Tính nhanh:
\(\dfrac{17}{13}:\dfrac{51}{26}=\dfrac{17}{13}x\dfrac{26}{51}=\dfrac{17x13x2}{13x17x3}=\dfrac{2}{3}\)
\(\dfrac{33}{38}:\dfrac{11}{19}\)=?
Tính nhanh:
\(\dfrac{17}{13}:\dfrac{51}{26}=\dfrac{17}{13}x\dfrac{26}{51}=\dfrac{17x13x2}{13x17x3}=\dfrac{2}{3}\)
\(\dfrac{33}{38}:\dfrac{11}{19}\)=?
\(\dfrac{33}{38}:\dfrac{11}{19}=\dfrac{33\times19}{38\times11}=\dfrac{3\times1}{2\times1}=\dfrac{3}{2}\)
Tìm số nguyên x, biết: ( \(\dfrac{31}{20}-\dfrac{26}{45}\) ) . \(\dfrac{-36}{35}< x< \left(\dfrac{51}{56}+\dfrac{8}{21}+\dfrac{1}{3}\right).\dfrac{8}{13}\)
=\(\dfrac{35}{36}.\dfrac{-36}{35}< x< \dfrac{13}{8}.\dfrac{8}{13}\)
= -1 < x < 1
vậy x = 0
Bài 3 : Tính
a) \(\dfrac{2}{5}+\dfrac{11}{15}\) b) \(\dfrac{2}{7}-\dfrac{2}{11}\) c) \(\dfrac{11}{13}\) x \(\dfrac{26}{31}\) d) \(\dfrac{1}{2}:\dfrac{1}{3}\) x \(\dfrac{2}{5}\)
giúp mik với , giải rõ ràng ra nha . ( đùưng vào nói ltinh gì zới mik nha )
a \(\dfrac{6}{15}+\dfrac{11}{15}=\dfrac{17}{15}\)
b \(\dfrac{22}{77}-\dfrac{14}{77}=\dfrac{8}{77}\)
c \(\dfrac{11}{13}\times\dfrac{26}{31}=11\times\dfrac{2}{31}=\dfrac{22}{31}\)
d \(\dfrac{1}{2}\times3\times\dfrac{2}{5}=\dfrac{3}{5}\)
a, 2/5 + 11/15 = 6/15 + 11/15 = 17/15
b,2/7 - 2/11 = 22/77 - 14/77 = 8/77
c, 11/13 x 26/31= 11 x 2/31 =22/31
d, 1/2 : 1/3 x 2/5
= ( 1/2 x 2/5 ) : 1/3
= 1/5 : 1/3
= 3/5
Thực hiện phét tính B=\(\dfrac{155-\dfrac{10}{7}-\dfrac{5}{11}+\dfrac{5}{23}}{403-\dfrac{26}{7}-\dfrac{13}{11}+\dfrac{13}{23}}+\dfrac{\dfrac{-3}{5}-\dfrac{3}{13}+0,9}{\dfrac{2}{5}+\dfrac{2}{13}-\dfrac{6}{10}}\)
GIẢI PHƯƠNG TRÌNH
1)\(\dfrac{x+1}{35}+\dfrac{x+3}{33}=\dfrac{x+5}{31}+\dfrac{x+7}{29}\)
2)x(x+1)(x+2)(x+3)=24
3)\(\dfrac{x-1}{13}-\dfrac{2x-13}{15}=\dfrac{3x-15}{27}-\dfrac{4x-27}{29}\)
4)\(\dfrac{1909-x}{91}+\dfrac{1907-x}{93}+\dfrac{1905-x}{95}+\dfrac{1903-x}{91}+4=0\)
1) PT \(\Leftrightarrow\left(\dfrac{x+1}{35}+1\right)+\left(\dfrac{x+3}{33}+1\right)=\left(\dfrac{x+5}{31}+1\right)+\left(\dfrac{x+7}{29}+1\right)\)
\(\Leftrightarrow\dfrac{x+36}{35}+\dfrac{x+36}{33}=\dfrac{x+36}{31}+\dfrac{x+36}{29}\)
\(\Leftrightarrow\left(x+36\right)\left(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}\right)=0\)
\(\Leftrightarrow x+36=0\) (Do \(\dfrac{1}{29}+\dfrac{1}{31}-\dfrac{1}{33}-\dfrac{1}{35}>0\))
\(\Leftrightarrow x=-36\).
Vậy nghiệm của pt là x = -36.
