Question

Rove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero.

Steps Reasons
1. a over b plus c over d Given
2. Multiply to get a common denominator
3. ad plus cb all over bd Simplify


Fill in the missing step in the proof.

Answer 1

`(ad+bc)/(bd)`

Explanation:

`Greetings!`

`I'm~Isabelle~Williams~and~I~will~be~answering~your~question!`

`Let,(a)/(b) ~and ~(c)/(d)~be~two~rational~numbers, ~where~ b ~and~ d ~are~ not~ zero ~and~ a, ~b, ~c ~and \\~d ~are~ integers.`

`1.~Given:`

`(a)/(b) +(c)/(d)`

`2.~Now,~we~multiply~to~get~a~common~denominator:`

`(a)/(b)+(c)/(d)=(ad)/(bd)+(cb)/(db)`

`3.~Then~simplify:`

`(a)/(b)+(c)/(d)=(ad)/(bd)+(cb)/(db)=(ad+bc)/(bd)`

`4.~Since,b\\eq 0,~d\\eq 0,~then,~bd,~ad,~bc~and~ad+bc~are~integers~too.~So~the\\ fraction~will~be:`

`(ad+bc)/(bd)`

`Thus,~making~it~a~rational~number!`

`Hope~this~answer~helps!~and~have~an~amazing~day~ahead!`

`-Isabelle~Williams`