Answer:
We conclude that the sum of two rational numbers is rational.
Hence, the fraction will be a rational number. i.e.
∵ 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}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D%2B%5Cfrac%7Bc%7D%7Bd%7D)
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}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bb%7D%2B%5Cfrac%7Bc%7D%7Bd%7D%3D%5Cfrac%7Bad%7D%7Bbd%7D%2B%5Cfrac%7Bcb%7D%7Bdb%7D)
![\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}](https://tex.z-dn.net/?f=%5Cmathrm%7BSince%5C%3Athe%5C%3Adenominators%5C%3Aare%5C%3Aequal%2C%5C%3Acombine%5C%3Athe%5C%3Afractions%7D%3A%5Cquad%20%5Cfrac%7Ba%7D%7Bc%7D%5Cpm%20%5Cfrac%7Bb%7D%7Bc%7D%3D%5Cfrac%7Ba%5Cpm%20%5C%3Ab%7D%7Bc%7D)
![=\frac{ad+cb}{bd}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bad%2Bcb%7D%7Bbd%7D)
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.
∵ b≠0, d≠0, so bd≠0