Odpowiedź:
zad 9
[tex]1\frac{4}{9}- \frac{1}{3}= 1\frac{4}{9}- \frac{3}{9}=1\frac{1}{9} - K[/tex]
[tex]5\frac{5}{9}:3\frac{1}{3} = \frac{50}{9}:\frac{10}{3}= \frac{50}{9}* \frac{3}{10}=\frac{5}{3}* \frac{1}{1}=1\frac{2}{3} - L[/tex]
[tex]2\frac{1}{4}* \frac{2}{3}=\frac{9}{4} *\frac{2}{3}= \frac{3}{2}*1=1\frac{1}{2 }- A[/tex]
[tex]\frac{5}{6}+1 \frac{2}{3}=\frac{5}{6}+1 \frac{4}{6}=1\frac{9}{6}=2\frac{3}{6}=2\frac{1}{2} - R[/tex]
[tex]1-\frac{1}{2} *\frac{1}{3}=1-\frac{1}{6}=\frac{5}{6}- N[/tex]
[tex]3\frac{2}{7}+ \frac{1}{7}*6=3\frac{2}{7}+\frac{6}{7}=3\frac{8}{7}=4 \frac{1}{7} - E[/tex]
[tex]2\frac{4}{5}: \frac{7}{12}=\frac{14}{5}* \frac{12}{7}=\frac{2}{5}* 12=\frac{24}{5} = 4\frac{4}{5}- T[/tex]
KLARNET
[tex]5-\frac{2}{3}* \frac{1}{2}=5-\frac{1}{3}=4\frac{2}{3} - O[/tex]
[tex]1\frac{5}{12}: \frac{1}{2}-2 \frac{1}{2}=\frac{17}{12}*2-2\frac{1}{2}=\frac{17}{6}-2\frac{3}{6}=2\frac{5}{6}-2\frac{3}{6} =\frac{2}{6} =\frac{1}{3} -B[/tex]
[tex]5\frac{1}{8}-3 \frac{1}{2}=5\frac{1}{8}-3\frac{4}{8}=1\frac{5}{8} -[/tex] Ó
[tex]\frac{7}{12}+ \frac{5}{8}+ \frac{1}{6}=\frac{14}{24}+ \frac{15}{24}+ \frac{4}{24}= \frac{33}{24}=1\frac{9}{24}= 1\frac{3}{8}[/tex] [tex]- J[/tex]
OBÓJ
[tex]6\frac{3}{5}:3\frac{2}{3}-1\frac{1}{2} =\frac{33}{5}: \frac{11}{3}-1 \frac{1}{2}=\frac{33}{5}* \frac{3}{11}-1 \frac{1}{2}= \frac{3}{5}*3 -1\frac{1}{2}= \frac{9}{5}-1\frac{1}{2}=\frac{18}{10}-1 \frac{5}{10}=\frac{3}{10} - P[/tex]
[tex]\frac{3}{5}: 1\frac{1}{2}= \frac{3}{5}: \frac{3}{2}=\frac{3}{5}* \frac{2}{3}=\frac{2}{5 }- U[/tex]
[tex]5\frac{1}{7}* (1-\frac{8}{9})= \frac{36}{7}* \frac{1}{9}=\frac{4}{7} - Z[/tex]
[tex]1\frac{1}{9}*2\frac{2}{5}+2=\frac{10}{9}* \frac{12}{5}+2=\frac{24}{9}+2=2\frac{24}{9}=4\frac{6}{9}=4\frac{2}{3} - O[/tex]
[tex]2\frac{3}{4}-1\frac{11}{12}=2\frac{9}{12}-1\frac{11}{12}=\frac{10}{12}=\frac{5}{6} - N[/tex]
PUZON
zad10
a) [tex]\frac{3}{4}+ \frac{1}{4}: \frac{2}{3}=\frac{3}{4}+ \frac{1}{4}* \frac{3}{2}=\frac{3}{4}+ \frac{3}{8}=\frac{6}{8}+ \frac{3}{8}=\frac{9}{8}=1 \frac{1}{8}[/tex]
b) [tex]\frac{1}{3}:3+5: \frac{1}{5} =\frac{1}{3}* \frac{1}{3}+5*5=\frac{1}{9}*25=\frac{25}{9}=2\frac{7}{9}[/tex]
c) [tex](3\frac{1}{3}- \frac{5}{6})*\frac{4}{15}=(\frac{10}{3}- \frac{5}{6})*\frac{4}{15}=(\frac{20}{6}- \frac{5}{6})*\frac{4}{15}=\frac{15}{6} *\frac{4}{15}=\frac{2}{3}[/tex]
