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8/9 x 5/4 + 3/5 = 10/9 + 3/5 = 77/45
5/8 + 1/4 = 5/9 + 2/8 = 7/8
1/2 + 5/9 = 9/18 + 5/9 = 14/9
9/8 x 3/4 - 4/7 = 27/32 - 4/7 = 61/224
a) \(\dfrac{8}{9}:\dfrac{4}{5}+\dfrac{3}{5}=\dfrac{8}{9}\times\dfrac{5}{4}+\dfrac{2}{5}=\dfrac{10}{9}+\dfrac{2}{5}=\dfrac{50}{45}+\dfrac{18}{45}=\dfrac{68}{45}\)
b) \(\dfrac{5}{8}+\dfrac{1}{4}=\dfrac{5}{8}+\dfrac{2}{8}=\dfrac{6}{8}=\dfrac{3}{4}\)
c) \(\dfrac{7}{8}\times\dfrac{4}{7}+\dfrac{5}{9}=\dfrac{1}{2}+\dfrac{5}{9}=\dfrac{9}{18}+\dfrac{10}{18}=\dfrac{19}{18}\)
d) \(\dfrac{9}{8}:\dfrac{4}{3}-\dfrac{4}{7}=\dfrac{9}{8}\times\dfrac{3}{4}-\dfrac{4}{7}=\dfrac{27}{32}-\dfrac{4}{7}=\dfrac{61}{244}\)
\(\dfrac{3}{4}=\dfrac{12}{16};\dfrac{5}{6}>\dfrac{7}{9};\dfrac{4}{15}< \dfrac{4}{13};\dfrac{5}{4}-\dfrac{5}{6}>\dfrac{3}{4}-\dfrac{2}{3}\)
\(\dfrac{2}{5}\times\dfrac{3}{4}-\dfrac{1}{8}=\dfrac{1}{5}\times\dfrac{3}{2}-\dfrac{1}{8}=\dfrac{3}{10}-\dfrac{1}{8}=\dfrac{24}{80}-\dfrac{10}{80}=\dfrac{14}{80}=\dfrac{7}{40}\\ \dfrac{4}{3}+\dfrac{1}{3}-\dfrac{1}{5}=\dfrac{5}{3}-\dfrac{1}{5}=\dfrac{25}{15}-\dfrac{3}{15}=\dfrac{22}{15}\\ \dfrac{9}{20}-\dfrac{3}{5}\times\dfrac{1}{4}=\dfrac{9}{20}-\dfrac{3}{20}=\dfrac{6}{20}=\dfrac{3}{10}\\ \dfrac{2}{8}+\dfrac{2}{3}:\dfrac{4}{5}=\dfrac{2}{8}+\dfrac{2}{3}\times\dfrac{5}{4}=\dfrac{2}{8}+\dfrac{1}{3}\times\dfrac{5}{2}=\dfrac{2}{8}+\dfrac{5}{6}=\dfrac{1}{4}+\dfrac{5}{6}=\dfrac{6}{24}+\dfrac{20}{24}=\dfrac{26}{24}=\dfrac{13}{12}\)
a) \(\dfrac{2}{7}\times\dfrac{4}{3}+\dfrac{2}{6}\)
\(=\dfrac{8}{21}+\dfrac{2}{6}\)
\(=\dfrac{5}{7}\)
b) \(\dfrac{4}{7}:2+\dfrac{4}{7}\)
\(=\dfrac{2}{7}+\dfrac{4}{7}\)
\(=\dfrac{6}{7}\)
c) \(\dfrac{1}{3}+\dfrac{3}{4}-\dfrac{1}{5}:\dfrac{2}{3}\)
\(=\dfrac{13}{12}-\dfrac{3}{10}\)
\(=\dfrac{47}{60}\)
a \(\dfrac{8}{21}+\dfrac{2}{6}=\dfrac{16}{42}+\dfrac{14}{42}=\dfrac{30}{42}=\dfrac{5}{7}\)
\(b\) \(\dfrac{4}{7}\times\dfrac{1}{2}+\dfrac{4}{7}=\dfrac{2}{7}+\dfrac{4}{7}=\dfrac{6}{7}\)
\(c\) \(\dfrac{1}{3}+\dfrac{3}{4}-\dfrac{1}{5}\times\dfrac{3}{2}=\dfrac{1}{3}+\dfrac{3}{4}-\dfrac{3}{10}=\dfrac{20}{60}+\dfrac{45}{60}-\dfrac{18}{60}=\dfrac{47}{60}\)
a) \(\dfrac{3}{5}+\dfrac{11}{20}=\dfrac{12}{20}+\dfrac{11}{20}=\dfrac{23}{20}\)
b) \(\dfrac{5}{8}-\dfrac{4}{9}=\dfrac{45}{72}-\dfrac{32}{72}=\dfrac{13}{72}\)
c) \(\dfrac{9}{16}\times\dfrac{4}{3}=\dfrac{3}{4}\)
d) \(\dfrac{4}{7}:\dfrac{8}{11}=\dfrac{4}{7}\times\dfrac{11}{8}=\dfrac{11}{14}\)
e) \(\dfrac{3}{5}+\dfrac{4}{5}:\dfrac{2}{5}=\dfrac{3}{5}+\dfrac{4}{5}\times\dfrac{5}{2}=\dfrac{3}{5}+2=\dfrac{3}{5}+\dfrac{10}{5}=\dfrac{13}{5}\)
\(\dfrac{4}{5142}-\dfrac{4}{5143}=\dfrac{2}{13222653}\)