Question

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.

Answer 1

Answer:

We conclude that the sum of two rational numbers is rational.

Hence, the fraction will be a rational number. i.e.

• $\frac{ad+cb}{bd}$       ∵ b≠0, d≠0, so bd≠0

Step-by-step explanation:

Let a, b, c, and d are integers.

Let a/b and c/d are two rational numbers and b≠0, d≠0

Proving that the sum of two rational numbers is rational.

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

As the least common multiplier of b, d: bd

Adjusting fractions based on the LCM

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

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

          $=\frac{ad+cb}{bd}$

As b≠0, d≠0, so bd≠0

Therefore, we conclude that the sum of two rational numbers is rational.

Hence, the fraction will be a rational number. i.e.

• $\frac{ad+cb}{bd}$       ∵ b≠0, d≠0, so bd≠0