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Bài 1:
a) \(\dfrac{5}{2}+\left(\dfrac{-3}{2}\right)^2\cdot6-\left|-5\right|\)
\(=\dfrac{5}{2}+\dfrac{9}{4}\cdot6-5\)
\(=2,5+13,5-5\)
\(=11\)
b) \(\dfrac{250^3}{50^3}=\dfrac{50^3\cdot5^3}{50^3}=5^3=125\)
Bài 2:
\(A=\left|x+1,5\right|-4,5\)
Vì \(\left|x+1,5\right|\ge0\forall x\)
\(\Rightarrow\left|x+1,5\right|-4,5\ge-4,5\ge0\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x+1,5=0\Rightarrow x=-1,5\)
Vậy MIN \(A=-4,5\Leftrightarrow x=-1,5\)
Bài 1 :
a. \(\dfrac{5}{2}+\left(\dfrac{-3}{2}\right)^2.6-\left|-5\right|\)
\(=\dfrac{5}{2}+\dfrac{9}{4}.6-5\)
\(=\dfrac{5}{2}+\dfrac{27}{2}-5\)
\(=11\)
b. \(\dfrac{250^3}{50^3}=\left(\dfrac{250}{50}\right)^3=5^3=125\)
c. \(\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{\left(5.3.3\right)^{10}.5^{20}}{\left(5.5.3\right)^{15}}=\dfrac{5^{10}.3^{10}.3^{10}.5^{20}}{5^{15}.5^{15}.3^{15}}=\dfrac{5^{30}.3^{20}}{5^{30}.3^{15}}=3^5=243\)
Bài 2 :
\(A=\left|x-1,5\right|-4,5\)
Vì \(\left|x-1,5\right|\ge0\) \(\forall x\)
\(\Rightarrow\left|x-1,5\right|-4,5\ge0-4,5=-4,5\)
hay Amin \(\ge-4,5\)
Amin = -4,5 khi :
\(\left|x-1,5\right|=0\)
\(\Rightarrow x+1,5=0\)
\(\Rightarrow x=-1,5\)
Vậy Amin = -4,5 khi \(x=-1,5\)
\(17.8+51.4=34.4+51.4=4\left(51+34\right)=4.84=336\) \(2.2.3.5.19=\left(2.5\right).\left(3.19\right).2=10.2.57=570.2=1140\) \(54.275+825.15+275=54.275+45.275+275=275\left(54+45+1\right)=100.275=27500\) \(\frac{167.198+98}{198.168-100}=\frac{167.198+98}{198.167+198-100}=\frac{167.198+98}{167.198+98}=1\)
\(\frac{1}{n}-\frac{1}{n+k}=\frac{k}{n\left(n+k\right)}\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{2019.2020}=1-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{2020}=1-\frac{1}{2020}=\frac{2019}{2020}\)
a) 17 x 8 + 51 x 4
= 17 x 4 x 2 + 17 x 3 x 4
= 17 x 4 x ( 2 + 3 )
= 14 x 4 x 5
= 14 x 20
= 280
b) 2 x 2 x 3 x 5 x 19
= ( 2 x 5 ) x ( 3 x 19 ) x 2
= 10 x 57 x 2
= 570 x 2
= 1140
c) 54 x 275 + 825 x 15 + 275
= 54 x 275 + 275 x 3 x 15 + 275 x 1
= 54 x 275 + 275 x 45 + 275 x 1
= 275 x ( 54 + 45 + 1 )
= 275 x 100
= 27500
d) 100 - 99 + 98 - 97 + 96 - 95 + 94 - 93 + ... + 4 - 3 + 2
= (100 - 99) + (98 - 97) + (96 - 95) + (94 - 93) + ... + (4 - 3) + 2
