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`@` `\text {Ans}`
`\downarrow`
`1,`
`a)`
`5 \times 72 \times 10 \times 2`
`= 5 \times 2 \times 10 \times 72`
`= 10 \times 10 \times 72`
`= 100 \times 72`
`= 7200`
`b)`
`40 \times 125`
`= 4 \times 10 \times 25 \times 5`
`= (5 \times 10) \times (4 \times 25)`
`= 50 \times 100`
`= 5000`
`c)`
`4 \times 2021 \times 25`
`= (4 \times 25) \times 2021`
`= 100 \times 2021`
`= 202100`
`d)`
`16 \times 6 \times 25`
`= 4 \times 4 \times 6 \times 25`
`= (4 \times 25) \times 4 \times 6`
`= 100 \times 24`
`= 2400`
`2,`
`a)`
`24 \times 57 + 43 \times 24`
`= 24 \times (57+43)`
`= 24 \times 100`
`= 2400`
`b)`
`12 \times 19 + 80 \times 12 +12`
`= 12 \times (19 + 80 + 1)`
`= 12 \times 100`
`= 1200`
`c)`
`(36 \times 15 \times 169) \div (5 \times 18 \times 13)`
`= 36 \times 15 \times 169 \div 5 \div 18 \div 13`
`= 6 \times 6 \times 3 \times 5 \times 13 \times 13 \div 5 \div 3 \times 6 \div 13`
`= (6 \div 6) \times (3 \div 3) \times (5 \div 5) \times (13 \div 13) \times 6 \times 13`
`= 6 \times 13`
`= 78`
`d)`
`(44 \times 52 \times 60) \div ( 11 \times 13 \times 15)`
`= 44 \times 52 \times 60 \div 11 \div 13 \div 15`
`= 4 \times 11 \times 13 \times 4 \times 15 \times 4 \div 11 \div 13 \div 15`
`= (11 \div 11) \times (13 \div 13) \times (15 \div 15) \times 4 \times 4 \times`
`= 4 \times 4 \times 4`
`= 64`
`3,`
`a)`
`x - 280 \div 35 = 5 \times 54`
`x - 8 = 270`
`x = 270 + 8`
`x = 278`
`b)`
`(x - 280) \div 35 = 54 \div 4`
`(x - 280) \div 35 = 13,5`
`x - 280 = 13,5 \times 35`
`x - 280 = 472,5`
`x = 472,5 + 280`
`x = 752,5`
`c)`
`(x - 128 + 20) \div 192 = 0`
`x - 128 + 20 = 0 \times 192`
`x - 128 + 20 = 0`
`x - 108 = 0`
`x = 0 + 108`
`x = 108`
`d)`
`4 \times (x + 200) = 460 + 85 \times 4`
`4 \times (x+200) = 460 + 340`
`4 \times (x+200) = 800`
`x + 200 = 800 \div 4`
`x + 200 = 200`
`x = 200 - 200`
`x = 0`
`4,`
`a)`
`7/12 - 5/12`
`= (7 - 5)/12`
`= 2/12`
`= 1/6`
`b)`
`8/11 + 19/11`
`= (8+19)/11`
`= 27/11`
`c)`
`3/8 + 5/12`
`= 9/24 + 10/24`
`= 19/24`
`d)`
`3/4 + 7/12`
`= 9/12 + 7/12`
`= 16/12`
`= 4/3`
`5,`
`a)`
`x - 6/7 = 5/2`
`x = 5/2 + 6/7`
`x = 47/14`
`b)`
`12/7 \div x + 2/3 = 7/5`
`12/7 \div x = 7/5 - 2/3`
`12/7 \div x = 11/15`
`x = 12/7 \div 11/15`
`x = 180/77`
`@` `\text {Kaizuu lv uuu}`
\(S=\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{496\cdot501}\)
\(S=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}-\frac{1}{501}\right)\)
\(S=\frac{1}{5}\left(1-\frac{1}{501}\right)\)
\(S=\frac{1}{5}\cdot\frac{500}{501}\)
\(S=\frac{100}{501}\)
a) \(85\times16+16\times15\)
\(=16\times\left(85+15\right)\)
\(=16\times100=1600\)
b) \(\left(\dfrac{3}{7}\times\dfrac{11}{15}+\dfrac{3}{7}\times\dfrac{4}{15}\right):\left(4+2\dfrac{6}{11}-\dfrac{6}{11}\right)\)
\(=\left[\dfrac{3}{7}\times\left(\dfrac{11}{15}+\dfrac{4}{15}\right)\right]:\left(4+\dfrac{28}{11}-\dfrac{6}{11}\right)\)
\(=\dfrac{3}{7}\times1:\left(4+2\right)\)
\(=\dfrac{3}{7}:6\)
\(=\dfrac{3}{7}\times\dfrac{1}{6}=\dfrac{3}{42}=\dfrac{1}{14}\)
c) \(x+\left(x+3\right)+\left(x+6\right)+...+\left(x+102\right)=1855\)
\(\Rightarrow35x+\left(3+6+...+102\right)=1855\)
\(\Rightarrow35x+\left(102+3\right)\times34:2=1855\)
\(\Rightarrow35x+1785=1855\)
\(\Rightarrow35x=1855-1785\)
\(\Rightarrow35x=70\)
\(\Rightarrow x=70:35\)
\(\Rightarrow x=2\)
Vậy...
\(#Tmiamm\)
Ta có:
A = 1 + 3 + 5 + 7 +... + 101
A = \(\frac{102.51}{2}=2601\)
M = 16 - 18 + 20 - 22 + 24 - 26 + .. + 64 - 66 + 68
M = ( 16 - 18 ) + ( 20 - 22 ) + ( 24 - 26 ) + ... + ( 64 - 66 ) + 68
M = (- 2 + - 2 + -2 + ... + - 2 ) + 68
M = 25/2 . ( - 2 ) + 68
M = -25 + 68
M = 43
H = ( 1 + 2 + 3 +...+ 99 ) x ( 13 x 15 - 12 x 15 - 15 )
H = ( 1 + 2 + 3 +...+ 99 ) x { (13 - 12 - 1) x 15 }
H = ( 1 + 2 + 3 +...+ 99 ) x 0
H = 0
G = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 + 13 + 14 - ... + 301 + 302
G = ( 1 + 2 ) + ( -3 - 4 ) + ( 5 + 6 ) + ( -7 - 8 ) + ( 9 + 10 ) + ( - 11 - 12 ) + ( 13 + 14 ) -...+ ( 301 + 302 )
G = ( 3 - 7 ) + ( 11 - 15 ) + ( 19 - 23 ) + 27 - ... + 603
G = -4 + - 4 + -4 + 27 - ... + 603
G = 75 x ( -4 ) + 603
G = -300 + 603
G = 303
2.
a) 1 + 2 + 3 + 4 +...+ 99 + 100 + 2 x X = 5052
= > \(\frac{100.101}{2}\)+ 2 x X = 5052
= > 5050 + 2 x X = 5052
= > 2X = 2
= > X = 1