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\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+\frac{2}{15.17}\)
\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{17}\)
\(A=1-\frac{1}{17}\)
\(A=\frac{16}{17}\)
\(B=\frac{4}{1.3}+\frac{4}{3.5}+...+\frac{4}{9.11}+\frac{4}{11.13}\)
\(B=\frac{4}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(B=\frac{4}{2}\left(1-\frac{1}{13}\right)\)
\(B=\frac{4}{2}\cdot\frac{12}{13}\)
\(B=\frac{24}{13}\)
=> A= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}\)
=> A= \(\frac{1}{1}-\frac{1}{17}\)
=> A= \(\frac{16}{17}\)
\(\Rightarrow B=2.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{1}-\frac{1}{13}\right)\)
\(\Rightarrow B=2.\frac{12}{13}\)
\(\Rightarrow B=\frac{24}{13}\)
a) \(1284-16401:231+58\) x\(11=1284-71+638\)
\(=1851\)
b)\(\frac{7}{4}+1\frac{1}{2}\)x \(1\frac{3}{2}:\frac{1}{4}=\frac{7}{4}+15\)
\(=\frac{67}{4}\)
c)\(2\frac{1}{4}+1\frac{2}{5}+\frac{4}{20}\)\(=\frac{9}{4}+\frac{7}{5}+\frac{1}{5}\)
\(=\frac{77}{20}\)
d)\(\left(\frac{12}{5}+\frac{2}{3}-\frac{11}{4}\right):\frac{3}{4}=\frac{19}{60}:\frac{3}{4}\)
\(=\frac{19}{60}\)x \(\frac{4}{3}\)
\(=\frac{19}{45}\)
\(8\frac{7}{10}+2\frac{3}{4}=\frac{87}{10}+\frac{11}{4}=\frac{174}{20}+\frac{55}{20}=\frac{229}{20}\)
Bạn chỉ cần đưa về phân số xong tính bình thường. Muốn đổi từ hỗn số sang phân số, ta chỉ cần lấy phần nguyên nhân cho mẫu rồi cộng với tử là xong. Chứ bạn cứ hỏi mấy bài dễ như thế này thì k giỏi đc đâu!!!
\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}+\frac{1}{3}\right)=\frac{4}{5}.\frac{3}{3}=\frac{4}{5}.1=\frac{4}{5}\)
\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}+\frac{1}{6}\right)=\frac{3}{4}:\frac{2}{3}=\frac{9}{8}\)
\(\frac{2}{3}.\frac{4}{5}-\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}-\frac{1}{3}\right)=\frac{4}{5}.\frac{1}{3}=\frac{4}{15}\)
\(\frac{1}{2}:\frac{3}{4}-\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{3}{4}:\frac{1}{3}=\frac{9}{4}\)
\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\left(\frac{2}{3}+\frac{1}{3}\right).\frac{4}{5}=1.\frac{4}{5}=\frac{4}{5}\)
\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{1}{2}.\frac{4}{3}+\frac{1}{6}.\frac{4}{3}=\left(\frac{1}{2}+\frac{1}{6}\right).\frac{4}{3}=\frac{2}{3}.\frac{4}{3}=\frac{8}{9}\)
c,d tương tự
\(2\frac{3}{4}< 2.\frac{3}{4}\left(s\right)\)
\(2\frac{3}{4}=2\cdot\frac{3}{4}\left(s\right)\)
\(2\frac{3}{4}>2.\frac{3}{4}\left(\text{đ}\right)\)
\(3\frac{3}{4}\times4=\frac{3\times4+3}{4}\times4=\frac{15}{4}\times4=\frac{15\times4}{4}=15\)
\(4\frac{3}{2}\div1\frac{1}{2}=\frac{4\times2+3}{2}\div\frac{1\times2+1}{2}=\frac{11}{2}\div\frac{3}{2}=\frac{11}{2}\times\frac{2}{3}=\frac{11}{3}\)
\(4\frac{3}{4}+2\frac{3}{2}=\frac{4\times4+3}{4}+\frac{2\times2+3}{2}=\frac{19}{4}+\frac{7}{2}=\frac{19}{4}+\frac{14}{4}=\frac{33}{4}\)
\(3\frac{8}{6}-4\frac{1}{3}=\frac{3\times8+6}{6}-\frac{4\times3+1}{3}=\frac{30}{6}-\frac{13}{3}=\frac{30}{6}-\frac{26}{6}=\frac{4}{6}=\frac{2}{3}\)
\(3\frac{2}{4}\)x 4 = \(\frac{14}{4}\)x 4 = \(\frac{56}{4}\)
\(4\frac{3}{2}\): \(1\frac{1}{2}\)= \(\frac{11}{2}\): \(\frac{3}{2}\)= \(\frac{11}{2}\)x \(\frac{2}{3}\)= \(\frac{22}{6}\)= \(\frac{11}{3}\)
\(4\frac{3}{4}\)+ \(2\frac{3}{2}\)= \(\frac{11}{4}\)+ \(\frac{7}{2}\)= \(\frac{25}{4}\)= 6,25
\(3\frac{8}{6}\)- \(4\frac{1}{3}\)= \(\frac{13}{3}\)- \(\frac{13}{3}\)= 0
\(\Leftrightarrow\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\)
\(\Rightarrow=\frac{1}{3}-\frac{1}{111}\)
\(=\frac{12}{37}\)
k nha
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\)
\(=\frac{1}{3}-\frac{1}{111}\)
\(=\frac{108}{333}=\frac{12}{37}\)