Question

1. Efectuati:
a) 0,(3):$\frac{1}{3}$
b) 1,3(5):$\frac{41}{45}$
c) 0,25:$\frac{3}{4}$
d) 1,2(7):0,(46)
e) 3,(12):$\frac{206}{11}$
f) 0,5:0,(5)

Answer 1

$a)0.(3) \div \frac{1}{3} = \frac{3}{9} \times 3 = \frac{3 \times 3}{9} = \frac{9}{9} = 1$

$b)1.3(5) \div \frac{41}{45}$

$= 1\frac{35 - 3}{90} \times \frac{45}{41}$

$= 1 \frac{32}{90} \times \frac{45}{41}$

$= \frac{1 \times 90 + 32}{90} \times \frac{45}{41}$

$= \frac{90 + 32}{90} \times \frac{45}{41}$

$= \frac{122}{90} \times \frac{45}{41}$

$= \frac{122 \times 45}{90 \times 41}$

$= \frac{5490}{3690}$

$= \frac{549}{369}$

$= \frac{183}{123}$

$= \frac{61}{41}$

$c)0.25 \div \frac{3}{4}$

$= \frac{25}{100} \times \frac{4}{3}$

$= \frac{1}{4} \times \frac{4}{3}$

$= \frac{1}{3}$

$d)1.2(7) \div 0.(46)$

$= 1 \frac{27 - 2}{90} \div \frac{46}{99}$

$= 1 \frac{25}{90} \times \frac{99}{46}$

$= \frac{1 \times 90 + 25}{90} \times \frac{99}{46}$

$= \frac{90 + 25}{90} \times \frac{99}{46}$

$= \frac{115}{90} \times \frac{99}{46}$

$= \frac{115}{10} \times \frac{11}{46}$

$= \frac{115 \times 11}{10 \times 46}$

$= \frac{1265}{460}$

$= \frac{253}{92}$

$e)3.(12) \div \frac{206}{11}$

$= 3 \frac{12}{99} \times \frac{11}{206}$

$= \frac{3 \times 99 + 12}{99} \times \frac{11}{206}$

$= \frac{297 + 12}{99} \times \frac{11}{206}$

$= \frac{309}{99} \times \frac{11}{206}$

$= \frac{309}{9} \times \frac{1}{206}$

$= \frac{309 \times 1}{9 \times 206}$

$= \frac{309}{1854}$

$= \frac{103}{618}$

$f)0.5 \div 0.(5)$

$= \frac{5}{10} \div \frac{5}{9}$

$= \frac{5}{10} \times \frac{9}{5}$

$= \frac{9}{10}$