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

Question

5104 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-22T05:34:46

Please see below.

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)

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