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

Answer:

$\frac{ad+bc}{bd}$

Step-by-step explanation:

$Greetings!$

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

$Let,\frac{a}{b} ~and ~\frac{c}{d}~be~two~rational~numbers, ~where~ b ~and~ d ~are~ not~ zero ~and~ a, ~b, ~c ~and \\~d ~are~ integers.$

$1.~Given:$

$\frac{a}{b} +\frac{c}{d}$

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

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}$

$3.~Then~simplify:$

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}=\frac{ad+bc}{bd}$

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

$\frac{ad+bc}{bd}$

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

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

$-Isabelle~Williams$