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a) 2/9 +1/5 +7/9+4/5
=( 2/9+7/9)+(1/5+4/5)
=1+1=2
b) 1/12+3/16+5/12+5/16
=(1/12 +5/12)+(3/16+5/16)
=1/2 +1/2=1
a) \(\left(\frac{3}{5}.\frac{5}{3}\right).\frac{8}{27}\)
= \(1.\frac{8}{27}\)
=\(\frac{8}{27}\)
b) \(\frac{7}{19}.\left(\frac{1}{3}.\frac{2}{3}\right)\)
= \(\frac{7}{19}.\frac{2}{9}\)
=\(\frac{14}{81}\)
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\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{6}{11}+\frac{16}{11}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)\)
\(=1+2+2\)
\(=5\)
a)\(\frac{8}{13}+\frac{4}{9}+\frac{1}{3}+\frac{5}{13}+3\)
\(=\left(\frac{8}{13}+\frac{5}{13}\right)+\left(\frac{4}{9}+\frac{1}{3}\right)+3\)
\(=1+\left(\frac{4}{9}+\frac{3}{9}\right)+3\)
\(=1+\frac{7}{9}+3\)
\(=1+3+\frac{7}{9}\)
\(=4\frac{7}{9}\)
\(=\frac{43}{9}\)
b)\(\frac{8}{5}\cdot\frac{4}{7}+\frac{4}{7}\cdot\frac{2}{5}-1\)
\(=\frac{4}{7}\cdot\left(\frac{8}{5}+\frac{2}{5}\right)-1\)
\(=\frac{4}{7}\cdot2-1\)
\(=\frac{8}{7}-1\)
\(=\frac{1}{7}\)
a) \(\frac{8}{13}+\frac{4}{9}+\frac{1}{3}+\frac{5}{13}+3\)
\(=\left(\frac{8}{13}+\frac{5}{13}\right)+\left(\frac{4}{9}+\frac{3}{9}\right)+3\)
\(=1+\frac{7}{9}+3=4\frac{7}{9}\)
b)\(\frac{8}{5}.\frac{4}{7}+\frac{4}{7}.\frac{2}{5}-1\)
\(=\frac{4}{7}.\left(\frac{8}{5}+\frac{2}{5}\right)-1\)
\(=\frac{4}{7}.2-1\)
\(=\frac{8}{7}-\frac{7}{7}=\frac{1}{7}\)
=7/9*[1/3+2/3]=7/9*1=7/9
a) \(\frac{3}{5}\times\frac{8}{27}\times\frac{5}{3}\)
\(=\left(\frac{3}{5}\times\frac{5}{3}\right)\times\frac{8}{27}\)
\(=1\times\frac{8}{27}\)
\(=\frac{8}{27}\)
b) \(\frac{7}{19}\times\frac{1}{3}+\frac{7}{19}\times\frac{2}{3}\)
\(=\frac{7}{19}\times\left(\frac{1}{3}+\frac{2}{3}\right)\)
\(=\frac{7}{19}\times1\)
\(=\frac{7}{19}\)