d) [tex](1\frac{1}{3}- \frac{5}{6})*(\frac{3}{5}+ \frac{1}{3} )= (\frac{4}{3}- \frac{5}{6})*(\frac{9}{15}+ \frac{5}{15})=(\frac{8}{6}- \frac{5}{6})*\frac{14}{15}= \frac{3}{6}*\frac{14}{15}=\frac{1}{3}* \frac{7}{5}=\frac{7}{15}[/tex]
e) [tex]1\frac{1}{5}*1\frac{2}{3}*\frac{1}{7}+(1\frac{1}{7})^2=\frac{6}{5}* \frac{5}{3}* \frac{1}{7}+ (\frac{8}{7})^2=\frac{6}{5}* \frac{5}{3}* \frac{1}{7}+\frac{64}{49}= \frac{2}{7}+ \frac{64}{49}=\frac{14}{49}+ \frac{64}{49}=\frac{78}{49}= 1\frac{29}{49}[/tex]
f) [tex](2\frac{1}{6} -\frac{2}{3})^2-2\frac{1}{5}=(\frac{13}{6}-\frac{4}{6})^2-2\frac{1}{5}=(\frac{9}{6})^2-2\frac{1}{5}= (\frac{3}{2})^2-2\frac{1}{5}=\frac{9}{4}-\frac{11}{5}=\frac{45}{20}- \frac{44}{20} = \frac{1}{20}[/tex]
g) [tex]10-2*(3\frac{1}{5}-2\frac{1}{4}*\frac{1}{3}) =10-2*(\frac{16}{5} -\frac{9}{4} *\frac{1}{3})=10-2*(\frac{16}{5}-\frac{3}{4})=10-2*(\frac{64}{20}- \frac{15}{20})=10-2*\frac{49}{20} =10-\frac{49}{10}=10-4\frac{9}{10}=5\frac{1}{10}[/tex]
h) [tex](\frac{7}{3}-\frac{5}{12}+1\frac{1}{2}):(2\frac{3}{4}-\frac{5}{6})=(\frac{28}{12}- \frac{5}{12}+1 \frac{6}{12}): (2\frac{9}{12}-\frac{10}{12})=1\frac{29}{12} : 1\frac{11}{12}=\frac{41}{12} :\frac{23}{12} = \frac{41}{12} *\frac{12}{23}= \frac{41}{23}= 1\frac{18}{23}[/tex]
Szczegółowe wyjaśnienie:
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Odpowiedź:
zad 9
[tex]1\frac{4}{9}- \frac{1}{3}= 1\frac{4}{9}- \frac{3}{9}=1\frac{1}{9} - K[/tex]
[tex]5\frac{5}{9}:3\frac{1}{3} = \frac{50}{9}:\frac{10}{3}= \frac{50}{9}* \frac{3}{10}=\frac{5}{3}* \frac{1}{1}=1\frac{2}{3} - L[/tex]
[tex]2\frac{1}{4}* \frac{2}{3}=\frac{9}{4} *\frac{2}{3}= \frac{3}{2}*1=1\frac{1}{2 }- A[/tex]
[tex]\frac{5}{6}+1 \frac{2}{3}=\frac{5}{6}+1 \frac{4}{6}=1\frac{9}{6}=2\frac{3}{6}=2\frac{1}{2} - R[/tex]
[tex]1-\frac{1}{2} *\frac{1}{3}=1-\frac{1}{6}=\frac{5}{6}- N[/tex]
[tex]3\frac{2}{7}+ \frac{1}{7}*6=3\frac{2}{7}+\frac{6}{7}=3\frac{8}{7}=4 \frac{1}{7} - E[/tex]
[tex]2\frac{4}{5}: \frac{7}{12}=\frac{14}{5}* \frac{12}{7}=\frac{2}{5}* 12=\frac{24}{5} = 4\frac{4}{5}- T[/tex]
KLARNET
[tex]5-\frac{2}{3}* \frac{1}{2}=5-\frac{1}{3}=4\frac{2}{3} - O[/tex]
[tex]1\frac{5}{12}: \frac{1}{2}-2 \frac{1}{2}=\frac{17}{12}*2-2\frac{1}{2}=\frac{17}{6}-2\frac{3}{6}=2\frac{5}{6}-2\frac{3}{6} =\frac{2}{6} =\frac{1}{3} -B[/tex]
[tex]5\frac{1}{8}-3 \frac{1}{2}=5\frac{1}{8}-3\frac{4}{8}=1\frac{5}{8} -[/tex] Ó
[tex]\frac{7}{12}+ \frac{5}{8}+ \frac{1}{6}=\frac{14}{24}+ \frac{15}{24}+ \frac{4}{24}= \frac{33}{24}=1\frac{9}{24}= 1\frac{3}{8}[/tex] [tex]- J[/tex]
