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a) \(\frac{55}{32}\)
b) \(\frac{90}{48}\)
c) \(\frac{76}{15}\)
d) \(\frac{552}{119}\)
\(\frac{9}{16}+\frac{37}{32}=\frac{18}{32}+\frac{37}{32}=\frac{55}{32}\)
\(\frac{126}{48}-\frac{12}{16}=\frac{21}{8}-\frac{6}{8}=\frac{15}{8}\)
\(\frac{19}{15}\times\frac{32}{8}=\frac{19}{15}\times4=\frac{76}{15}\)
\(\frac{23}{17}:\frac{7}{24}=\frac{23}{17}.\frac{24}{7}=4\frac{76}{119}\)
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x + 7/6=16/25
x = 16/25 - 7/6
x = -79/150.
x - 13/6 = 8/5+3/10
x - 13/5 = 19/10
x = 19/10 +13/5
x = 9/2
x : 9/8 = 14/6
x = 14/6 * 9/8
x = 21/8
x * 11/7 = 3/2
x = 3/2 : 11/7
x = 21/22
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\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\)
\(=3.\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)
\(=3.A\)với \(A=\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\)
\(\Rightarrow2^2A=\left(2+\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}\right)\)
\(\Rightarrow2^2A-A=\left(2+\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}\right)-\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)
\(\Rightarrow4A-A=2-\frac{1}{2^9}\)
\(\Rightarrow3A=2-\frac{1}{512}=\frac{1023}{512}\Rightarrow A=\frac{1023}{512}:3\)
\(\Rightarrow\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}=3.\left(\frac{1023}{512}:3\right)=\frac{1023}{512}\)
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\(a,\frac{8}{15}+\frac{2}{3}=\frac{8+10}{15}=\frac{18}{15}=\frac{6}{5}\)
\(b,\frac{3}{7}+\frac{4}{8}=\frac{24+28}{56}=\frac{62}{56}=\frac{31}{28}\)
a) \(\frac{8}{15}+\frac{2}{3}=\frac{8}{15}+\frac{10}{15}=\frac{8+10}{15}=\frac{18}{15}=\frac{6}{5}\)
b) \(\frac{3}{7}+\frac{4}{8}=\frac{24}{56}+\frac{28}{56}=\frac{24+28}{56}=\frac{52}{56}=\frac{13}{14}\)
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Bài 1:
a) \(\frac{1}{5},\frac{6}{15},\frac{12}{20},\frac{7}{7},\frac{13}{6},\frac{12}{5}\)
b) \(\frac{43}{41},\frac{91}{81},\frac{11}{8},\frac{7}{4}\)
Bài 2:
Nhân cả 2 phân số với 3 ta được :
\(\frac{1.3}{3.3}=\frac{3}{9};\frac{2.3}{3.3}=\frac{6}{9}\)
Vậy 2 phân số lớn hơn \(\frac{3}{9}\)và nhỏ hơn\(\frac{6}{9}\)là \(\frac{4}{9}\)và \(\frac{5}{9}\)
hay 2 phân số lớn hơn \(\frac{1}{3}\)và nhỏ hơn\(\frac{2}{3}\)là \(\frac{4}{9}\)và \(\frac{5}{9}\)
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\(\frac{4}{15}:\frac{4}{7}< x< \frac{2}{5}.\frac{10}{3}\Leftrightarrow\frac{7}{15}< x< \frac{20}{15}\)
\(\Rightarrow x\in\left(8;9;10;11;12;13;14;15;16;17;18;19\right)\)
Ta có : \(\frac{4}{15}:\frac{4}{7}< x< \frac{2}{5}\cdot\frac{10}{3}\)
\(\Rightarrow\frac{4}{15}\cdot\frac{7}{4}< x< \frac{2}{5}\cdot\frac{10}{3}\)
\(\Rightarrow\frac{7}{15}< x< \frac{20}{15}\)
\(\Rightarrow7< x< 20\)
\(\Rightarrow x\in\left\{8;9;10;11;12;...;19\right\}\)
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\(1.a,\frac{5}{7}=\frac{5.9}{7.9}=\frac{45}{63};\frac{4}{9}=\frac{4.7}{9.7}=\frac{28}{63}.\)
\(b,\frac{7}{15},\frac{5}{3}=\frac{5.5}{3.5}=\frac{25}{15}\)
\(c,\frac{11}{12}=\frac{11.4}{12.4}=\frac{44}{48};\frac{7}{48}\)
\(d,\frac{3}{2}=\frac{3.3}{2.3}=\frac{9}{6};\frac{2}{3}=\frac{2.2}{3.2}=\frac{4}{6}\)
\(e,\frac{1}{3}=\frac{1.4}{3.4}=\frac{4}{12};\frac{5}{4}=\frac{5.3}{4.3}=\frac{15}{12};\frac{10}{12}\)
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a) \(\frac{16}{35}+\frac{8}{35}=\frac{24}{35}\)
b)\(\frac{160}{77}-\frac{28}{77}=\frac{132}{77}=\frac{12}{1}=12\)
c)\(\frac{72}{180}=\frac{18}{45}\)
d) \(\frac{90}{360}=\frac{1}{4}\)
\(\frac{8}{15}+\frac{7}{10}+\frac{2}{3}\)
\(=\frac{37}{30}+\frac{2}{3}\)
\(=\frac{19}{10}\)
#Học tốt!