Question

Show that in the Denominator Addition/Subtraction Property of proportions: If `a/ b = c/ d`, then `( a + b)/ b = ( c + d)/ d` or `( a − b)/ b = ( c − d)/ d`?

Show that in the Denominator Addition/Subtraction Property of proportions: If `a/ b = c/ d`, then `( a + b)/ b = ( c + d)/ d` or `( a − b)/ b = ( c − d)/ d`?

Answer 1

Please see below.

Explanation:

As `a/b=c/d` ............(1)

adding `1` to both sides

`a/b+1=c/d+1` or `a/b+b/b=c/d+d/d` or

`(a+b)/b=(c+d)/d` ............(2)

Now subtracting `1` from both sides

`a/b-1=c/d-1` or `a/b-b/b=c/d-d/d` or

`(a-b)/b=(c-d)/d` ............(3)

In fact dividing (2) by (3) also gives us

`(a+b)/(a-b)=(c+d)/(c-d)` ............(2)