Question

3.Calculati
a) (-2/5)+(-3/10)+(+1/2)+(+4/15)
b) (-5/3)+(-5/6)+(+5/2)+(-5/12)
c) (+7/18)+(-3/2)+(-11/9)+(+4/1)
d) (-2/21)+(-3/7)+(+5/42)+(-9/14)
e)(-7/11)+(-1/4)+(+1/2)+(-5/22)
f)2/7+(-1/14)+(+5/6)+(-13/42)​

Answer 1

Explicație pas cu pas:

a)

$(- \frac{2}{5} )+(- \frac{3}{10} )+(+ \frac{1}{2} )+(+ \frac{4}{15} ) = \frac{ - 2 \times 6 - 3 \times 3 + 1 \times 15 + 4 \times 2}{30} = \frac{ - 12 - 9 + 15 + 8}{30} = \frac{23 - 21}{30} = \frac{2}{30} = \frac{1}{15}$

b)

$(- \frac{5}{3} )+(- \frac{5}{6} )+(+ \frac{5}{2} )+(- \frac{5}{12}) = \frac{ - 5 \times 4 - 5 \times 2 + 5 \times 6 - 5}{12} = \frac{ - 20 - 10 + 30 - 5}{12} = \frac{30 - 35}{12} = - \frac{5}{12}$

c)

$(+ \frac{7}{18} )+(- \frac{3}{2} )+(- \frac{11}{9} )+(+ \frac{4}{1} ) = \frac{7 \times 1 - 3 \times 9 - 11 \times 2 + 4 \times 18}{18} = \frac{7 - 27 - 22 + 72}{18} = \frac{79 - 49}{18} = \frac{30}{18} = \frac{5}{3}$

d)

$(- \frac{2}{21} )+(- \frac{3}{7} )+(+ \frac{5}{42} )+(- \frac{9}{14}) = \frac{ - 2 \times 2 - 3 \times 6 + 5 \times 1 - 9 \times 3}{42} = \frac{ - 4 - 18 + 5 - 27}{42} = \frac{5 - 49}{42} = - \frac{44}{42} = - \frac{22}{21}$

e)

$(- \frac{7}{11} )+(- \frac{1}{4} )+(+ \frac{1}{2} )+(- \frac{5}{22} ) = \frac{ - 7 \times 4 - 1 \times 11 + 1 \times 22 - 5 \times 2}{44} = \frac{ - 28 - 11 + 22 - 10}{44} = \frac{22 - 49}{44} = - \frac{27}{44}$

f)

$\frac{2}{7} +(- \frac{1}{14})+(+ \frac{5}{6} )+(- \frac{13}{42} ) = \frac{2 \times 6 - 1 \times 3 + 5 \times 7 - 13 \times 1}{42} = \frac{12 - 3 + 35 - 13}{42} = \frac{47 - 16}{42} = \frac{31}{42}$