9/11 + 1/12 : 11/24
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`9/11+1/12:11/24=9/11+1/12xx24/11=9/11+[2xx12]/[12xx11]=9/11+2/11=11/11=1`
2/3-6/12+1/4 = 5/12
4/12-18/24+5/2 = 25/12
-5/7*11/9+5/7*4/9 = -5/9
-3/8*13/11-3/8*3/11 = -6/11
\(a.\)
\(\dfrac{5}{16}-\dfrac{5}{24}=\dfrac{5\cdot3-5\cdot2}{48}=\dfrac{15-10}{48}=\dfrac{5}{48}\)
\(b.\)
\(\dfrac{2}{11}+\left(\dfrac{-5}{11}-\dfrac{9}{11}\right)=\dfrac{2-5-9}{11}=-\dfrac{12}{11}\)
\(c.\)
\(\dfrac{1}{10}-\left(\dfrac{5}{12}-\dfrac{1}{15}\right)=\dfrac{1}{10}-\dfrac{5}{12}+\dfrac{1}{15}=\dfrac{6-5\cdot5+4}{60}=-\dfrac{15}{60}=-\dfrac{1}{4}\)
a) \(\dfrac{5}{16}-\dfrac{5}{24}=\dfrac{15}{48}-\dfrac{10}{48}=\dfrac{15-10}{48}=\dfrac{5}{48}\)
b)\(\dfrac{2}{11}+\left(\dfrac{-5}{11}-\dfrac{9}{11}\right)=\dfrac{2}{11}-\dfrac{5}{11}-\dfrac{9}{11}=\dfrac{2-5-9}{11}=\dfrac{-12}{11}\)
c)\(\dfrac{1}{10}-\left(\dfrac{5}{12}-\dfrac{1}{15}\right)=\dfrac{1}{10}-\dfrac{7}{20}=\dfrac{2}{20}-\dfrac{7}{20}=\dfrac{-5}{20}=\dfrac{-1}{4}\)
\(\left(-\dfrac{1}{2}\right)^2\div\dfrac{1}{4}-2\times\left(-\dfrac{1}{2}\right)^2\\= \dfrac{1}{4}\div\dfrac{1}{4}-2\times\dfrac{1}{4}\\ =1-\dfrac{1}{2}\\ =\dfrac{1}{2}\)
\(\left(-2\right)^3\times-\dfrac{1}{24}+\left(\dfrac{4}{3}-1\dfrac{5}{6}\right)\div\dfrac{5}{12}\)
= \(-6\times-\dfrac{1}{24}+\left(\dfrac{4}{3}-\dfrac{11}{6}\right)\div\dfrac{5}{12}\)
= \(\dfrac{1}{4}+-\dfrac{1}{2}\div\dfrac{5}{12}\)
= \(\dfrac{1}{4}+-\dfrac{6}{5}\)
= \(\dfrac{1}{4}-\dfrac{6}{5}\)
= \(-\dfrac{19}{20}\)
\(\left(6\dfrac{4}{9}+\dfrac{7}{11}\right)-\left(4\dfrac{4}{9}-2\dfrac{4}{11}\right)\\ =\dfrac{58}{9}+\dfrac{7}{11}-\dfrac{40}{9}+\dfrac{26}{11}\\ =\dfrac{58}{9}-\dfrac{40}{9}+\dfrac{7}{11}+\dfrac{26}{11}\\ =12+3\\ =15\)
\(a,\left(\dfrac{-1}{2}\right)^2:\dfrac{1}{4}-2\left(-\dfrac{1}{2}\right)^2\)
\(=\left(-\dfrac{1}{2}\right)^2\left(4-2\right)\)
\(=\dfrac{1}{4}.2=\dfrac{1}{2}\)
\(b,\left(-2\right)^3.\dfrac{-1}{24}+\left(\dfrac{4}{3}-1\dfrac{5}{6}\right):\dfrac{5}{12}\)
\(=\left(-8\right).\dfrac{-1}{24}+\left(-\dfrac{1}{2}\right).\dfrac{12}{5}\)
\(=\dfrac{1}{3}+\left(-\dfrac{1}{5}\right)=\dfrac{2}{15}\)
\(c,\left(6\dfrac{4}{9}+\dfrac{7}{11}\right)-\left(4\dfrac{4}{9}-2\dfrac{4}{11}\right)\)
\(=\dfrac{701}{99}-\dfrac{206}{99}=\dfrac{495}{99}=5\)
\(d,10\dfrac{1}{5}-5\dfrac{1}{2}.\dfrac{60}{11}+\dfrac{3}{15\%}\)
\(=\dfrac{51}{5}-30+20=\dfrac{1}{5}\)
\(e,\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}\)
\(=\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}.\left(-\dfrac{7}{11}\right)\)
\(=-\dfrac{5}{11}\)
\(f,\dfrac{-5}{7}.\dfrac{2}{11}+\left(-\dfrac{5}{7}\right).\dfrac{9}{11}+1\dfrac{5}{7}\)
\(=\left(-\dfrac{5}{7}\right)\left(\dfrac{2}{11}+\dfrac{9}{11}\right)+\dfrac{12}{7}\)
\(=\left(-\dfrac{5}{7}\right)+\dfrac{12}{7}=1\)
=9/11+2/11
=1
`9/11 + 1/12 : 11/24 = 9/11 + 1/12 xx 24/11 = 9/11 + 2/11 = 11/11= 1`