Answer: midpoint = (ad + bc)/2bd
Explanation:
The number that lies at the midpoint between these two points will be an average of the two numbers.
To get an average, we add the two numbers and then multiply by one-half (or divide by 2, same thing).
x = (1/2) * ( a/b + c/d)
To add a/b and c/d, we must use the least common denominator (LCD). Since we don't have numerical values, we can only multiply the two denominators together and not worry about whether to 'reduce' the result. So the LCD = b*d
To give a/b a denominator of bd, we must multiple top and bottom both by 'd' and we get a/b ---> ad/bd
To give c/d a denominator of bd, we must multiple top and bottom both by 'b' and we get c/d ---> bc/bd
This gives us x = (1/2)( ad/bd + bc/bd )
Since the two fractions in the second set of parentheses now have the same denominator, we can add them.
x = (1/2) * [ (ad + bc)/bd ]
Now we have two fractions to multiply.
The numerators ---> 1 * (ad + bc) = ad + bc
The denominators ---> 2 * bd = 2bd
So, we get a final answer of
x = (ad + bc)/2bd
midpoint = (ad + bc)/2bd
I hope this helps.