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a) Ta thấy \(\frac{1}{2}< \frac{2}{3};\frac{3}{4}< \frac{4}{5};...;\frac{99}{100}< \frac{100}{101}\)
\(\Rightarrow A=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}< B=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\)
b) \(A.B=\left(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}\right).\left(\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\right)\)
\(A.B=\frac{1.\left(3.5...99\right).\left(2.4.6...100\right)}{\left(2.4.6...100\right).\left(3.5.7...99\right).101}=\frac{1}{101}\)
c) vì A < b nên A . A < A . B < \(\frac{1}{101}< \frac{1}{100}\)
do đó : A . A < \(\frac{1}{10}.\frac{1}{10}\)suy ra A < \(\frac{1}{10}\)
a) \(\frac{1.3+3.5+5.7+7.9}{3.6+9.10+15.14+21.18}\)
= \(\frac{1.3+3.5+5.7+7.9}{1.3.2.3+3.5.2.3+5.7.2.3+7.9.2.3}\)
= \(\frac{1.3+3.5+5.7+7.9}{1.3.6+3.5.6+5.7.6+7.9.6}\)
= \(\frac{1.3+3.5+5.7+7.9}{6.\left(1.3+3.5+5.7+7.9\right)}=\frac{1}{6}\)
Dấu "." là dấu nhân cấp 2
b) \(\frac{1.2+2.3+3.4+4.5}{3.6+6.9+9.12+12.15}\)
= \(\frac{1.2+2.3+3.4+4.5}{1.2.3.3+2.3.3.3+3.4.3.3+4.5.3.3}\)
= \(\frac{1.2+2.3+3.4+4.5}{1.2.9+2.3.9+3.4.9+4.5.9}\)
= \(\frac{1.2+2.3+3.4+4.5}{9.\left(1.2+2.3+3.4+4.5\right)}=\frac{1}{9}\)
Dấu "." là dấu nhân cấp 2
c) \(\frac{0,3+\frac{3}{7}+\frac{3}{11}}{0,4+\frac{4}{7}+\frac{4}{11}}\)= \(\frac{\frac{3}{10}+\frac{3}{7}+\frac{3}{11}}{\frac{4}{10}+\frac{4}{7}+\frac{4}{11}}\)= \(\frac{3.\left(\frac{1}{10}+\frac{1}{7}+\frac{1}{11}\right)}{4.\left(\frac{1}{10}+\frac{1}{7}+\frac{1}{11}\right)}=\frac{3}{4}\)
a)\(\left(x+3\right)\times5+1=20\Leftrightarrow5x+15=19\)
\(\Leftrightarrow5x=4\Leftrightarrow x=\frac{4}{5}\)
b)sai đề
c)\(2\frac{3}{7}\times x+1\frac{5}{4}=5\frac{3}{42}\)\(\Leftrightarrow\frac{17}{7}\times x+\frac{9}{4}=\frac{71}{14}\) \(\Leftrightarrow\frac{17}{7}\times x+\frac{63}{28}=\frac{142}{28}\)
\(\Leftrightarrow\frac{17}{7}\times x=\frac{79}{28}\Leftrightarrow x=\frac{17}{7}:\frac{79}{28}\) \(\Leftrightarrow x=\frac{17}{7}\times\frac{28}{79}\Leftrightarrow x=\frac{476}{553}=\frac{68}{79}\)
d)\(10\frac{2}{3}-x:\frac{6}{7}=8\frac{1}{3}-6\frac{2}{7}\Leftrightarrow\frac{32}{3}-x:\frac{6}{7}=\frac{25}{3}-\frac{44}{7}\) \(\Leftrightarrow\frac{224}{21}-x:\frac{6}{7}=\frac{75}{21}-\frac{132}{21}\Leftrightarrow-\frac{57}{21}-\frac{224}{21}\)
\(\Leftrightarrow-x:\frac{6}{7}=-\frac{281}{21}\Leftrightarrow-x=-\frac{281}{21}\times\frac{6}{7}\) \(\Leftrightarrow-x=-\frac{1686}{147}\Leftrightarrow x=\frac{562}{49}=11\frac{23}{49}\)
Bn thấy cái nào cùng mẫu hoặc dễ quy đồng thì nhóm vào 1 nhóm nha!
Xin đừng ném đá, mk chỉ nói đúng
Hội con 🐄 chúc bạn học tốt!!!
\(=\frac{5}{6}x\left(\frac{7}{12}+\frac{5}{12}\right)+\frac{1}{6}=\frac{5}{6}x1+\frac{1}{6}=1\)
a) \(\frac{5}{6}x\frac{7}{12}+\frac{5}{12}x\frac{5}{6}+\frac{1}{6}=\frac{5}{6}x\left(\frac{7}{12}+\frac{5}{12}\right)+\frac{1}{6}=\frac{5}{6}x1+\frac{1}{6}=\frac{5}{6}+\frac{1}{6}=1\)
b) \(\left(\frac{8}{15}x\frac{3}{4}x\frac{5}{4}\right):\frac{7}{8}=\frac{4x2x3x5}{5x3x4x4}x\frac{8}{7}=\frac{2}{4}x\frac{8}{7}=\frac{2x8}{4x7}=\frac{2x4x2}{4x7}=\frac{4}{7}\)
Chúc bạn học tốt.
😁😁😁
