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Số cam trong vườn là :
450 . \(\frac{2}{5}\) = 180 ( cây )
Số hồng xiêm trong vườn là :
450 . 50% = 225 ( cây )
Số bưởi trong vườn là :
450 - 180 - 225 = 45 ( cây )
Đ/s : 45 cây bưởi
Công thức
(x-\(\frac{1}{3}\)):\(\frac{-12}{45}\)+1=\(\frac{1}{3}\)
(x-\(\frac{1}{3}\)):\(\frac{-12}{45}\)=\(\frac{1}{3}\)+1
(x-\(\frac{1}{3}\)):\(\frac{-12}{45}\)=\(\frac{4}{3}\)
(x-\(\frac{1}{3}\))=\(\frac{4}{3}\)x\(\frac{-12}{45}\)
(x-\(\frac{1}{3}\))=\(\frac{-16}{45}\)
x=\(\frac{-16}{45}\)+\(\frac{1}{3}\)
x=\(\frac{-1}{45}\)
\(H=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(\Rightarrow H=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(\Rightarrow\frac{3H}{5}=\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\)
\(\Rightarrow\frac{3H}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\)
\(\Rightarrow\frac{3H}{5}=\frac{1}{4}-\frac{1}{28}\)
\(\Rightarrow\frac{3H}{5}=\frac{3}{14}\)
\(\Rightarrow H=\frac{3}{14}.\frac{5}{3}\)
\(\Rightarrow H=\frac{5}{14}\)
Vậy \(H=\frac{5}{14}\)
BÀI 1:
a)
\(\dfrac{1}{2}-\dfrac{2}{3}+\dfrac{3}{4}\\ =\dfrac{6}{12}-\dfrac{8}{12}+\dfrac{9}{12}\\ =\dfrac{6-8+9}{12}\\ =\dfrac{7}{12}\)
b)
\(-4\dfrac{1}{2}+1,2\cdot\left(-5\right)-30\%\\ =\dfrac{-9}{2}+\dfrac{6}{5}\cdot\left(-5\right)-\dfrac{3}{10}\\ =\dfrac{-9}{2}+\left(-6\right)-\dfrac{3}{10}\\ =\dfrac{-45}{10}+\dfrac{-60}{10}-\dfrac{3}{10}\\ =\dfrac{\left(-45\right)+\left(-60\right)-3}{10}\\ =\dfrac{-108}{10}\\ =\dfrac{54}{5}\)
c)
\(\dfrac{-7}{9}\cdot\dfrac{6}{13}+\dfrac{-7}{9}\cdot\dfrac{7}{13}+5\dfrac{7}{9}\\ =\dfrac{-7}{9}\cdot\left(\dfrac{6}{13}+\dfrac{7}{13}\right)+5\dfrac{7}{9}\\ =\dfrac{-7}{9}\cdot1+5\dfrac{7}{9}\\ =\dfrac{-7}{9}+5\dfrac{7}{9}\\ =5\)
BÀI 2
a)
\(\dfrac{3}{2}x-\dfrac{2}{3}=\dfrac{2}{3}:\dfrac{3}{2}\\ \dfrac{3}{2}x-\dfrac{2}{3}=\dfrac{4}{9}\\ \dfrac{3}{2}x=\dfrac{4}{9}+\dfrac{2}{3}\\ \dfrac{3}{2}x=\dfrac{10}{9}\\ x=\dfrac{10}{9}:\dfrac{3}{2}\\ x=\dfrac{20}{27}\)
b)
\(\left(\dfrac{9}{11}-x\right):\left(\dfrac{-10}{11}\right)=1-\dfrac{4}{5}\\ \left(\dfrac{9}{11}-x\right):\left(\dfrac{-10}{11}\right)=\dfrac{1}{5}\\ \dfrac{9}{11}-x=\dfrac{1}{5}\cdot\left(\dfrac{-10}{11}\right)\\ \dfrac{9}{11}-x=\dfrac{-2}{11}\\ x=\dfrac{9}{11}-\dfrac{-2}{11}\\ x=1\)
c)
\(\left(1,2x-\dfrac{4}{7}\right):\dfrac{4}{7}=75\%\\ \left(\dfrac{6}{5}x-\dfrac{4}{7}\right):\dfrac{4}{7}=\dfrac{3}{4}\\ \dfrac{6}{5}x:\dfrac{4}{7}-\dfrac{4}{7}:\dfrac{4}{7}=\dfrac{3}{4}\\ \dfrac{6}{5}x:\dfrac{4}{7}-1=\dfrac{3}{4}\\ \dfrac{6}{5}x:\dfrac{4}{7}=\dfrac{3}{4}+1\\ \dfrac{6}{5}x:\dfrac{4}{7}=\dfrac{7}{4}\\ \dfrac{6}{5}x=\dfrac{7}{4}\cdot\dfrac{4}{7}\\ \dfrac{6}{5}x=1\\ x=1:\dfrac{6}{5}\\ x=\dfrac{5}{6}\)
B) \(\dfrac{-11}{6}+\dfrac{2}{5}+\dfrac{-1}{6}+\dfrac{13}{5}=\left(\dfrac{-11}{6}-\dfrac{1}{6}\right)+\left(\dfrac{2}{5}+\dfrac{13}{5}\right)=\dfrac{-12}{6}+\dfrac{15}{5}=-2+3=-1\)
C) \(\dfrac{1}{7}+\dfrac{-1}{5}+\dfrac{-1}{7}+\dfrac{2}{-5}+\dfrac{-7}{5}=\left(\dfrac{1}{7}-\dfrac{1}{7}\right)+\left(\dfrac{-1}{5}-\dfrac{2}{5}-\dfrac{7}{5}\right)=0-\dfrac{10}{5}=0-2=-2\)
D) \(\dfrac{-5}{8}+\dfrac{12}{7}+\dfrac{13}{8}+\dfrac{2}{7}=\left(\dfrac{13}{8}-\dfrac{5}{8}\right)+\left(\dfrac{12}{7}+\dfrac{2}{7}\right)=\dfrac{8}{8}+\dfrac{14}{7}=12=3\)
E)\(\dfrac{1}{7}+\dfrac{-1}{5}+\dfrac{1}{-7}+\dfrac{2}{-5}+\dfrac{-7}{5}=\left(\dfrac{1}{7}-\dfrac{1}{7}\right)+\left(\dfrac{-1}{5}-\dfrac{2}{5}-\dfrac{7}{5}\right)=0-\dfrac{10}{5}=-2=-2\)
b: =(-11/6-1/6)+(2/5+13/5)
=-2+3
=1
c: =(3/13+10/13)+(-3/7-4/7)
=1-1=0
d: =(-5/8+13/8)+(12/7+2/7)
=-1+2
=1