Question

Calculează , scriind rezultatul ca fracție ireductibilă:

a) 2 supra 3 : 1 supra 6
b) 7 supra 6 : 21 supra 22
c) 4 : 2 supra 3
d) 7 supra 8 : 3
e) 13 supra 6 : 13 supra 3
f) 1 supra 8 : 11 supra 5
g) 5 : 1 supra 6 : 3 supra 4
h) 25 supra 8 : 11 supra 5 : 5 supra 4
i) 16 supra 3 : (5 supra 2 : 15 supra 4)
j) 14 supra 3 : (21 supra 4 : 7 supra 2) : 28 supra 9
k) 1 supra 5 la puterea 2 * 3 : 1 supra 3 la puterea 2 * 5
l) 1 supra 2 la puterea 1000 : 1 supra 4 la puterea 4500

Dau coroană

Answer 1

$a) \frac{2}{3} \div \frac{1}{6} = \frac{2}{3} \times 6 = \frac{12}{3} = 4$

$b) \frac{7}{6} \div \frac{21}{22} = \frac{7}{6} \times \frac{22}{21} = \frac{1}{3} \times \frac{11}{7} = \frac{11}{21}$

$c)4 \div \frac{2}{3} = 4 \times \frac{3}{2} = \frac{12}{2} = 6$

$d) \frac{7}{8} \div 3 = \frac{7}{8} \times \frac{1}{3} = \frac{7}{24}$

$e) \frac{13}{6} \div \frac{13}{3} = \frac{13}{6} \times \frac{3}{13} = \frac{1}{2}$

$f) \frac{1}{8} \div \frac{11}{5} = \frac{1}{8} \times \frac{5}{11} = \frac{5}{88}$

$g)5 \div \frac{1}{6} \div \frac{3}{4} = 5 \times 6 \times \frac{4}{3} = \frac{120}{3} = 40$

$h) \frac{25}{8} \div \frac{11}{5} \div \frac{5}{4} = \frac{25}{8} \times \frac{5}{11} \times \frac{4}{5} = \frac{25}{2 \times 11} = \frac{25}{22}$

$i) \frac{16}{3} \div ( \frac{5}{2} \div \frac{15}{4} ) = \frac{16}{3} \div ( \frac{5}{2} \times \frac{4}{15} )$

$= \frac{16}{3} \div \frac{2}{3}$

$= \frac{16}{3} \times \frac{3}{2}$

$= 8$

$j) \frac{14}{3} \div ( \frac{21}{4} \div \frac{7}{2} ) \div \frac{28}{9}$

$= \frac{14}{3} \div ( \frac{21}{4} \times \frac{2}{7} ) \times \frac{9}{28}$

$= \frac{14}{3} \div \frac{3}{2} \times \frac{9}{28}$

$= \frac{14}{3} \times \frac{2}{3} \times \frac{9}{28}$

$= \frac{6}{6}$

$= 1$

$k)( { \frac{1}{5} })^{2} \times 3 \div ({ \frac{1}{3} })^{2} \times 5$

$= \frac{1}{25} \times 3 \div \frac{1}{9} \times 5$

$= \frac{3}{25} \times 9 \times 5$

$= \frac{27}{5}$

$l)( { \frac{1}{2} })^{1000} \div ({ \frac{1}{4} })^{4500}$

$= ({ \frac{1}{2} })^{1000} \div ({ \frac{1}{2} })^{2 \times 4500}$

$= ({ \frac{1}{2} })^{1000} \div ({ \frac{1}{2} })^{9000}$

$= ( { \frac{1}{2} })^{1000 - 9000}$

$= ( { \frac{1}{2} })^{ - 8000}$

$= {2}^{8000}$