\(\dfrac{50}{75}=\dfrac{10}{ }=\dfrac{ }{30}=\dfrac{2}{ }\)
Tính rồi viết kết quả dưới dạng số thập phân:
a) \(\dfrac{1}{10}\) + \(\dfrac{4}{20}\) + \(\dfrac{9}{30}\) + \(\dfrac{16}{40}\) + \(\dfrac{25}{50}\) + \(\dfrac{36}{60}\) + \(\dfrac{49}{70}\) + \(\dfrac{64}{80}\) + \(\dfrac{81}{90}\)
b) ( \(\dfrac{4}{5}\) x \(\dfrac{3}{8}\) + \(\dfrac{4}{5}\) x \(\dfrac{5}{8}\) - \(\dfrac{4}{5}\) x \(\dfrac{7}{8}\) ) : \(\dfrac{1}{2}\)
\(a,=\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}=\dfrac{45}{10}=4,5\\ b,=\dfrac{4}{5}\times\left(\dfrac{3}{8}+\dfrac{5}{8}-\dfrac{7}{8}\right)\times2=\dfrac{8}{5}\times\dfrac{1}{8}=\dfrac{1}{5}=0,2\)
a) Rút gọn các phân số về tối giản, ta được:
\(\dfrac{1}{10}\)+\(\dfrac{2}{10}\)+\(\dfrac{3}{10}\)+\(\dfrac{4}{10}\)+\(\dfrac{5}{10}\)+\(\dfrac{6}{10}\)+\(\dfrac{7}{10}\)+\(\dfrac{8}{10}\)+\(\dfrac{9}{10}\)= kết quả là \(\dfrac{45}{10}\) ra số thập phân = \(4,5\)
b) \(\dfrac{4}{5}\) \(\times\) \(\left(\dfrac{3}{8}+\dfrac{5}{8}-\dfrac{7}{8}\right)\) = \(\dfrac{4}{5}\times\dfrac{1}{8}\) = \(\dfrac{4}{40}=\dfrac{1}{10}\)\(\div\dfrac{1}{2}\)
= \(\dfrac{2}{10}=0,2\)
tìm x, biết:
e) \(\dfrac{2}{7-x}\)=\(\dfrac{18}{45}\) f)\(\dfrac{2x+3}{3}\)=\(\dfrac{50}{15}\) g)\(2\dfrac{x}{7}\)=\(\dfrac{75}{35}\) h)\(2\dfrac{3}{x}\)=\(\dfrac{13}{x}\)(x khác 0)
e: =>2/7-x=2/5
=>7-x=5
=>x=2
f: =>2x+3/3=10/3
=>2x+3=10
=>2x=7
=>x=7/2
g: =>(14+x)/7=15/7
=>x+14=15
=>x=1
h: =>(2x+3)/x=13/x
=>2x+3=13
=>2x=10
=>x=5
Bài 2: Đúng ghi Đ, sai ghi S
a)\(\dfrac{48}{300}\)= 48%
b)\(\dfrac{48}{300}\) =\(\dfrac{16}{100}\) = 16%
c)\(\dfrac{30}{50}\)=\(\dfrac{60}{100}\)= 60%
d)\(\dfrac{30}{50}\)=\(\dfrac{60}{100}\)=6%
\(\dfrac{2\sqrt{30}}{\sqrt{5}+\sqrt{6}+\sqrt{7}} \)
\(\sqrt{24}+6\sqrt{\dfrac{2}{3}+\dfrac{10}{\sqrt{6}-1}}\)
\(\dfrac{2\sqrt{15}+\sqrt{16}}{\sqrt{84}+\sqrt{6}}\)
\(2\sqrt{40\sqrt{2}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)
\(\dfrac{\left(2+\sqrt{3}\right)^2-1}{\left(\sqrt{3}+1\right)^2}:\dfrac{\left(3+\sqrt{5}\right)^2-4}{\left(\sqrt{5}+1\right)^2}\)
giúp em với ạ
\(2\sqrt{40\sqrt{3}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}\)
\(=2\cdot\sqrt{40\sqrt{3}}-2\cdot\sqrt{5\sqrt{3}}-3\cdot\sqrt{20\sqrt{3}}\)
\(=2\cdot2\sqrt{10}\cdot\sqrt{\sqrt{3}}-2\cdot\sqrt{5}\cdot\sqrt{\sqrt{3}}-6\sqrt{5}\cdot\sqrt{\sqrt{3}}\)
