Question

Calculeaza : 1) (1/2-3/4)-(5/2-5/4)-(3/2-3/4) ;

2) (-2/3+4/5+1)-(-4/3+2/5-2)+(-2+3/5) ;

3) (1-3/4+2/3)-(1-5/3+1/4)-(1-4/3-3/4) ;

4) (1/2-(1/3+1/4-1/5) ;

5) 2/3-(2 1/2-1 1/4) ;


La a cincea parte daca sunt spatii goale inseamna ca o cifra este la mijlocul barei de fractie , eu n-am gasit simbolul ca sa fac asa , sper ca rezolvati corect . Exercitiul din cartea de matematica era mai mare dar atata m-i s-a cerut :) . Astept un raspuns cat mai repede :) .

Answer 1

$1) \left(\frac{1}{2}-\frac{3}{4}\right)-\left(\frac{5}{2}-\frac{5}{4}\right)-\left(\frac{3}{2}-\frac{3}{4}\right)=\frac{1}{2}-\frac{3}{4}-\left(\frac{5}{2}-\frac{5}{4}\right)-\left(\frac{3}{2}-\frac{3}{4}\right)=\frac{1}{2}-\frac{3}{4}-\frac{5}{4}-\frac{3}{4}=\frac{1}{2}-\frac{11}{4}=\frac{2}{4}-\frac{11}{4}=\frac{-9}{4}=-\frac{9}{4}$

$2) \left(-\frac{2}{3}+\frac{4}{5}+1\right)-\left(-\frac{4}{3}+\frac{2}{5}-2\right)+\left(-2+\frac{3}{5}\right)=-\frac{2}{3}+\frac{4}{5}+1-\left(-\frac{4}{3}+\frac{2}{5}-2\right)-2+\frac{3}{5}=-\frac{2}{3}+\frac{4}{5}+1+\frac{44}{15}-2+\frac{3}{5}=\frac{7}{5}+\frac{44}{15}-1-\frac{2}{3}=-\frac{1\cdot \:3}{3}+\frac{7}{5}+\frac{44}{15}-\frac{2}{3}=-\frac{15}{15}+\frac{21}{15}+\frac{44}{15}-\frac{10}{15}=\frac{-15+21+44-10}{15}=\frac{40}{15}=\frac{8}{3}$

$3)\left(1-\frac{3}{4}+\frac{2}{3}\right)-\left(1-\frac{5}{3}+\frac{1}{4}\right)-\left(1-\frac{4}{3}-\frac{3}{4}\right)==1-\frac{3}{4}+\frac{2}{3}-\left(1-\frac{5}{3}+\frac{1}{4}\right)-\left(1-\frac{4}{3}-\frac{3}{4}\right)=1-\frac{3}{4}+\frac{2}{3}+\frac{5}{12}+\frac{13}{12}=1-\frac{3}{4}+\frac{2}{3}+\frac{3}{2}=\frac{12}{12}-\frac{9}{12}+\frac{8}{12}+\frac{18}{12}=\frac{12-9+8+18}{12}=\frac{29}{12}$

$4) \left(\frac{1}{2}\right)-\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}\right)=\frac{1}{2}-\frac{23}{60}=\frac{30}{60}-\frac{23}{60}=\frac{30-23}{60}=\frac{7}{60}$

$5)\left(\frac{2}{3}\right)-\left(2\frac{1}{2}-1\frac{1}{4}\right)==\left(\frac{2}{3}\right)-\left(\frac{5}{2}-1\frac{1}{4}\right)=\left(\frac{2}{3}\right)-\left(\frac{5}{2}-\frac{5}{4}\right)=\frac{2}{3}-\left(\frac{5}{2}-\frac{5}{4}\right)=\frac{2}{3}-\frac{5}{4}=\frac{8}{12}-\frac{15}{12}=\frac{-7}{12}=-\frac{7}{12}$