Question

Se considera fractiile echivalete  A/B si C/D . Aratati ca: 
1.a/a+b = c/c+d
2.a-b/b=c-d/d pentru a mai mare sau egal cu b si c ma mare sau egal cu d.

Answer 1

1.
[tex] \frac{a}{b}= \frac{c}{d} [/tex] 
adunam 1 si in stanga si in dreapta:
$\frac{a}{b}+1= \frac{c}{d} +1$
aducem la acelasi numitor:
$\frac{a}{b}+ \frac{b}{b} = \frac{c}{d}+ \frac{d}{d}$
rezulta:
$\frac{a+b}{b}= \frac{c+d}{d}$
si daca le rasturnam obtinem ce cautam:
$\frac{a}{a+b}= \frac{c}{c+d}$
 
2.$\frac{a}{b}= \frac{c}{d}$
scadem 1 si in stanga si in dreapta:
$\frac{a}{b}-1= \frac{c}{d}-1$
aducem la acelasi numitor:
$\frac{a}{b}- \frac{b}{b} = \frac{c}{d}- \frac{d}{d}$
rezulta:
$\frac{a-b}{b}= \frac{c-d}{d}$

Answer 2

1.a/a+a/b=c/c+c/d
1+a/b=1+c/d
a/b=cd
2.a/b-b/b=c/d-d/d
a/b-1=c/d-1
a/b=c/d