\(=4\sqrt{10}\sqrt{\sqrt{3}}-4\cdot\sqrt{5}\cdot\sqrt{\sqrt{3}}\)
Tìm x biếi: \(\dfrac{3x-40}{50}+\dfrac{3x-10}{40}+\dfrac{x+30}{20}+\dfrac{x-90}{10}=0\)
\(\dfrac{3x-40}{50}+\dfrac{3x-10+2x+60+4x-360}{40}=0\)
=> \(\dfrac{3x-40}{50}+\dfrac{9x-310}{40}=0\)
=> \(\dfrac{3x-40}{50}=\dfrac{-9x+310}{40}\)
=> \(40\left(3x-40\right)=50\left(-9x+310\right)\)
=> \(120x-1600=-450x+15500\)
=> \(120x+450x=15500+1600\)
Hay \(570x=17100\)
=>x = 30
Hơi dài nhé bạn
\(\dfrac{3x-40}{50}\)+\(\dfrac{3x-10+2x+60+4x-360}{40}\)=0
⇒\(\dfrac{3x-40}{50}\)+\(\dfrac{9x-310}{40}\)=0
⇒\(\dfrac{3x-40}{50}\)=\(\dfrac{9x-310}{40}\)
⇒40(3x -40) = 50(-9x+310)
⇒120x - 1600 = -450x + 15500
⇒120x + 450x = 15500 + 1600
Mặt khác: 570x = 17100
⇒x = 30
\(\dfrac{\left(1,16-x\right).5,25}{\left(10\dfrac{5}{9}-7\dfrac{1}{4}\right).2\dfrac{2}{17}}=75\%\)
Mỗi lớp có chưa đến 50 học sinh, cuối năm có 30% là học sinh giỏi, \(\dfrac{3}{8}\)là loại khá . Hỏi có bao nhiêu học sinh trung bình.
Chứng minh rằng mọi n∈N có :
\(\dfrac{1}{1.6}+\dfrac{1}{6.11}+..+\dfrac{1}{\left(5.n+1\right).\left(5.n+6\right)}=\dfrac{n+1}{5.n+6}\)
\(\dfrac{3}{8}\) loại khá còn lại là trung bình
Adu! đề cc gì v?
B1: \(\dfrac{\left(1,16-x\right).5,25}{\left(10\dfrac{5}{9}-7\dfrac{1}{4}\right).2\dfrac{2}{17}}=75\%\Rightarrow\dfrac{\left(\dfrac{29}{25}-x\right).\dfrac{21}{4}}{\left(\dfrac{95}{9}-\dfrac{29}{4}\right).\dfrac{36}{17}}=\dfrac{3}{4}\)
\(\Rightarrow\dfrac{\left(\dfrac{29}{25}-x\right).\dfrac{21}{4}}{\dfrac{119}{36}.\dfrac{36}{17}}=\dfrac{3}{4}\Rightarrow\dfrac{\left(\dfrac{29}{25}-x\right).\dfrac{21}{4}}{7}=\dfrac{3}{4}\Rightarrow\dfrac{29}{25}-x=\dfrac{3}{4}.7:\dfrac{21}{4}=1\)
\(\Rightarrow x=\dfrac{29}{25}-1=\dfrac{4}{25}\)
B2: Đề chưa rõ :V
B3: Lười giải lắm (hihi)
Quy đồng mẫu các phân số
f) \(\dfrac{165}{270}\) ; \(\dfrac{91}{156}\) ; \(\dfrac{210}{1134}\)
g) \(\dfrac{21}{9}\) ; \(\dfrac{120}{50}\) ; \(\dfrac{63}{54}\)
h) \(\dfrac{75}{500}\) ; \(\dfrac{150}{90}\) ; \(\dfrac{250}{900}\)
bài 18: tìm 2 số tự nhiên a, b biết rằng a + b = 128 và ƯCLN (a,b) = 16
nhanh + chi tiết = tick
f, \(\dfrac{165}{270}\) = \(\dfrac{165:15}{270:15}\) = \(\dfrac{11}{18}\) = \(\dfrac{11\times6}{18\times6}\) = \(\dfrac{66}{108}\)
\(\dfrac{91}{156}\) = \(\dfrac{91:13}{156:13}\) = \(\dfrac{7}{12}\) = \(\dfrac{7\times9}{12\times9}\) = \(\dfrac{63}{108}\)
