tính bằng cách thuận tiện
a. \(\frac{1}{2}\times\frac{2}{3}\div\frac{4}{3}\times\frac{4}{5}\div\frac{6}{5}\times\frac{6}{7}\div\frac{7}{8}\times\frac{8}{9}\div\frac{10}{9}\)
b.\(\frac{27}{49}\times\frac{49}{50}\times\frac{15}{51}\times(\frac{5}{10}-\frac{1}{2})\)
(7x6=5+2+6x7) =
\(A=\left(1\frac{1}{6}\times\frac{6}{7}\times6:\frac{3}{5}\right):\left(4\frac{1}{5}\times\frac{10}{11}+5\frac{2}{10}\right)\)
\(B=1\frac{13}{15}\times25\%\times3+\left(\frac{8}{15}-\frac{79}{60}\right):1\frac{23}{4}\)
\(C=\frac{123}{4567}\times\frac{1}{8}+\frac{123}{4567}\times\frac{1}{2}-\frac{123}{4567}\times\frac{13}{8}\)
\(D=\frac{10\frac{1}{3}\times\left(24\frac{1}{2}-15\frac{6}{7}\right)-\frac{12}{11}\times\left(\frac{10}{3}-1,75\right)}{\left(\frac{5}{9}-0,25\right)\times\frac{60}{11}+194\frac{8}{99}}\)
\(\frac{1}{3}\times\frac{2}{5}\times\frac{3}{7}\times\frac{4}{9}\times\frac{5}{11}\times\frac{6}{15}\times\frac{7}{15}\times\frac{8}{15}\times\frac{9}{19}\times\frac{10}{21}\times\frac{11}{32}\times\frac{12}{25}\times\left\{\frac{126}{252}-\frac{2}{4}\right\}\)
Để nhân các phân số này, ta chỉ cần nhân tử số với nhau và mẫu số với nhau:
\[
\frac{1}{3} \times \frac{2}{5} \times \frac{3}{7} \times \frac{4}{9} \times \frac{5}{11} \times \frac{6}{15} \times \frac{7}{15} \times \frac{8}{15} \times \frac{9}{19} \times \frac{10}{21} \times \frac{11}{32} \times \frac{12}{25} \times \left( \frac{126}{252} - 4 \right)
\]
Sau đó, ta thực hiện các phép tính:
1. Nhân tử số:
\[1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10 \times 11 \times 12 \times 126 = 997920\]
2. Nhân mẫu số:
\[3 \times 5 \times 7 \times 9 \times 11 \times 15 \times 15 \times 15 \times 19 \times 21 \times 32 \times 25 \times 252 = 7621237680\]
Kết quả là:
\[\frac{997920}{7621237680}\]
Bây giờ, ta có thể rút gọn phân số này bằng cách chia tử số và mẫu số cho 160:
\[ \frac{997920}{7621237680} = \frac{997920 ÷ 160}{7621237680 ÷ 160} = \frac{6237}{47695230} \]
1. tìm tích của A= \(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times..\times\frac{899}{900}\)
2. CMR \(\frac{1}{5}+\frac{1}{6}+..+\frac{1}{17}< 2\)
3. tính \(M=\frac{1}{1.2.3}+\frac{1}{2.3.4}+..+\frac{1}{10.11.12}\)
3. \(M=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{10.11.12}\)
\(\Leftrightarrow2M=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{10.11.12}\)
\(\Leftrightarrow2M=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{10.11}-\frac{1}{11.12}\)
\(\Leftrightarrow2M=\frac{1}{1.2}-\frac{1}{11.12}\)
\(\Leftrightarrow2M=\frac{1}{2}-\frac{1}{132}\)
\(\Leftrightarrow2M=\frac{65}{132}\)
