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\(-\frac{3}{6}=\frac{x}{-2}=-\frac{18}{y}=-\frac{z}{24}\)
Ta có :+) \(-\frac{3}{6}=\frac{x}{-2}\)
\(\Rightarrow x=\frac{\left(-3\right)\left(-2\right)}{6}\)
\(\Rightarrow x=1\)
+)\(-\frac{3}{6}=-\frac{18}{y}\)
\(\Rightarrow y=\frac{6.\left(-18\right)}{-3}\)
\(\Rightarrow y=36\)
+)\(-\frac{3}{6}=-\frac{z}{24}\)
\(\Rightarrow-z=\frac{\left(-3\right)24}{6}\)
\(\Rightarrow-z=-12\)
\(\Rightarrow z=12\)
Vậy........................
a) \(\frac{2.7.13}{26.35}=\frac{2.7.13}{2.13.5.7}=\frac{1}{5}\)
b) \(\frac{23.5-23}{4-27}=\frac{23.\left(5-1\right)}{-23}=\frac{23.4}{-23}=\frac{23.\left(-4\right)}{23}=-4\)
c) \(\frac{2130-15}{3550-25}=\frac{142.15-15}{142.25-25}=\frac{15.\left(142-1\right)}{25.\left(142-1\right)}=\frac{15.141}{25.141}=\frac{15}{25}=\frac{3.5}{5.5}=\frac{3}{5}\)
d) \(\frac{1717-101}{2828+404}=\frac{17.101-101}{28.101+101.4}=\frac{101.\left(17-1\right)}{101.\left(28+4\right)}=\frac{101.16}{101.32}=\frac{16}{32}=\frac{4.4}{2.4.4}=\frac{1}{2}\)
e) \(\frac{3.5.11.13}{33.35.27}=\frac{3.5.11.13}{3.11.5.7.3^3}=\frac{13}{7.3^3}=\frac{13}{189}\)
f) \(\frac{85-17+34}{51-102}=\frac{5.17-17+2.17}{3.17-6.17}=\frac{17.\left(5-1+2\right)}{17.\left(3-6\right)}=\frac{17.6}{17.\left(-3\right)}=\frac{6}{-3}=-2\)
a) +/ \(\dfrac{1}{3}\) và \(\dfrac{-2}{6}\)
Vì\(\dfrac{1}{3}\) > 0 và \(\dfrac{-2}{6}\) < 0 nên \(\dfrac{1}{3}>\dfrac{-2}{6}\)
+/\(\dfrac{-4}{5}\)và \(\dfrac{-20}{25}\)
\(\dfrac{-20}{25}=\dfrac{-20:5}{25:5}=\dfrac{-4}{5}\)
Vì\(\dfrac{-4}{5}\)=\(\dfrac{-4}{5}\)nên \(\dfrac{-4}{5}=\dfrac{-20}{25}\)
+/\(\dfrac{2}{3}\) và \(\dfrac{-5}{-8}\)
\(\dfrac{2}{3}=\dfrac{2.8}{3.8}=\dfrac{16}{24}\) ;\(\dfrac{-5}{-8}=\dfrac{5}{8}=\dfrac{5.3}{8.3}=\dfrac{15}{24}\)
Vì\(\dfrac{16}{24}>\dfrac{15}{24}\) nên \(\dfrac{2}{3}>\dfrac{-5}{-8}\)
Các cặp phân số bằng nhau từ đẳng thức 4.6=12.2 là :
\(\dfrac{4}{12}=\dfrac{2}{6};\dfrac{12}{4}=\dfrac{6}{2};\dfrac{12}{6}=\dfrac{4}{2};\dfrac{6}{12}=\dfrac{2}{4}.\)
a) \(\frac{2.7.13}{26.35}=\frac{2.7.13}{2.13.7.5}=\frac{1}{5}\)
b) \(\frac{3.5.11.13}{33.35.37}=\frac{3.5.11.13}{3.11.7.5.37}=\frac{13}{259}\)
c) \(\frac{23.5-23}{4-27}=\frac{23.\left(5-1\right)}{-23}=\frac{4}{-1}=-4\)
d) \(\frac{1717-101}{2828+404}=\frac{101.17-101}{404.7+404}=\frac{101.\left(17-1\right)}{404.\left(7+1\right)}=\frac{101.16}{404.8}=\frac{101.2.8}{101.4.8}=\frac{1}{2}\)
3. Gọi d là ƯCLN(2n + 3, 4n + 8), d ∈ N*
\(\Rightarrow\hept{\begin{cases}2n+3⋮d\\4n+8⋮d\end{cases}\Rightarrow\hept{\begin{cases}2\left(2n+3\right)⋮d\\4n+8⋮d\end{cases}\Rightarrow}\hept{\begin{cases}4n+6⋮d\\4n+8⋮d\end{cases}}}\)
\(\Rightarrow\left(4n+8\right)-\left(4n+6\right)⋮d\)
\(\Rightarrow2⋮d\)
\(\Rightarrow d\in\left\{1;2\right\}\)
Mà 2n + 3 không chia hết cho 2
\(\Rightarrow d=1\)
\(\RightarrowƯCLN\left(2n+3,4n+8\right)=1\)
\(\Rightarrow\frac{2n+3}{4n+8}\) là phân số tối giản.
B2:
a) \(\dfrac{2.7.13}{26.35}=\dfrac{2.7.13}{2.13.7.5}=\dfrac{1}{5}\)
b) \(\dfrac{23.5-23}{4.27}=\dfrac{23.4}{4.27}=\dfrac{23}{27}\)
Phùng Tuệ Minh mk nghĩ câu c thế này :
c) \(\dfrac{85-17+34}{51-102}=\dfrac{34+51-17+34}{51-17+85}\)
\(=\dfrac{34+51-17+34}{51-17+34+51}\)
\(=\dfrac{34}{51}\)