This document contains notes from a mathematics lesson about rational numbers. It defines integers and rational numbers, and explains that rational numbers include both integers and fractions. It then presents several properties of rational numbers, including how to add, subtract, multiply and divide rational numbers in fractional form. Examples are given for each property showing the calculations involved in operations on rational numbers expressed as fractions.

2. Name of the college : Fatima Memorial
Training College
Name of the teacher : Soumya.S
Name of the subject : Mathematics
Reg.no : 13352019

3. `n¶IkwJyIÄ

4. ]qÀ®kwJyIÄ (integers)
F®Â kwJyIÄ, AhbpsS yq §Ä Chsb
FÃmw s]mXphmbn ]qÀ®kwJyIÄ
F¶mWv ]dbp¶Xv.

5. `n¶IkwJyIÄ (Rational Numbers)
]qÀ® kwJyIÄ, `n¶kwJyIÄ (A[n kwJyIfpw
yqkwJyIfpw) F¶nhbvs¡ Ãmw
s]mXphmbn¸dbp¶ t]cmWv `n¶I kwJyIÄ

6. `n¶Icq]w
GXp `n¶I kwJytbbpw (`n¶kwJy
bmbmepw ]q˨kwJybmbmepw)
F¶o]qÀ®kwJyIÄ D]tbmKn¨v
F¶ cq]¯nsegpXmw
x, y
x
y

7. hnhn[ cq]§Ä
Hcp `n¶IkwJybpsS Awit¯bpw tOZt¯bpw Htc ]
qÀ®kwJy sIm­v
(0 HgnsI) KpWn¨m B `n¶I¯nsâ
Xs¶ ]e ]e cq]§Ä In«pw.
a = ax ( x ¹
0)
b bx

8. `n¶I§fpsS XpI
Fa , P ¶nh `n¶I§fmbmÂ,
b q
a + p = a ´ q + b ´
p
b q b ´
q
aq bp
bq
= +

9. `n¶I§fpsS hyXymkw
Fa , P ¶nh `n¶I§fmbmÂ,
b q
a - p = a ´ q - b ´
p
b q b ´
q
aq bp
bq
= -

10. `n¶I§fpsS KpWw
Fa , P ¶nh `n¶I§fmbmÂ,
b q
a ´ p = a ´
p
b q b ´
q
ap
bq
=

11. `n¶I§fpsS lcWw
Fa , P ¶nh `n¶I§fmbmÂ,
b q
a ¸ P = a ´
q
b q b p
a q
b p
aq
bp
= ´
´
=