\(a,\dfrac{9}{17}+\dfrac{15}{4}=\dfrac{36}{68}+\dfrac{255}{68}=\dfrac{291}{68}\\ b,\dfrac{19}{121}-\dfrac{1}{11}=\dfrac{19}{121}-\dfrac{11}{121}=\dfrac{8}{121}\\ c,\dfrac{4}{15}+3=\dfrac{4}{15}+\dfrac{45}{15}=\dfrac{49}{15}\\ d,3-\dfrac{5}{9}=\dfrac{27}{9}-\dfrac{5}{9}=\dfrac{22}{9}\)

\(a,\dfrac{9}{17}+\dfrac{15}{4}=\dfrac{36}{68}+\dfrac{255}{68}=\dfrac{291}{68}\)

\(b,\dfrac{19}{121}-\dfrac{1}{11}=\dfrac{19}{121}-\dfrac{11}{121}=\dfrac{8}{121}\)

\(c,\dfrac{4}{15}+3=\dfrac{4}{15}+\dfrac{3}{1}=\dfrac{4}{15}+\dfrac{45}{15}=\dfrac{49}{15}\)

\(d,3-\dfrac{5}{9}=\dfrac{3}{1}-\dfrac{5}{9}=\dfrac{27}{9}-\dfrac{5}{9}=\dfrac{22}{9}\)

`A) 9/17 + 15/4 = 36/68 + 255/68 = 291/68 `

` B) 19/121 - 1/11= 19/121 - 11/121 = 8/121 ` 

` C) 4/15 + 3 = 4/15 + 45/15 = 49/15 `

` D) 3 - 5/9 = 27/9 - 5/9 = 22/9 `

1. So sánh

a) \(25^{50}\) và \(2^{300}\)

\(25^{50}=25^{1.50}=\left(25^1\right)^{50}=25^{50}\)

\(2^{300}=2^{6.50}=\left(2^6\right)^{50}=64^{50}\)

Vì \(25< 64\) nên \(25^{50}< 64^{50}\)

Vậy \(25^{50}< 2^{300}\)

b) \(625^{15}\) và \(12^{45}\)

\(625^{15}=625^{1.15}=\left(625^1\right)^{15}=625^{15}\)

\(12^{45}=12^{3.15}=\left(12^3\right)^{15}=1728^{15}\)

Vì \(625< 1728\) nên \(625^{15}< 1728^{15}\)

Vậy \(625^{15}< 12^{45}\)

1.So sánh

a)\(25^{50}\) và \(2^{300}\)

Ta có : \(2^{300}=\left(2^6\right)^{50}=64^{50}\)

Vì \(25^{50}< 64^{50}\) nên \(25^{50}< 2^{300}\)

b)\(625^{15}\) và \(12^{45}\)

Ta có : \(12^{45}=\left(12^3\right)^{15}=1728^{15}\)

Vì \(625^{15}< 1728^{15}\) nên \(625^{15}< 12^{45}\)

\(\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{121}{120}.\frac{144}{143}\)

\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}...\frac{11.11}{10.12}.\frac{12.12}{11.13}\)

\(=\frac{2.2.3.3.4.4.5.5...11.11.12.12}{1.3.2.4.3.5.4.6...10.12.11.13}\)

\(=\frac{\left(2.3.4.5...11.12\right).\left(2.3.4.5...11.12\right)}{\left(1.2.3.4...10.11\right).\left(3.4.5.6...12.13\right)}\)

\(=\frac{12.2}{1.13}\)

\(=\frac{24}{13}\)

  ( Dấu \(.\)là dấu \(\times\)nha )

`a, 4/9 + 2/5 + 5/9= (4/9 +5/9) + 2/5= 1 + 2/5= 5/5 + 2/5= 7/5`

`b, 6/13 + 5/8 + 7/13=(6/13 + 7/13) + 5/8=1+5/8= 8/8 + 5/8= 13/8`

`c, 5/11 + 6/25 + 66/121 = ( 5/11 + 66/121 ) + 6/25=1 + 6/25 = 25/25 + 6/25 = 31/25`

`d, 1/2 + 1/3 + 1/4 + 1/6 + 1/12 + 1/24= (1/2 + 1/4) +(1/3 + 1/6) + (1/12 + 1/24)= 3/4 + 1/2 + 1/8=  6/8 + 4/8 + 1/8= 11/8`

`@ yl`

BAI 1 ; 

Bài 2: 

a, \(\dfrac{5}{23}\) \(\times\) \(\dfrac{17}{26}\) + \(\dfrac{5}{23}\) \(\times\) \(\dfrac{9}{26}\) 

= \(\dfrac{5}{23}\) \(\times\) ( \(\dfrac{17}{26}\) + \(\dfrac{9}{26}\))

= \(\dfrac{5}{23}\) \(\times\) \(\dfrac{26}{26}\)

= \(\dfrac{5}{23}\) 

b, \(\dfrac{3}{4}\) \(\times\) \(\dfrac{7}{9}\) + \(\dfrac{7}{4}\)  \(\times\) \(\dfrac{3}{9}\)

= \(\dfrac{7}{12}\) + \(\dfrac{7}{12}\)

= \(\dfrac{14}{12}\)

= \(\dfrac{7}{6}\)

1,a) \(\dfrac{17}{20}=\dfrac{51}{60};\dfrac{13}{15}=\dfrac{52}{60}\)

\(a,121-\left(115+x\right)=3x-\left(25-9-5x\right)-8\\ 121-115-x=3x-25+9+5x-8\\ 6-x=8x-24\\ 8x+x=-24-6\\ 9x=-30\\ x=-\dfrac{30}{9}=-\dfrac{10}{3}\\ ----\\ b,2^{x+2}.3^{x+1}.5^x=10800\\ \left(2.3.5\right)^x.2^2.3=10800\\ 30^x.12=10800\\ 30^x=\dfrac{10800}{12}=900=30^2\\ Vậy:x=2\)

a) \(A=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}.....\dfrac{120}{121}.\dfrac{143}{144}\)

= \(\dfrac{1.3.2.4.3.5.4.6....10.12.11.13}{2^2.3^2.4^2.5^2...11^2.12^2}\)

= \(\dfrac{1.2.12.13}{2^2.12^2}=\dfrac{13}{2.12}=\dfrac{13}{24}\)

b) \(B=\dfrac{5}{9}.\dfrac{21}{25}.\dfrac{45}{49}.\dfrac{77}{81}....\dfrac{357}{361}.\dfrac{437}{441}\)

= \(\dfrac{1.5.3.7.5.9.7.11.....17.21.19.23}{3^2.5^2.7^2....19^2.21^2}=\dfrac{1.3.21.23}{3^2.21^2}\)

= \(\dfrac{23}{3.21}=\dfrac{23}{63}\)