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7/19 . 1/3 + 7/19 . 2/3 =7/19 .(1/3 + 2/3)= 7/19 . 1 = 7/19
a) 3 2/7 - 2/5 + 5/7 - 3/5
= 3 + 2/7 - (2/5 + 3/5) + 5/7
= 3 + (2/7 + 5/7) - 1
= 3 + 1 - 1
= 3
b) 5 4/7 - 4/9 + 1 3/7 - 5/9
= 5 + 4/7 - 4/9 + 1 + 3/7 - 5/9
= (5 + 1) + (4/7 + 3/7) - (4/9 + 5/9)
= 6 + 1 - 1
= 6
a) \(3\dfrac{2}{7}-\dfrac{2}{5}+\dfrac{5}{7}-\dfrac{3}{5}\)
\(=\left(\dfrac{23}{7}+\dfrac{5}{7}\right)-\left(\dfrac{2}{5}+\dfrac{3}{5}\right)\)
\(=4-1\)
\(=3\)
b) \(5\dfrac{4}{7}-\dfrac{4}{9}+1\dfrac{3}{7}-\dfrac{5}{9}\)
\(=\left(\dfrac{32}{7}+\dfrac{10}{7}\right)-\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\)
\(=6-1\)
\(=5\)
\(A=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+.......+\frac{2}{99.101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+......+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\frac{100}{101}\)
\(=\frac{350}{101}\)
\(A=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+.....+\frac{2}{99.101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-.....+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)
\(=\frac{7}{2}.\frac{100}{101}\)
\(=\frac{350}{101}\)
\(\dfrac{7}{19}\times\dfrac{1}{3}+\dfrac{7}{13}\times\dfrac{2}{3}\)
\(=\dfrac{7}{19}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)
\(=\dfrac{7}{19}\times1\)
\(=\dfrac{7}{19}\)
a)3/5x5/3x8/27=1x8/27=8/27
b)7/19x(1/3+2/3)=7/19x1=7/19
\(\frac{3}{5}x\frac{8}{27}x\frac{5}{3}=\frac{3}{3}x\frac{5}{5}x\frac{8}{27}=\frac{8}{27}\)
\(\frac{7}{19}x\frac{1}{3}+\frac{7}{19}x\frac{2}{3}=\frac{7}{19}x\left(\frac{1}{3}+\frac{2}{3}\right)=\frac{7}{19}\)