\(\Leftrightarrow M=\frac{65}{132}\div2\)
\(\Leftrightarrow M=\frac{65}{264}\)
1\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{899}{900}\)
\(\Leftrightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{29.31}{30.30}\)
\(\Leftrightarrow A=\frac{1.3.2.4.3.5...29.31}{2.2.3.3.4.4...30.30}\)
\(\Leftrightarrow A=\frac{\left(1.2.3....29\right)\left(3.4.5...31\right)}{\left(2.3.4...30\right)\left(2.3.4...30\right)}\)
\(\Leftrightarrow A=\frac{1.31}{30.2}\)
\(\Leftrightarrow A=\frac{31}{60}\)
2. Đặt \(A=\frac{1}{5}+\frac{1}{6}+...+\frac{1}{17}\)
\(\Rightarrow A< \frac{1}{5}+\frac{1}{5}+...+\frac{1}{5}+\frac{1}{8}+\frac{1}{8}+...+\frac{1}{8}\)
\(\Rightarrow A< 1+1=2\)
Vậy a < 2 (đpcm)
Tính hợp lí:
A =\((\frac{2}{7}\times\frac{1}{4}-\frac{1}{3}\times\frac{2}{7})\div(\frac{2}{7}\times\frac{3}{9}-\frac{2}{7}\times\frac{2}{5})\)
B = \(\frac{(\frac{1}{5}-\frac{2}{7})\times\frac{3}{4}-\frac{3}{4}\times(\frac{1}{3}-\frac{2}{7})}{\frac{1}{5}\times\frac{2}{7}-\frac{1}{3}\times(\frac{2}{7}+\frac{3}{9})+\frac{3}{9}\times\frac{1}{5}}\)
CÓ LỜI GIẢI THÍCH CHI TIETS NHÉ AI NHANH MK TICK
A=\([\)\(\frac{2}{7}\)\(\times\)(\(\frac{1}{4}-\frac{1}{3}\))\(]\)\(\div\)\([\)(\(\frac{2}{7}\times\)(\(\frac{3}{9}-\frac{2}{5}\))\(]\)
=(\(\frac{2}{7}\times\)\(\frac{-1}{12}\))\(\div(\)\(\frac{2}{7}\times\)\(\frac{-1}{15}\))
=\(\frac{-1}{42}\)\(\div\)\(\frac{-2}{35}\)
=\(\frac{-1}{42}\)\(\times\)\(\frac{35}{-2}\)
=\(\frac{5}{12}\)
TÍNH : E=\(\frac{2^2}{3}\times\frac{3^2}{8}\times\frac{4^2}{15}\times\frac{5^2}{24}\times\frac{6^2}{35}\times\frac{7^2}{48}\times\frac{8^2}{63}\times\frac{9^2}{80}\)
\(E=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}...\frac{9^2}{8.10}=\frac{\left(2.3.4...9\right)^2}{1.2.\left(3.4...8\right)^2.9.10}=\frac{2^2.9^2}{1.2.9.10}=\frac{18}{10}=\frac{9}{5}\)
Tính.
a) $\frac{1}{6} \times \frac{2}{3}$
b) $\frac{6}{5} \times \frac{3}{8}$
c) $\frac{4}{3} \times \frac{8}{9}$
d) $\frac{5}{{12}} \times \frac{{12}}{5}$
a) $\frac{1}{6} \times \frac{2}{3} = \frac{{1 \times 2}}{{6 \times 3}} = \frac{2}{{18}} = \frac{1}{9}$
b) $\frac{6}{5} \times \frac{3}{8} = \frac{{6 \times 3}}{{5 \times 8}} = \frac{{18}}{{40}} = \frac{9}{{20}}$
c) $\frac{4}{3} \times \frac{8}{9} = \frac{{4 \times 8}}{{3 \times 9}} = \frac{{32}}{{27}}$
d) $\frac{5}{{12}} \times \frac{{12}}{5} = \frac{{5 \times 12}}{{12 \times 5}} = \frac{{60}}{{60}} = 1$
Cho biểu thức A= \(\frac{2}{1}\times\frac{4}{3}\times\frac{6}{5}\times\frac{8}{7}\times\frac{10}{9}\times...\times\frac{100}{99}\)Chứng minh rằng 12<A<13
Cho \(A=\frac{2}{1}\times\frac{3}{2}\times\frac{6}{5}\times...\times\frac{200}{199}\)
CMR: A < 20