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\(\frac{15x8+15x4}{12x3}\)
\(=\frac{15x\left(8+4\right)}{12x3}\)
\(=\frac{15x12}{12x3}=\frac{15}{3}=5\)
\(a.-\dfrac{8}{12}=\dfrac{-2\cdot4}{4\cdot3}=-\dfrac{2}{3}\)
\(b.\dfrac{15}{-60}=\dfrac{15}{15\cdot-4}-\dfrac{1}{4}\)
\(c.\dfrac{-16}{-72}=\dfrac{-2\cdot8}{-9\cdot8}=\dfrac{2}{9}\)
\(d.\dfrac{35}{14\cdot15}=\dfrac{7\cdot5}{7\cdot2\cdot5\cdot3}=\dfrac{1}{6}\)
\(\dfrac{8}{12}\)=\(\dfrac{2}{31}\)
\(\dfrac{15}{-60}\)=\(\dfrac{-1}{4}\)
\(\dfrac{-16}{72}\)=\(\dfrac{-2}{9}\)
\(\dfrac{35}{14.15}=\dfrac{35}{210}=\dfrac{1}{6}\)
Rút gọn rồi tính:
a) \(\frac{8}{10}-\frac{12}{9}+\frac{10}{15}\)
\(=\frac{4}{5}-\frac{4}{3}+\frac{2}{3}\)
\(=\frac{12-20+10}{15}\)
\(=\frac{2}{15}\)
b) \(\left(\frac{20}{16}-\frac{15}{12}\right)\div\left(\frac{6}{8}-\frac{9}{12}\right)\)
\(=\left(\frac{5}{4}-\frac{5}{4}\right)\div\left(\frac{3}{4}-\frac{3}{4}\right)\)
\(=1\div1\)
\(=1\)
\(a,\frac{8}{10}-\frac{12}{9}+\frac{10}{15}\)
\(=\frac{4}{5}-\frac{4}{3}+\frac{2}{3}\)
\(=\frac{4}{5}-\left(\frac{4}{3}+\frac{2}{3}\right)\)
\(=\frac{4}{5}-2\)
\(=\frac{4}{5}+\frac{-10}{5}\)
\(=\frac{-6}{5}\)
\(b,\left(\frac{20}{16}-\frac{15}{12}\right):\left(\frac{6}{8}-\frac{9}{12}\right)\)
\(=\left(\frac{5}{4}-\frac{5}{4}\right):\left(\frac{3}{4}-\frac{3}{4}\right)\)
\(=0:0\)
\(=0\)
\(\dfrac{-8}{12}=\dfrac{-8:4}{12:4}=\dfrac{-2}{3}\\ \dfrac{15}{-60}=\dfrac{15:15}{-60:15}=\dfrac{1}{-4}\\ \dfrac{-16}{-72}=\dfrac{-16:\left(-8\right)}{-72:\left(-8\right)}=\dfrac{2}{9}\\ \dfrac{35}{14.15}=\dfrac{5.7}{7.2.5.3}=\dfrac{1}{2.3}=\dfrac{1}{6}\)
\(\frac{-11\cdot13^7}{11^{15}\cdot13^8}=\frac{-1\cdot13}{11^{14}\cdot13^7}\)
A = \(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{15}\right)\)\(...\left(1+\frac{1}{2499}\right)\)
A = \(\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{8}{8}+\frac{1}{8}\right)\left(\frac{15}{15}+\frac{1}{15}\right)\)\(...\left(\frac{2499}{2499}+\frac{1}{2499}\right)\)
A = \(\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.....\frac{2500}{2499}\)
A = \(\frac{4.9.16.....2500}{3.8.15.....2499}\)
A = \(\frac{\left(2.2\right)\left(3.3\right)\left(4.4\right)...\left(50.50\right)}{3.8.15.24.....2499}\)
A = \(\frac{2.3.4.....50}{3.4.5.6.....51}\)
A = \(\frac{2}{51}\)
Vậy A = \(\frac{2}{51}\)
( Nếu sai mong bạn thông cảm ạ ! )
_HT_
Answer:
\(A=\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{15}\right)...\left(1+\frac{1}{2499}\right)\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}...\frac{2500}{2499}\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}\)
\(=\frac{2^2.3^2.4^2...50^2}{1.3.2.4.3.5...49.51}\)
\(=\frac{2.50}{51}\)
\(=\frac{100}{51}\)
Rút gọn
\(\dfrac{8}{15}=\dfrac{8}{15}\)
Phân số tối giản rồi nha bạn