 232.5 = 187.5
As you can see, the halfway number is 187.5 higher than 45 and 187.5 lower than 420. Therefore, our halfway between answer of 232.5 above is correct.
Halfway Between
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Halfway Between 45 and 421
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