Question

$- \frac{4}{29} + \frac{23}{28})+ \frac{33}{29}+(- \frac{1}{7})=$
$2 \frac{1}{6}-0,(3)- \frac{7}{10}-1,0(6)- \frac{7}{5} =$
$4 \frac{1}{6} -10 \frac{1}{24}-7 \frac{1}{18} +2 \frac{3}{4}+7 \frac{5}{8}+7 \frac{5}{27} -3 \frac{7}{18}- \frac{1}{54}=$

Answer 1

a) se aduc fractiile la acelasi numitor:
=[(-4*29+28*23)+33*28+(-1)*4*29]/(29*28)=[(-116+644)+924-116]/(29*28)=
=(528+924-116)/(29*28)=1336/(29*28)=(334*4)/(29*4*7)=334/(29*7)=334/203

b) =(2*6+1)/6-3/9-7/10-(106-10)/90=13/6-3/9-7/10-96/90=13/(2*3)-3/3²-7/(2*5)-96/(2*5*3²)=
=(13*5*3-3*2*5-7*3²-96)/90=6/90=1/15

c) =(4*6+1)/(2*3)-(10*24+1)/(2³ * 3)-(7*18+1)/(2*3²)+(2*4+3)/2²+(7*8+5)/2³+(7*27+5)/3³-
-(3*18+7)/(2*3²)-1/(2*3³)=
=25/(2*3)-241/(2³ * 3)-127/(2*3²)+11/2²+61/2³+194/3³-61/(2*3²)-1/(2*3³)=
=(25*2²*3²-241*3²-127*2²*3+11*2*3³+61*3³+194*2³-61*2²*3-1*2²)/(2³ * 3³)=
=(900-2169-1524+594+1647+1552-732-4)/(2³ * 3³)=
=264/(2³ * 3³)=(2³ * 3*11)/(2³ * 3³)=11/9