OBÓJ
[tex]6\frac{3}{5}:3\frac{2}{3}-1\frac{1}{2} =\frac{33}{5}: \frac{11}{3}-1 \frac{1}{2}=\frac{33}{5}* \frac{3}{11}-1 \frac{1}{2}= \frac{3}{5}*3 -1\frac{1}{2}= \frac{9}{5}-1\frac{1}{2}=\frac{18}{10}-1 \frac{5}{10}=\frac{3}{10} - P[/tex]
[tex]\frac{3}{5}: 1\frac{1}{2}= \frac{3}{5}: \frac{3}{2}=\frac{3}{5}* \frac{2}{3}=\frac{2}{5 }- U[/tex]
[tex]5\frac{1}{7}* (1-\frac{8}{9})= \frac{36}{7}* \frac{1}{9}=\frac{4}{7} - Z[/tex]
[tex]1\frac{1}{9}*2\frac{2}{5}+2=\frac{10}{9}* \frac{12}{5}+2=\frac{24}{9}+2=2\frac{24}{9}=4\frac{6}{9}=4\frac{2}{3} - O[/tex]
[tex]2\frac{3}{4}-1\frac{11}{12}=2\frac{9}{12}-1\frac{11}{12}=\frac{10}{12}=\frac{5}{6} - N[/tex]
PUZON
zad10
a) [tex]\frac{3}{4}+ \frac{1}{4}: \frac{2}{3}=\frac{3}{4}+ \frac{1}{4}* \frac{3}{2}=\frac{3}{4}+ \frac{3}{8}=\frac{6}{8}+ \frac{3}{8}=\frac{9}{8}=1 \frac{1}{8}[/tex]
b) [tex]\frac{1}{3}:3+5: \frac{1}{5} =\frac{1}{3}* \frac{1}{3}+5*5=\frac{1}{9}*25=\frac{25}{9}=2\frac{7}{9}[/tex]
c) [tex](3\frac{1}{3}- \frac{5}{6})*\frac{4}{15}=(\frac{10}{3}- \frac{5}{6})*\frac{4}{15}=(\frac{20}{6}- \frac{5}{6})*\frac{4}{15}=\frac{15}{6} *\frac{4}{15}=\frac{2}{3}[/tex]
d) [tex](1\frac{1}{3}- \frac{5}{6})*(\frac{3}{5}+ \frac{1}{3} )= (\frac{4}{3}- \frac{5}{6})*(\frac{9}{15}+ \frac{5}{15})=(\frac{8}{6}- \frac{5}{6})*\frac{14}{15}= \frac{3}{6}*\frac{14}{15}=\frac{1}{3}* \frac{7}{5}=\frac{7}{15}[/tex]
e) [tex]1\frac{1}{5}*1\frac{2}{3}*\frac{1}{7}+(1\frac{1}{7})^2=\frac{6}{5}* \frac{5}{3}* \frac{1}{7}+ (\frac{8}{7})^2=\frac{6}{5}* \frac{5}{3}* \frac{1}{7}+\frac{64}{49}= \frac{2}{7}+ \frac{64}{49}=\frac{14}{49}+ \frac{64}{49}=\frac{78}{49}= 1\frac{29}{49}[/tex]
f) [tex](2\frac{1}{6} -\frac{2}{3})^2-2\frac{1}{5}=(\frac{13}{6}-\frac{4}{6})^2-2\frac{1}{5}=(\frac{9}{6})^2-2\frac{1}{5}= (\frac{3}{2})^2-2\frac{1}{5}=\frac{9}{4}-\frac{11}{5}=\frac{45}{20}- \frac{44}{20} = \frac{1}{20}[/tex]
g) [tex]10-2*(3\frac{1}{5}-2\frac{1}{4}*\frac{1}{3}) =10-2*(\frac{16}{5} -\frac{9}{4} *\frac{1}{3})=10-2*(\frac{16}{5}-\frac{3}{4})=10-2*(\frac{64}{20}- \frac{15}{20})=10-2*\frac{49}{20} =10-\frac{49}{10}=10-4\frac{9}{10}=5\frac{1}{10}[/tex]
h) [tex](\frac{7}{3}-\frac{5}{12}+1\frac{1}{2}):(2\frac{3}{4}-\frac{5}{6})=(\frac{28}{12}- \frac{5}{12}+1 \frac{6}{12}): (2\frac{9}{12}-\frac{10}{12})=1\frac{29}{12} : 1\frac{11}{12}=\frac{41}{12} :\frac{23}{12} = \frac{41}{12} *\frac{12}{23}= \frac{41}{23}= 1\frac{18}{23}[/tex]
Szczegółowe wyjaśnienie: