rút gọn :
\(\frac{90^3}{15^3}\)
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\(a) \frac{1}{4};\frac{3}{7};\frac{101}{131}\)
\(15\div\frac{15}{45}\div15=\frac{1}{3}\)
\(\frac{72}{90}=72\div\frac{18}{90}\div18=\frac{4}{5}\)
\(50\div\frac{10}{120}\div10=\frac{5}{12}\)
1000000000000% đúng nha
a. \(-\frac{15}{90}=-\frac{1}{6};\frac{120}{600}=\frac{1}{5};-\frac{75}{150}=-\frac{1}{2}\)
Mẫu chung: 30
\(-\frac{1}{6}=-\frac{5}{30};\frac{1}{5}=\frac{6}{30};-\frac{1}{2}=-\frac{15}{30}\)
b. \(\frac{54}{-90}=\frac{3}{-5}=-\frac{3}{5};-\frac{180}{288}=-\frac{5}{8};\frac{60}{-135}=\frac{4}{-9}=-\frac{4}{9}\)
Mẫu chung: 360
\(-\frac{3}{5}=-\frac{216}{360};-\frac{5}{8}=-\frac{225}{360};-\frac{4}{9}=-\frac{160}{360}\).
a: \(\dfrac{15}{90}=\dfrac{15:3}{90:3}=\dfrac{5}{30}=\dfrac{5:5}{30:5}=\dfrac{1}{6}\)
b: \(\dfrac{15}{90}=\dfrac{15\cdot2}{90\cdot2}=\dfrac{30}{180}\)
\(\dfrac{15}{90}=\dfrac{15\cdot3}{90\cdot3}=\dfrac{45}{270}\)
\(\dfrac{15}{90}=\dfrac{15\cdot4}{90\cdot4}=\dfrac{60}{360}\)
\(\dfrac{15}{90}=\dfrac{15\cdot5}{90\cdot5}=\dfrac{75}{450}\)
\(\dfrac{15}{90}=\dfrac{15\cdot6}{90\cdot6}=\dfrac{90}{540}\)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{29.31}{30.30}\)
\(=\frac{1.2.3....29}{2.3.4....30}.\frac{3.4.5....31}{2.3.4....30}\)
\(=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
Đặt \(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)
\(\Rightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{29.31}{30.30}\)
\(\Rightarrow A=\frac{1.3.2.4.3.5...29.31}{2.2.3.3.4.4...30.30}\)
\(\Rightarrow A=\frac{\left(1.2.3...29\right).\left(3.4.5...31\right)}{\left(2.3.4...30\right).\left(2.3.4...30\right)}\)
\(\Rightarrow A=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
Vậy \(A=\frac{31}{60}\)
\(\frac{90^3}{15^3}=\left(\frac{90}{15}\right)^3=\left(\frac{90:15}{15:15}\right)^3=6^3=216\)
\(\frac{90^3}{15^3}=\frac{15^3.6^3}{15^3}=6^3=216\)