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\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}+\frac{1}{3}\right)=\frac{4}{5}.\frac{3}{3}=\frac{4}{5}.1=\frac{4}{5}\)
\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}+\frac{1}{6}\right)=\frac{3}{4}:\frac{2}{3}=\frac{9}{8}\)
\(\frac{2}{3}.\frac{4}{5}-\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}-\frac{1}{3}\right)=\frac{4}{5}.\frac{1}{3}=\frac{4}{15}\)
\(\frac{1}{2}:\frac{3}{4}-\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{3}{4}:\frac{1}{3}=\frac{9}{4}\)
\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\left(\frac{2}{3}+\frac{1}{3}\right).\frac{4}{5}=1.\frac{4}{5}=\frac{4}{5}\)
\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{1}{2}.\frac{4}{3}+\frac{1}{6}.\frac{4}{3}=\left(\frac{1}{2}+\frac{1}{6}\right).\frac{4}{3}=\frac{2}{3}.\frac{4}{3}=\frac{8}{9}\)
c,d tương tự
\(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\)
=\(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\)
=3-3\4-4x\(\frac{5}{2}\)
=\(\frac{5}{2}\)
\(1\frac{1}{2}x1\frac{1}{3}:1\frac{1}{4}:1\frac{1}{5}\)
\(=\frac{3}{2}x\frac{4}{3}:\frac{5}{4}:\frac{6}{5}\)
\(=\frac{3}{2}x\frac{4}{3}x\frac{4}{5}x\frac{5}{6}\)
\(=\frac{4x4}{2x6}=\frac{2x2x4}{2x2x3}=\frac{4}{3}\)
\(1\frac{1}{2}\times1\frac{1}{3}\div1\frac{1}{4}\div1\frac{1}{5}=\frac{3}{2}\times\frac{4}{3}\div\frac{5}{4}\div\frac{6}{5}=\frac{3}{2}\times\frac{4}{3}\times\frac{4}{5}\times\frac{5}{6}\)
\(=\frac{3\times4\times4\times5}{2\times3\times5\times6}=\frac{4}{3}\)
\(=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}\)có 9 p/số
\(=\frac{1}{10}.9=\frac{9}{10}\)
\(2\frac{3}{4}+1\frac{5}{6}+3\frac{1}{4}+2\frac{1}{6}\)
= \(\frac{11}{4}+\frac{11}{6}+\frac{13}{4}+\frac{13}{6}\)
= \(\left(\frac{11}{4}+\frac{13}{4}\right)+\left(\frac{11}{6}+\frac{13}{6}\right)\)
= \(\frac{24}{4}+\frac{24}{6}\)
= \(6+4\)
= \(10\)
B1 Nhân biểu tthức trên với 1/2 được
1/6+1/12/+1/20+....+1/110=1/2×3+1/3×4+.....+1/10×11
=1/2-1/3+1/3-1/4+.....+1/10-1/11=1/2-1/11=9/22
B2
B.1/1×2+1/2×3+.....+1/99×100=1-1/2 +1/2-1/3+....+1/99-1/100=1-1/100=99/100
Phần a sai đề phải llà1/2×4+1/4×6+.....+1/8×10 mới làm đc nhé
\(=\frac{1}{10}+\)\(\frac{1}{10}+\)\(\frac{1}{10}+\)\(\frac{1}{10}+\)\(\frac{1}{10}+\)\(\frac{1}{10}+\)\(\frac{1}{10}+\)\(\frac{1}{10}+\)\(\frac{1}{10}\)
\(=\frac{1}{10}.9\)
\(=\frac{9}{10}\)
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\(\frac{1}{10}+\frac{2}{20}+\frac{3}{30}+\frac{4}{40}+\frac{5}{50}+\frac{6}{60}+\frac{7}{70}+\frac{8}{80}+\frac{9}{90}\)
\(=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}\)
\(=\frac{1}{10}\times9\)
\(=\frac{9}{10}\)
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