50 + \(\frac{15}{12}\)= ?
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rõ ràng ta chỉ cần so sánh giữa \(15^{30}+16^{12}+17^{50}-16^8\) và \(17^{30}+16^8+15^{50}-16^{12}\)
Áp dụng tính chất nếu a>b thì a-b>0 ta được:
\(15^{30}+16^{12}+17^{50}-16^8\)- \(\left(17^{30}+16^8+15^{50}-16^{12}\right)\)
= \(\left(17^{50}-17^{30}\right)+\left(16^{12}+16^{12}\right)+\left(15^{30}-15^{50}\right)-\left(16^8+16^8\right)\)
= \(\left(17^{50}-17^{30}\right)+\left(15^{30}-15^{50}\right)+2\left(16^{12}-16^8\right)\)
Vì 17^50 - 17^30 > l 15^30 - 15^50 l
nên \(\left(17^{50}-17^{30}\right)+\left(15^{30}-15^{50}\right)>0\)
=>\(15^{30}+16^{12}+17^{50}-16^8\)> \(17^{30}+16^8+15^{50}-16^{12}\)
=> Phân số thứ nhất > 1 và p/s thứ hai < 1
Lúc này bạn tự so sánh nha
\(\dfrac{18}{6}=18:6\)
\(\dfrac{50}{10}=50:10\)
\(\dfrac{15}{15}=15:15\)
\(\dfrac{12}{24}=12:24\)
\(\frac{60^8}{12^7.5^8}=\frac{2^{16}.3^8.5^8}{2^{14}.3^7.5^8}=\frac{2^2.3}{1}=12\)
\(\frac{50^{15}.13^{18}}{25^7.26^{15}.5^{16}}=\frac{2^{15}.5^{30}.13^{18}}{5^{30}.2^{15}.13^{15}}=2197\)
\(\frac{10^4}{5^3}=\frac{5^4.2^4}{5^3}=80\)
\(\frac{60^8}{12^7.5^8}=\frac{2^3.3}{1}=12\)
\(\frac{50^{15}.13^{18}}{25^7.26^{15}}=2197\)
\(10^4:5^3=10000:125=80\)
b ) \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}=\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
215 - 15 x { 25 - 15 : [ 3 x 45 - 3 x ( 50 - 2 x 3 ) ] }
= 215 - 15 x { 25 - 15 : [ 3 x 45 - 3 x 44 ] }
= 215 - 15 x { 25 - 15 : 3 }
= 215 - 15 x 20
= 215 - 300
= -85
b) \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
[\(\frac{-75}{59}\).\(\frac{-107}{93}\)]\(\frac{31}{50}\)=\(\frac{2675}{1829}\).\(\frac{31}{50}\)=\(\frac{107}{118}\)
\(\left[\frac{1\frac{11}{31}\cdot4\frac{3}{7}-\left(15-6\frac{1}{3}\cdot\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-5\frac{1}{3}\right)}\cdot\left(-1\frac{14}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\frac{\frac{42}{31}\cdot\frac{31}{7}-\left(15-\frac{19}{3}\cdot\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-\frac{16}{3}\right)}\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\frac{6-\left(15-\frac{2}{3}\right)}{\frac{29}{6}+\frac{1}{6}\cdot\frac{20}{3}}\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\frac{6-15+\frac{2}{3}}{\frac{29}{6}+\frac{10}{9}}\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\frac{-\frac{25}{3}}{\frac{107}{18}}\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\left(-\frac{150}{107}\right)\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}=\frac{50}{31}\cdot\frac{31}{50}=1\)
\(=\frac{12}{15}.\left(\frac{2}{7}+\frac{3}{7}+\frac{1}{7}+\frac{1}{7}\right)\)
\(=\frac{12}{15}.1\)
\(=\frac{12}{15}=\frac{4}{5}\)
A =\(\frac{\frac{12}{13}+\frac{12}{131}-\frac{12}{1313}+\frac{12}{13131}}{\frac{15}{13}+\frac{15}{131}-\frac{15}{1313}+\frac{15}{13131}}=\frac{12.\left(\frac{1}{13}+\frac{1}{131}-\frac{1}{1313}+\frac{1}{13131}\right)}{15.\left(\frac{1}{13}+\frac{1}{131}-\frac{1}{1313}+\frac{1}{13131}\right)}=\frac{12}{15}=\frac{4}{5}\)
Tick ủng hộ nha mọi người
205/4
\(\frac{205}{4}\)