2) x(x+1)(x+2)(x+3)= 24
⇔ x.(x+3) . (x+2).(x+1) = 24
⇔(\(x^2\) + 3x) . (\(x^2\) + 3x + 2) = 24
Đặt \(x^2\)+ 3x = b
⇒ b . (b+2)= 24
Hay: \(b^2\) +2b = 24
⇔\(b^2\) + 2b + 1 = 25
⇔\(\left(b+1\right)^2\)= 25
+ Xét b+1 = 5 ⇒ b=4 ⇒ \(x^2\)+ 3x = 4 ⇒ \(x^2\)+4x-x-4=0 ⇒x(x+4)-(x+4)=0
⇒(x-1)(x+4)=0⇒x=1 và x=-4
+ Xét b+1 = -5 ⇒ b=-6 ⇒ \(x^2\)+3x=-6 ⇒\(x^2\) + 3x + 6=0
⇒\(x^2\) + 2.x.\(\dfrac{3}{2}\) + (\(\dfrac{3}{2}\))2 = - \(\dfrac{15}{4}\) Hay ( \(x^2\) +\(\dfrac{3}{2}\) )2= -\(\dfrac{15}{4}\) (vô lí)
⇒x= 1 và x= 4
Bài 1 : Tìm các số nguyên x , biết :
a) \(\dfrac{2}{3}\left(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{1}{3}\right)\le\dfrac{x}{18}\le\dfrac{7}{13}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)\)
b) \(\left(\dfrac{31}{20}-\dfrac{26}{45}\right).-\dfrac{36}{35}< x< \left(\dfrac{51}{56}+\dfrac{8}{21}+\dfrac{1}{3}\right).\dfrac{8}{13}\)
Bài 2 :
C = \(\dfrac{-1}{3}.\dfrac{141}{17}-\dfrac{39}{9}.\dfrac{-1}{7}\)
Bài 1:
a: \(\Leftrightarrow\dfrac{2}{3}\cdot\dfrac{6+9-4}{12}< =\dfrac{x}{18}< =\dfrac{7}{13}\cdot\dfrac{3-1}{6}\)
\(\Leftrightarrow\dfrac{22}{36}< =\dfrac{x}{18}< =\dfrac{14}{78}=\dfrac{7}{39}\)
\(\Leftrightarrow\dfrac{11}{9}< =\dfrac{x}{9}< =\dfrac{7}{13}\)
=>143<=x<=63
hay \(x\in\varnothing\)
b: \(\Leftrightarrow\dfrac{31\cdot9-26\cdot4}{180}\cdot\dfrac{-36}{35}< x< \dfrac{153+64+56}{168}\cdot\dfrac{8}{13}\)
\(\Leftrightarrow-1< x< 1\)
=>x=0
CHỨNG TỎ RẰNG :
\(\dfrac{1}{31}\)+\(\dfrac{1}{32}\)+\(\dfrac{1}{33}\)+\(\dfrac{1}{35}\)+.....+\(\dfrac{1}{148}\)+\(\dfrac{1}{149}\)\(\dfrac{1}{150}\)<\(\dfrac{13}{6}\)
bài 1 tính :
\(\dfrac{-8}{9}\) . \(\dfrac{12}{19}\) . \(\dfrac{9}{-4}\) . \(\dfrac{19}{24}\) \(\dfrac{-5}{16}\) . \(\dfrac{17}{15}\) : \(\dfrac{-17}{8}\)
\(\dfrac{4}{13}\) . \(\dfrac{2}{7}\) + \(\dfrac{-3}{26}\) + \(\dfrac{4}{13}\) . \(\dfrac{5}{7}\) \(\dfrac{6}{11}\) . \(\dfrac{3}{4}\) + \(\dfrac{-12}{60}\) +\(\dfrac{-3}{4}\) .\(\dfrac{-5}{11}\)
giúp mk vs mn ơi , mai cô giáo ktra mk r
a: \(=\dfrac{8}{9}\cdot\dfrac{9}{4}\cdot\dfrac{12}{19}\cdot\dfrac{19}{24}=\dfrac{1}{2}\cdot2=1\)
b: \(=\dfrac{5}{16}\cdot\dfrac{17}{15}\cdot\dfrac{8}{17}=\dfrac{5}{16}\cdot\dfrac{8}{15}=\dfrac{40}{240}=\dfrac{1}{6}\)
c: \(=\dfrac{4}{13}\left(\dfrac{2}{7}+\dfrac{5}{7}\right)-\dfrac{3}{26}=\dfrac{4}{13}-\dfrac{3}{26}=\dfrac{5}{26}\)
c: \(=\dfrac{3}{4}\left(\dfrac{6}{11}+\dfrac{5}{11}\right)-\dfrac{1}{5}=\dfrac{3}{4}-\dfrac{1}{5}=\dfrac{11}{20}\)
4. Tính hợp lí :
\(\dfrac{5}{13}\) . \(\dfrac{8}{15}\) + \(\dfrac{5}{13}\) . \(\dfrac{26}{15}\) - \(\dfrac{5}{13}\) . \(\dfrac{8}{15}\)
\(\dfrac{5}{13}.\dfrac{8}{15}+\dfrac{5}{13}.\dfrac{26}{15}-\dfrac{5}{13}.\dfrac{8}{15}.\\ =\dfrac{5}{13}.\left(\dfrac{8}{15}+\dfrac{26}{15}-\dfrac{8}{15}\right).\\ =\dfrac{5}{13}.\dfrac{26}{15}=\dfrac{2}{3}.\)
\(\dfrac{5}{13}\times\dfrac{8}{15}+\dfrac{5}{13}\times\dfrac{26}{15}-\dfrac{5}{13}\times\dfrac{8}{15}\)
\(=\dfrac{5}{13}\times\left(\dfrac{8}{15}+\dfrac{26}{15}-\dfrac{8}{15}\right)\)
\(=\dfrac{5}{13}\times\dfrac{26}{15}\)
\(\dfrac{2}{3}\)
tính:
\(2\dfrac{3}{13}\) x \(\dfrac{26}{58}\) x 4 x \(2\dfrac{15}{24}\) x \(\dfrac{8}{21}\)
\(=\dfrac{29}{13}\cdot\dfrac{13}{29}\cdot4\cdot\dfrac{21}{8}\cdot\dfrac{8}{21}=4\)