Rút gọn pân số:\(\frac{20^{20}.3^{40}.6^{20}}{12^{50}.3^{15}}\)
Rút gọn phân số sau:
\(M=\frac{\text{2 . 6 . 10 + 4 . 12 . 20 + 6 . 18 . 30 + ..... + 20 . 60 . 100 }}{\text{1 . 2 . 3 + 2 . 4 . 6 + 3 . 6 . 9 + ..... + 10 . 20 . 30}}\)
\(M=\frac{2.6.10+4.12.20+6.18.30+...+20.60.100}{1.2.3+2.4.6+3.6.9+...+10.20.30}\)
\(=\frac{2.6.10.\left(1+2+3+...+10\right)}{1.2.3.\left(1+2+3+...+10\right)}\)
\(=20\)
Rút gọn bt
\(a,A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(b,B=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
\(a,A=\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}\)
\(=\sqrt{\left(\sqrt{5}^2+2\sqrt{5}+2\sqrt{2}\cdot\sqrt{5}\right)+\sqrt{2}^2+2\sqrt{2}\cdot1+1^2}\)
\(=\sqrt{\sqrt{5}^2+2\cdot\sqrt{5}\left(\sqrt{2}+1\right)+\left(\sqrt{2}+1\right)^2}\)
\(=\sqrt{\left(\sqrt{5}+\sqrt{2}+1\right)^2}\)
\(=\sqrt{5}+\sqrt{2}+1\)
\(b,B=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
\(=\left(\frac{3\cdot\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}{\sqrt{6}+1}+\frac{2\left(\sqrt{6}-2\right)\left(\sqrt{6}+2\right)}{\sqrt{6}-2}-\frac{4\left(3-\sqrt{6}\right)\left(3+\sqrt{6}\right)}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
\(=\left[3\cdot\left(\sqrt{6}-1\right)+2\left(\sqrt{6}+2\right)-4\left(3+\sqrt{6}\right)\right]\left(\sqrt{6}+11\right)\)
\(=\left(\sqrt{6}+11\right)\left(\sqrt{6}-11\right)=-115\)
Rút gọn:
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}\)
\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{20}\cdot2^{20}-2^{20}+2^{20}\cdot3^{20}}{2^{20}\cdot3^{20}-3^{20}+3^{20}\cdot3^{20}}=\frac{2^{20}\left[2^{20}-1+3^{20}\right]}{3^{20}\left[2^{20}-1+3^{20}\right]}=\frac{2^{20}}{3^{20}}\)
3. Rút gọn rồi tính: A) 5/10 - 2/15. B) 5/20 - 1/6. C) 6/18 - 6/24. D) 5/9 - 3/12.
A) \(\dfrac{5}{10}-\dfrac{2}{15}\)
\(=\dfrac{1}{2}-\dfrac{2}{15}\)
\(=\dfrac{15}{30}-\dfrac{4}{30}\)
\(=\dfrac{11}{30}\)
B)\(\dfrac{5}{20}-\dfrac{1}{6}\)
\(=\dfrac{1}{4}-\dfrac{1}{6}\)
\(=\dfrac{6}{24}-\dfrac{4}{24}\)
\(=\dfrac{2}{24}=\dfrac{1}{12}\)
C) \(\dfrac{6}{18}-\dfrac{6}{24}\)
\(=\dfrac{1}{3}-\dfrac{1}{4}\)
\(=\dfrac{4}{12}-\dfrac{3}{12}\)
\(=\dfrac{1}{12}\)
D) \(\dfrac{5}{9}-\dfrac{3}{12}\)
\(=\dfrac{5}{9}-\dfrac{1}{4}\)
\(=\dfrac{20}{36}-\dfrac{9}{36}\)
\(=\dfrac{11}{36}\).
a: =1/2-2/15
=15/30-4/30
=11/30
b: =1/4-1/6
=3/12-2/12
=1/12
c: =1/3-1/4
=1/12
d: =20/36-9/36
=11/36
Rút gọn : \(A=\frac{20^{15}.15^{12}}{25^{14}.6^{14}.8^5}\)
\(A=\frac{4^{15}.5^{15}.3^{12}.5^{12}}{5^{28}.2^{14}.3^{14}.2^{15}}=\frac{2.2^{29}.5^{27}.3^{12}}{5.5^{27}.2^{29}.3^{12}.3^2}=\frac{2}{45}\)
\(A=\frac{20^{15}.15^{12}}{25^{14}.6^{14}.8^5}=\frac{\left(2^2.5\right)^{15}.\left(3.5\right)^{12}}{\left(5^2\right)^{14}.\left(2.3\right)^{14}.\left(2^3\right)^5}=\frac{\left(2^2\right)^{15}.5^{15}.3^{12}.5^{12}}{5^{28}.2^{14}.3^{14}.2^{15}}\)
=\(\frac{2^{30}.3^{12}.5^{15}.5^{12}}{5^{28}.3^{14}.2^{14}.2^{15}}=\frac{2^{30}.3^{12}.5^{27}}{5^{28}.3^{14}.2^{29}}=\frac{2}{5.3^2}=\frac{2}{45}\)
Rút gọn rồi tính
A.12/18 + 12/42
B.1/2 + 2/4 + 3/6 + 4/8 + 5/10 + 6/12
D.1/3 + 1/4 + 1/5 + 8/10 + 15/20 +20/30
nhanh nha đang gấp
12/18 + 12/42 = 2/3 + 2/7 = 14/21 + 6/21 = 20/21
1/2 + 2/4 + 3/6 + 4/8 + 5/10 + 6/12
= 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2
= 1/2 x 6
=6/2
=3
rút gọn phân số:15*8-10*7/5*6+20*3
Rút gọn phân số: \(D=\frac{10^8.48^6.18^8-50^2.36^8.12^6}{240^5.72^8.9^3-20^5.96^6.27^7}\)
Mk ghét nhất những dạng bài kiểu như thế này
Rút gọn rồi so sánh hai phân số:
a) 18/72 và 15/20.
b) 24/36 và 20/50.
a. 18/72 = 1/4
15/20 = 3/4
vì 1/4<3/4 nên 18/72<15/20
b. 24/36 = 2/3
20/50 = 2/5
2/3>2/5 nên 24/36>20/50
a, \(\dfrac{18}{72}\) = \(\dfrac{18:18}{72:18}\) = \(\dfrac{1}{4}\); \(\dfrac{15}{20}\) = \(\dfrac{3}{4}\)
Vì \(\dfrac{1}{4}\) < \(\dfrac{3}{4}\) nên \(\dfrac{18}{72}\) < \(\dfrac{15}{20}\)
b, \(\dfrac{24}{36}\) = \(\dfrac{24:12}{36:12}\) = \(\dfrac{2}{3}\); \(\dfrac{20}{50}\) = \(\dfrac{20:10}{50:10}\) = \(\dfrac{2}{5}\)
Vì \(\dfrac{2}{3}\) > \(\dfrac{2}{5}\) nên \(\dfrac{24}{36}\) > \(\dfrac{20}{50}\)
` @ L I N H `
a. 18/72 = 1/4
15/20 = 3/4
vì 1/4<3/4 nên 18/72<15/20
b. 24/36 = 2/3
20/50 = 2/5
2/3>2/5 nên 24/36>20/50