Question

Scrieti cate 3 proportii derivate prin amplificare sau simplifiacre ,din urmatoarele proporti:
a) 48/200=36/150 b) 16/32=68/136 c)14/75=42/225

Answer 1

48/200=36/150=>200/48=150/36
                         48/36=200/150
                           24/100=18/75
                           96/400=72/300

16/32=68/136=>32/16=136/68
                       16/136=68/32
                         8/16=34/68
                         4/8=17/34

14/75=42/225=>14/42=75/225
                             75/14=225/42
                             28/150=84/450

Answer 2

a) $\frac{48}{200}= \frac{36}{150}$ ⇒ 

$\frac{48\div2}{200\div2}= \frac{36\div2}{150\div2}$ ⇒ $\frac{24}{100}= \frac{18}{75}$

$\frac{48\cdot3}{200\cdot3}= \frac{36}{150}$ ⇒ $\frac{144}{600}= \frac{36}{150}$

$\frac{48\cdot2}{200\cdot2}= \frac{36\div3}{150\div3}$ ⇒ $\frac{96}{400}= \frac{12}{50}$

b.) $\frac{16}{32}= \frac{68}{136}$

$\frac{16\div16}{32\div16}= \frac{68\div68}{136\div68}$ ⇒ $\frac{1}{2}= \frac{1}{2}$

$\frac{16\div4}{32\div4}= \frac{68\cdot2}{136\cdot2}$ ⇒ $\frac{4}{8}= \frac{136}{272}$

$\frac{16\cdot2}{32\cdot2}= \frac{68\div4}{136\div4}$ ⇒ $\frac{32}{64}= \frac{17}{34}$

c.) $\frac{14}{75}= \frac{42}{225}$

$\frac{14\cdot2}{75\cdot2}= \frac{42\div3}{225\div3}$ ⇒ $\frac{28}{150}= \frac{14}{75}$


 $\frac{14}{75}\cdot \frac{75}{14}= \frac{42}{225}\cdot \frac{225}{42}$ ⇒ $1=1$

$\frac{14}{75}= \frac{42\div3}{225\div3}$ ⇒ $\frac{14}{75}= \frac{14}{75}$