Question

Vă rog frumos exercitiile 12, 13​

Answer 1

Răspuns:

12. a) le aducem la acelasi numitor 8

$\frac{4*1+2*1-1}{8}$= $\frac{4-2-1}{8}$=$\frac{1}{8}$

b) $\frac{5- 7*3}{6}$ +($\frac{-10*10+11*5+2*6}{30}$  +$\frac{-13*6+10*10+1*15}{30}$)= $\frac{-16}{6}$ + ($\frac{-100+55+12}{30}$ + $\frac{-78+100+15}{30}$)

=$\frac{-16*5}{30}$ -  $\frac{33}{30}$ +  $\frac{37}{30}$ = $\frac{-80-33+37}{30}$$=\frac{-76}{30}$$=\frac{-38}{15}$

c)$\frac{-1*6 -1*3-1*2}{18}$= $\frac{-6-3-2}{18}$= $\frac{-11}{18}$

d) $\frac{19}{36}$ + ( $\frac{4}{9}$ - $\frac{37}{24}$  - $\frac{5}{18}$)                 aducem la acelasi numitor 72

 aflam numitor comun 36= 2²*3²  9=3²     24=3¹*2³   18= 2¹* 3²

nc=2³*3²= 8*9=72

$\frac{19*2+ 4*8 -37*3- 5*4}{72}$ = $\frac{38 +32- 111-20}{72}$= $\frac{-61}{72}$

13. a) $\frac{183-18}{90} - \frac{52}{10} + \frac{5}{6} - \frac{416-41}{900} - 2$  = $\frac{11}{6} - \frac{52}{10} + \frac{5}{6} -\frac{5}{12} -2$=

$\frac{16}{6} -\frac{26}{5} - \frac{5}{12} -2$=  $\frac{16*10-26*12- 5*5- 2*60}{60}$= $\frac{160-312- 25-120}{60}$= $\frac{-297}{60}$ =$\frac{-99}{20}$

b) 24= 3¹*2³     36= 2²*3²     40= $2^{3}$*5    48= 3¹*2⁴

n.c= 2⁴ *3²*5= 16*9*5=720

$\frac{-13*30+ 11*20-1*15 +7*18}{720}$= $\frac{-390+220-15+126}{720}$= $\frac{-59}{720}$

c)$\frac{-11}{101} -\frac{37}{110} + \frac{112}{101} - \frac{346}{220}$= $\frac{112-11}{101} - \frac{173+ 37}{110}$= $\frac{101}{101}$ - $\frac{210}{110}$= 1-  $\frac{21}{11}$= $\frac{1*11-21}{11}$= $\frac{-10}{11}$

d) $\frac{-24}{35}$ - $\frac{14*1+3}{14}$ - 1 - $\frac{16}{15}$ + $\frac{189}{45}$= $\frac{-24}{35} - \frac{17}{14} - 1 - \frac{16}{15} + \frac{63}{15}$=      n.c = 2*3*5*7=210

= $\frac{-24*6 - 17*15- 210*1 - 16*14 +63*14}{210}$ = $\frac{-166- 210-255- 224+ 882}{210}$=$\frac{27}{210}$= $\frac{9}{70}$