Question

question 9 (1 point) (03.01 mc) prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. fill in the missing step in the proof.
steps

1. a/b + c/d

given

1. multiply to get a common denominator

ad/cb + ad/bd

1. simplify

ad + cb/bd
options:
a) ad • cb/bd
b) ad + cb/bd
c) ad - cb/bd
d) ad + cb/2bd

Explanation:

Step1: Find common denominator

When adding fractions $\frac{a}{b}+\frac{c}{d}$, the common - denominator is $bd$. We rewrite the fractions with the common denominator: $\frac{a}{b}\times\frac{d}{d}=\frac{ad}{bd}$ and $\frac{c}{d}\times\frac{b}{b}=\frac{cb}{bd}$.

Step2: Add the fractions

$\frac{ad}{bd}+\frac{cb}{bd}=\frac{ad + cb}{bd}$ (since when adding fractions with the same denominator $\frac{m}{n}+\frac{p}{n}=\frac{m + p}{n}$).

Answer:

C. $\frac{ad+cb}{bd}$