\(\dfrac{210}{1134}\) = \(\dfrac{210:42}{1134:42}\) = \(\dfrac{5}{27}\) = \(\dfrac{5\times4}{27\times4}\) = \(\dfrac{20}{108}\)
g, \(\dfrac{21}{9}\) = \(\dfrac{21:3}{9:3}\) = \(\dfrac{7}{3}\) = \(\dfrac{7\times10}{3\times10}\) = \(\dfrac{70}{30}\)
\(\dfrac{120}{50}\) = \(\dfrac{120:10}{50:10}\) = \(\dfrac{12}{5}\) = \(\dfrac{12\times6}{5\times6}\) = \(\dfrac{72}{30}\)
\(\dfrac{63}{54}\) = \(\dfrac{63:9}{54:9}\) = \(\dfrac{7}{6}\) = \(\dfrac{7\times5}{6\times5}\) = \(\dfrac{35}{30}\)
h, \(\dfrac{75}{100}\) = \(\dfrac{75:25}{100:4}\) = \(\dfrac{3}{4}\) = \(\dfrac{3\times9}{4\times6}\) = \(\dfrac{27}{36}\)
\(\dfrac{150}{90}\) = \(\dfrac{150:30}{90:30}\) = \(\dfrac{5}{3}\) = \(\dfrac{5\times12}{3\times12}\) = \(\dfrac{60}{36}\)
\(\dfrac{250}{900}\) = \(\dfrac{250:50}{900:50}\) = \(\dfrac{5}{18}\) = \(\dfrac{5\times2}{18\times2}\) = \(\dfrac{10}{36}\)
Câu 10:
a) \(-3\dfrac{1}{4}.x-75\%+\dfrac{3x}{2}=-1,2:-\dfrac{9}{10}-1\dfrac{1}{4}\)
b) \(\dfrac{5}{3}+\dfrac{5}{15}+\dfrac{5}{35}+...+\dfrac{5}{x\left(x+2\right)}=2\dfrac{8}{17}\)(x thuộc N sao)
a) Ta có: \(-3\dfrac{1}{4}\cdot x-75\%+\dfrac{3x}{2}=-1.2:\dfrac{-9}{10}-1\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{-13x}{4}-\dfrac{3}{4}+\dfrac{3x}{2}=\dfrac{-6}{5}\cdot\dfrac{10}{-9}-\dfrac{5}{4}\)
\(\Leftrightarrow\dfrac{-13x-3+6x}{4}=\dfrac{4}{3}-\dfrac{5}{4}\)
\(\Leftrightarrow\dfrac{-7x-3}{4}=\dfrac{1}{12}\)
\(\Leftrightarrow-7x-3=\dfrac{1}{3}\)
\(\Leftrightarrow-7x=\dfrac{10}{3}\)
hay \(x=-\dfrac{10}{21}\)
b) Ta có: \(\dfrac{5}{3}+\dfrac{5}{15}+\dfrac{5}{35}+...+\dfrac{5}{x\left(x+2\right)}=2\dfrac{8}{17}\)
\(\Leftrightarrow\dfrac{5}{2}\left(\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+...+\dfrac{2}{x\left(x+2\right)}\right)=2\dfrac{8}{17}\)
\(\Leftrightarrow\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+2}\right)=2+\dfrac{8}{17}\)
\(\Leftrightarrow\left(1-\dfrac{1}{x+2}\right)=\dfrac{42}{17}:\dfrac{5}{2}\)
\(\Leftrightarrow\dfrac{x+1}{x+2}=\dfrac{42}{17}\cdot\dfrac{2}{5}=\dfrac{84}{85}\)
\(\Leftrightarrow85x+85=84x+168\)
\(\Leftrightarrow x=83\)
Tính : A = \(\dfrac{\dfrac{1}{14}-\dfrac{1}{30}-\dfrac{1}{46}}{\dfrac{2}{35}-\dfrac{2}{75}-\dfrac{2}{115}}\):\(\frac{\frac{3}{8}-\frac{15}{17}+\frac{30}{31}}{\frac{1}{6}-\frac{20}{51}+\frac{40}{93}}\)