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= \(\frac{9}{1x4}+\frac{9}{4x7}+\frac{9}{7x10}+.........+\frac{9}{19x22}+\frac{9}{22x25}\)
= \(\frac{1}{3}x\left(\frac{9}{1}-\frac{9}{4}\right)+\left(\frac{9}{4}-\frac{9}{7}\right)x\frac{1}{3}+........+\left(\frac{9}{22}-\frac{9}{25}\right)x\frac{1}{3}\)
= \(\frac{1}{3}\left(\frac{9}{1}-\frac{9}{4}+\frac{9}{4}-\frac{9}{7}+....+\frac{9}{22}-\frac{9}{25}\right)\)
= \(\frac{1}{3}x\left(\frac{9}{1}-\frac{9}{25}\right)\)
= \(\frac{1}{3}x\frac{216}{25}\)
= \(\frac{72}{25}\)
nhớ ********** nha bn thân
\(\frac{9}{4}+\frac{9}{28}+\frac{9}{70}+\frac{9}{130}+...+\frac{9}{418}+\frac{9}{550}\)
\(=3\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{19.22}+\frac{3}{22.25}\right)\)
\(=3\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{22}-\frac{1}{25}\right)\)
\(=3\left(1-\frac{1}{25}\right)\)
\(=3.\frac{24}{25}=\frac{72}{25}\)
a) x+ \(\frac{4}{5}\)= \(\frac{4}{5}\)+ ( \(\frac{3}{7}\)+ \(\frac{3}{5}\))
x + \(\frac{4}{5}\)= \(\frac{4}{5}\)+ \(\frac{36}{35}\)
=> x = \(\frac{36}{35}\)
Vậy : x = \(\frac{36}{35}\)
b) \(\frac{4}{9}\)+\(\frac{8}{9}\)+ \(\frac{12}{9}\)+ ... + \(\frac{56}{9}\)
= \(\frac{4+8+12+...+56}{9}\)
Ta có : 4+8+12 + ... +56
Số các số hạng của dẫy số trên là : ( 56 -4) + 4 +1 = 14 ( số hạng )
=> Tổng trên = ( 4+56) x 14 : 2 = 420
=> \(\frac{4}{9}\)+ \(\frac{8}{9}\)+ ... + \(\frac{56}{9}\)= \(\frac{420}{9}\)= \(\frac{140}{3}\)
a)x=3/7+3/5=3x(1/7+1/5)=36/35
b)=(4+8+...+56)/9=(56+4)x14/9=280/3
a) \(\frac{3}{5}+\frac{4}{7}+\frac{2}{5}+\frac{1}{7}+\frac{2}{7}\)
\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{4}{7}+\frac{1}{7}+\frac{2}{7}\right)\)
\(=\frac{5}{5}+\frac{7}{7}=1+1=2\)
a) \(\frac{3}{5}+\frac{4}{7}+\frac{2}{5}+\frac{1}{7}+\frac{2}{7}\)
\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{4}{7}+\frac{1}{7}+\frac{2}{7}\right)\)
= 1 + 1
= 2
b) \(\frac{4}{9}+\frac{8}{9}+\frac{12}{9}+\frac{16}{9}+...+\frac{48}{9}+\frac{52}{9}+\frac{56}{9}\)
\(=\frac{4+8+12+16+...+48+52+56}{9}\)
Xét 4 + 8 + 12 + 16 + ... + 48 + 52 + 56
Số các số hạng là:
(56 - 4) : 4 + 1 = 14 (số)
4 + 8 + 12 + 16 + ... + 48 + 52 + 56 = (56 + 4) x 14 : 2 = 420
\(\frac{4+8+12+16+...+48+52+56}{9}=\frac{420}{9}=\frac{140}{3}\)
\(\frac{4}{9}+\frac{4}{9}=\frac{5+3}{9}=\frac{8}{9}\)
a) $\frac{7}{9} \times \frac{{15}}{{28}} \times \frac{9}{7} = (\frac{7}{9} \times \frac{9}{7}) \times \frac{{15}}{{28}} = 1 \times \frac{{15}}{{28}} = \frac{{15}}{{28}}$
b) $\frac{9}{{32}} \times \left( {\frac{2}{3} \times \frac{{14}}{{21}}} \right) = \frac{9}{{32}} \times \left( {\frac{2}{3} \times \frac{2}{3}} \right) = \frac{9}{{32}} \times \frac{4}{9} = \frac{{36}}{{288}} = \frac{1}{8}$
Câu 1:\(\frac{12}{23}\times\frac{9}{28}+\frac{11}{23}\times\frac{9}{28}\)
\(=\frac{9}{28}\times\left(\frac{12}{23}+\frac{11}{23}\right)\)
\(=\frac{9}{28}\times\frac{23}{23}\)
\(=\frac{9}{28}\times1\)
\(=\frac{9}{28}\)
Câu 2:
\(3+\frac{1}{9}+\frac{3}{9}+2+\frac{5}{9}+3+2\)
\(=\left(3+2+2+3\right)+\left(\frac{1}{9}+\frac{3}{9}+\frac{5}{9}\right)\)
\(=10+\frac{9}{9}\)
\(=10+1\)
\(=11\)
\(\frac{12}{23}x\frac{9}{28}+\frac{11}{23}x\frac{9}{28}=\)\(\left(\frac{12}{23}+\frac{11}{23}\right)x\frac{9}{28}\)\(=\) \(1x\frac{9}{28}=\frac{9}{28}\)
\(3+\frac{1}{9}+\frac{3}{9}+2+\frac{5}{9}+3+2\)\(=\) \(\left(\frac{1}{9}+\frac{3}{9}+\frac{5}{9}\right)+\left(3+2+3+2\right)\)\(=\) \(1+3+2+3+2=\)\(11\)
$\frac{2}{3} = \frac{{2 \times 3}}{{3 \times 3}} = \frac{6}{9}$
$\frac{3}{4} = \frac{{3 \times 3}}{{4 \times 3}} = \frac{9}{{12}}$
Vậy $\frac{2}{3} = \frac{6}{9}$ ; $\frac{3}{4} = \frac{9}{{12}}$
\(\dfrac{2}{3}=\dfrac{6}{9}\)
\(\dfrac{3}{4}=\dfrac{9}{12}\)
\(\frac{9}{9}+\frac{9}{9}=1+1=2\)
Tích tớ nha
\(\frac{9}{9}+\frac{9}{9}=\frac{9+9}{9}=\frac{18}{9}=2\)
ủng hộ nha