= (1 + 1 + ... + 1) + 2
( 49 số 1 )
= 49 + 2
= 51
k) 1,5 + 2,5 + 3,5 + 4,5 + 5,5 + 6,5 + 7,5 + 8,5
= ( 1,5 + 8,5 ) + ( 2,5 + 7,5 ) + ( 3,5 + 6,5 ) + ( 4,5 + 5,5 )
= 10 + 10 + 10 + 10
= 40
0,48x700-2,4x45x2
=0,48x(700-5x45x2)
=0,48x(700-450)
=0,48x250
=120
4,5+3,5+2,5+1,5+0,5-4-3-2-1
=(4,5-4)+(3,5-3)+(2,5-2)+(1,5-1)+0,5
=0,5+0,5+0,5+0,5+0,5
=0,5x5
=2,5
\(\frac{15}{21}+\frac{4}{42}=\frac{30}{42}+\frac{4}{42}=\frac{30+4}{42}=\frac{34}{42}=\frac{17}{21}\)
\(\frac{75}{100}-\frac{2}{4}=\frac{75}{100}-\frac{50}{100}=\frac{75-50}{100}=\frac{25}{100}=\frac{1}{4}\)
\(\frac{15}{21}+\frac{4}{42}=\frac{15+2}{21}=\frac{17}{21}\)
\(\frac{75}{100}-\frac{2}{4}=\frac{15-10}{20}=\frac{5}{20}=\frac{1}{4}\)
Bài 2 :
1) \(x-70=-45\) 2) \(\frac{4}{7}:x=\frac{12}{28}\)
\(\Rightarrow\) \(x=-45+70\) \(\Rightarrow x=\frac{4}{7}:\frac{12}{28}\)
\(\Rightarrow\) \(x=25\) \(\Rightarrow x=\frac{4}{3}\)
Vậy \(x=25\) Vậy \(x=\frac{4}{3}\)
3) Giống câu c) ở bài 1
4) \(x-50=-35\) 5) \(\frac{4}{7}.x=\frac{11}{18}\)
\(\Rightarrow x=-35+50\) \(\Rightarrow x=\frac{11}{28}:\frac{4}{7}\)
\(\Rightarrow x=15\) \(\Rightarrow x=\frac{77}{72}\)
Vậy \(x=15\) Vậy \(x=\frac{77}{72}\)
6) \(\left(\frac{2}{3}x+2,5\right):2\frac{2}{6}=6\)
\(\Rightarrow\)\(\left(\frac{2}{3}x+2,5\right):\frac{14}{6}=6\)
\(\Rightarrow\) \(\frac{2}{3}x+2,5=6.\frac{14}{6}\)
\(\Rightarrow\frac{2}{3}x+2,5=14\)
\(\Rightarrow\frac{2}{3}x=\frac{23}{2}\)
\(\Rightarrow x=\frac{23}{2}:\frac{2}{3}\)
\(\Rightarrow x=\frac{69}{4}\)
Vậy \(x=\frac{69}{4}\)
Bài 1:
1) \(\frac{7}{5}+\frac{-8}{5}=-\frac{1}{5}\)
2) \(-\frac{6}{5}.\frac{15}{24}=-\frac{3}{4}\)
3) \(\left(\frac{2}{3}+1,5\right)-3,5:7\frac{1}{2}=\)\(\frac{13}{6}-\frac{7}{15}=\frac{17}{10}\)
4) \(\frac{5}{8}-\frac{-7}{9}=\frac{5}{8}+\frac{7}{9}=\frac{101}{72}\)
5)\(\frac{-7}{3}.\frac{12}{28}=-1\)
\(\left(30:\frac{7}{2}+0,5\times3-1,5\right)\times\left(\frac{9}{2}-\frac{9}{2}\right):\left(4,5\times100\right)\)
\(=\left(30:\frac{7}{2}+0,5\times3-1,5\right)\times0:\left(4,5\times100\right)\)
\(=0\)
\(\frac{3}{4}.4,5+\frac{15}{10}.3,5-\frac{75}{100}.1,5\)
\(=0,75+4,5+0,5+3,5+0,75+1,5\)
\(=0,75+\left(4,5+3,5+1,5\right)+0,5\)
\(=0,75+10+0,5\)
\(=10,75+0,5\)
\(=11,25\)