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\(a.\) \(\frac{4}{15}.\frac{7}{9}+\frac{4}{15}.\frac{2}{9}\)
\(=\frac{4}{15}\left(\frac{7}{9}+\frac{2}{9}\right)\)
\(=\frac{4}{15}.\frac{9}{9}\)
\(=\frac{4}{15}.1\)
\(=\frac{4}{15}\)
\(b.\) \(\frac{13}{19}.\frac{23}{11}-\frac{13}{19}.\frac{8}{11}-\frac{13}{19}.\frac{4}{11}\)
\(=\frac{13}{19}\left(\frac{23}{11}-\frac{8}{11}-\frac{4}{11}\right)\)
\(=\frac{13}{19}.\frac{11}{11}\)
\(=\frac{13}{19}.1\)
\(=\frac{13}{19}\)
a)4/15 x(7/9+2/9)=4/15x1=4/15
b)13/19x(23/11-8/11-4/11)13/19x1=13/19
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a) \(\dfrac{2}{4}\times\dfrac{9}{5}=\dfrac{1}{2}\times\dfrac{9}{5}=\dfrac{1\times9}{2\times5}=\dfrac{9}{10}\)
b) \(\dfrac{13}{8}\times\dfrac{5}{15}=\dfrac{13}{8}\times\dfrac{1}{3}=\dfrac{13}{24}\)
c) \(\dfrac{3}{9}\times\dfrac{6}{12}=\dfrac{1}{3}\times\dfrac{1}{2}=\dfrac{1}{3\times2}=\dfrac{1}{6}\)
a: =18/20=9/10
b: \(=\dfrac{13\cdot5}{8\cdot15}=\dfrac{13}{8}\cdot\dfrac{1}{3}=\dfrac{13}{24}\)
c: \(=\dfrac{1}{3}\cdot\dfrac{1}{2}=\dfrac{1}{6}\)
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a) \(\dfrac{4}{7}\times\dfrac{3}{5}=\dfrac{4\times3}{7\times5}=\dfrac{12}{35}\)
b) \(\dfrac{1}{3}\times\dfrac{9}{10}=\dfrac{1\times9}{3\times10}=\dfrac{9}{30}=\dfrac{3}{10}\)
c) \(\dfrac{1}{6}\times\dfrac{1}{4}=\dfrac{1}{4\times6}=\dfrac{1}{24}\)
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a) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19
= (1 + 19) + (3 + 17) + (5 + 15) + (7 + 13) + (9 + 11)
= 20 + 20 + 20 + 20 + 20
= 100
b) 15 × 25 + 25 × 34 + 51 × 25
= 25 × (15 + 34 + 51)
= 25 × 100
= 2500
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a) $\frac{2}{5} \times \frac{3}{8} \times \frac{3}{4} = \frac{{2 \times 3 \times 3}}{{5 \times 8 \times 4}} = \frac{{18}}{{160}} = \frac{9}{{80}}$
b) $\frac{1}{3} \times \frac{1}{6} \times \frac{1}{9} = \frac{{1 \times 1 \times 1}}{{3 \times 6 \times 9}} = \frac{1}{{162}}$
c) $\frac{3}{4}:\frac{1}{5}:\frac{7}{8} = \frac{3}{4} \times \frac{5}{1} \times \frac{8}{7} = \frac{{3 \times 5 \times 8}}{{4 \times 1 \times 7}} = \frac{{120}}{{28}} = \frac{{30}}{7}$
d) $\frac{3}{5}:\frac{1}{5}:\frac{3}{8} = \frac{3}{5} \times \frac{5}{1} \times \frac{8}{3} = \frac{{3 \times 5 \times 8}}{{5 \times 1 \times 3}} = 8$
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a: \(\dfrac{3}{9}\times\dfrac{5}{4}=\dfrac{5}{4}\times\dfrac{1}{3}=\dfrac{5\times1}{4\times3}=\dfrac{5}{12}\)
b: \(\dfrac{10}{15}\times\dfrac{3}{5}=\dfrac{3}{5}\times\dfrac{2}{3}=\dfrac{3\times2}{5\times3}=\dfrac{2}{5}\)
c: \(\dfrac{5}{8}\times\dfrac{4}{12}=\dfrac{5}{8}\times\dfrac{1}{3}=\dfrac{5}{3\times8}=\dfrac{5}{24}\)
d: \(\dfrac{9}{27}\times\dfrac{3}{21}=\dfrac{1}{7}\times\dfrac{1}{3}=\dfrac{1\times1}{7\times3}=\dfrac{1}{21}\)