Bài 3. Phép cộng, phép trừ phân số

\(a.\)

\(-\dfrac{2}{9}+\dfrac{7}{-9}=\dfrac{-2}{9}-\dfrac{7}{9}=\dfrac{-2-7}{9}=\dfrac{-9}{9}=-1\)

\(b.\)

\(\dfrac{1}{-6}+\dfrac{13}{-15}=-\dfrac{1}{6}-\dfrac{13}{15}=\dfrac{\left(-1\right)\cdot5-13\cdot2}{30}=\dfrac{-5-26}{30}=\dfrac{-31}{30}\)

\(c.\)

\(\dfrac{5}{-6}+\dfrac{-5}{12}+\dfrac{7}{18}=\dfrac{-5}{6}-\dfrac{5}{12}+\dfrac{7}{18}=\dfrac{\left(-5\right)\cdot6-5\cdot3+7\cdot2}{36}=\dfrac{-31}{36}\)

\(a.\)

\(\dfrac{2}{9}+\dfrac{-3}{10}+-\dfrac{7}{10}=\dfrac{2}{9}-1=\dfrac{2}{9}-\dfrac{9}{9}=-\dfrac{7}{9}\)

\(b.\)

\(\dfrac{-11}{6}+\dfrac{2}{5}+\dfrac{-1}{6}=\left(-\dfrac{11}{6}+-\dfrac{1}{6}\right)+\dfrac{2}{5}=-2+\dfrac{2}{5}=\dfrac{-10}{5}+\dfrac{2}{5}=\dfrac{-8}{5}\)

\(c.\)

\(-\dfrac{5}{8}+\dfrac{12}{7}+\dfrac{13}{8}+\dfrac{2}{7}=\left(-\dfrac{5}{8}+\dfrac{13}{8}\right)+\left(\dfrac{12}{7}+\dfrac{2}{7}\right)=1+2=3\)

Số đối của mỗi phân số: 
\(\dfrac{9}{25}\Rightarrow-\dfrac{9}{25}\)

\(-\dfrac{8}{27}\Rightarrow\dfrac{8}{27}\)

\(-\dfrac{15}{31}\Rightarrow\dfrac{15}{31}\)

\(\dfrac{-3}{-5}\Rightarrow\dfrac{-3}{5}\)

\(\dfrac{5}{-6}\Rightarrow\dfrac{5}{6}\)

\(a.\)

\(\dfrac{5}{16}-\dfrac{5}{24}=\dfrac{5\cdot3-5\cdot2}{48}=\dfrac{15-10}{48}=\dfrac{5}{48}\)

\(b.\)

\(\dfrac{2}{11}+\left(\dfrac{-5}{11}-\dfrac{9}{11}\right)=\dfrac{2-5-9}{11}=-\dfrac{12}{11}\)

\(c.\)

\(\dfrac{1}{10}-\left(\dfrac{5}{12}-\dfrac{1}{15}\right)=\dfrac{1}{10}-\dfrac{5}{12}+\dfrac{1}{15}=\dfrac{6-5\cdot5+4}{60}=-\dfrac{15}{60}=-\dfrac{1}{4}\)

\(a.\)

\(\dfrac{27}{13}-\dfrac{106}{111}+-\dfrac{5}{111}=\dfrac{27}{13}-\dfrac{106}{111}-\dfrac{5}{111}=\dfrac{27}{13}-\left(\dfrac{106+6}{111}\right)=\dfrac{27}{13}-1=\dfrac{14}{13}\)

\(b.\)

\(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+\dfrac{7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+1=\dfrac{23}{11}\)

\(c.\)

\(\dfrac{5}{17}-\dfrac{25}{31}+\dfrac{12}{17}+-\dfrac{6}{31}=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)-\left(\dfrac{25}{31}+\dfrac{6}{31}\right)=1-1=0\)

\(a.\)

\(x-\dfrac{5}{6}=\dfrac{1}{2}\)

\(\Leftrightarrow x=\dfrac{1}{2}+\dfrac{5}{6}=\dfrac{3+5}{6}=\dfrac{8}{6}=\dfrac{4}{3}\)

\(b.\)

\(-\dfrac{3}{4}-x=-\dfrac{7}{12}\)

\(\Leftrightarrow x=-\dfrac{3}{4}--\dfrac{7}{12}=-\dfrac{3}{4}+\dfrac{7}{12}=\dfrac{\left(-3\right)\cdot3+7}{12}=\dfrac{-2}{12}=-\dfrac{1}{6}\)

Một quý gồm 3 tháng, coi số phần kế hoạch của Quý I là 1

Gọi số phần kế hoạch quý I mà tháng Ba đạt được là x

\(TC:\)

\(x=1-\left(\dfrac{3}{8}+\dfrac{2}{7}\right)=1-\left(\dfrac{3\cdot7+2\cdot8}{56}\right)=1-\dfrac{37}{56}=\dfrac{19}{56}\left(kh\right)\)

Coi số sách quyên góp của cả lớp là 1

Gọi số sách tổ IV quên góp là x

\(TC:\)

\(x=1-\left(\dfrac{1}{4}+\dfrac{9}{40}+\dfrac{1}{5}\right)\)

\(\Leftrightarrow x=1-\left(\dfrac{10+9+8}{40}\right)=1-\dfrac{27}{40}=\dfrac{13}{40}\left(ps\right)\)