Quy đồng các phân số sau:
a)\(\frac{9}{70};\frac{3}{-20};\frac{-5}{14}\)
b)\(\frac{3469-54}{6398-108}và\frac{2468-98}{3072-147}\)
c)\(\frac{4.3+3.7}{6.5+9}và\frac{6.9-2.17}{3.63-119}\)
d)\(\frac{10}{42};\frac{-3}{28};\frac{-55}{132}\)
e)\(\frac{1010}{1008.8-994}và\frac{1.2.3+2.4.6+3.6.9+5.10.15}{1.3.6+2.6.12+3.9.18+5.15.30}\)
Quy đồng
\(\frac{3469-54}{6398-108}và\frac{2468-98}{3072-147}\)
Chứng minh rằng:
1)B=\(\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+...+\frac{3^{98}+1}{3^{98}}< 100\)
2)C=\(\frac{5}{5.8.11}+\frac{5}{8.11.14}+...+\frac{5}{302.305.308}\)<\(\frac{1}{48}\)
3)D=\(\frac{11}{9}+\frac{18}{16}+\frac{27}{25}+...+\frac{1766}{1764}\)
\(40\frac{20}{43}< D< 40\frac{20}{21}\)
1.tính các biểu thức sau bằng một cách hợp lí
a.\(\frac{108}{119}.\frac{107}{211}+\frac{108}{119}.\frac{104}{211}\)
b.\(\frac{15}{19}.\frac{27}{33}+\frac{15}{19}.\frac{19}{33}-\frac{15}{19}.\frac{13}{33}\)
c.\(\frac{-4}{5}.\frac{13}{10}+\frac{-4}{5}.\frac{7}{10}-\frac{-4}{5}\)
d.\(\frac{\frac{-2}{7}-\frac{-2}{15}+\frac{-2}{39}}{\frac{5}{7}-\frac{5}{15}+\frac{5}{39}}\)
e.\(\frac{3}{5}.\frac{15}{7}-\frac{15}{7}.\frac{8}{5}\)
f.\(\frac{2}{3}+\frac{1}{3}.\left(\frac{-4}{9}+\frac{5}{6}\right):\frac{7}{12}\)
h.\(\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}\)
g.\(\frac{3}{-4}+\frac{2}{7}+\frac{-1}{4}+\frac{5}{7}+\frac{21}{22}.\frac{66}{7}\)
k.\(\frac{27.18+27.103-120.27}{15.33+33.12}\)
l.\(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
\(a,\frac{16}{15}\cdot\frac{-5}{14}\cdot\frac{54}{24}\cdot\frac{56}{21}\)
\(b,5\cdot\frac{7}{5}\) \(c,\frac{1}{7}\cdot\frac{5}{9}+\frac{5}{9}\cdot\frac{1}{7}+\frac{5}{9}\cdot\frac{3}{7}\)
\(d,4\cdot11\cdot\frac{3}{4}\cdot\frac{9}{121}\)
\(e,\frac{3}{4}\cdot\frac{16}{9}-\frac{7}{5}:\frac{-21}{20}\)
\(g,2\frac{1}{3}-\frac{1}{3}\cdot\left[\frac{-3}{2}+\left(\frac{2}{3}+0,4\cdot5\right)\right]\)
\(a,\left(9,75.21\frac{3}{7}+\frac{39}{4}.18\frac{4}{7}\right).\frac{15}{78}\)
\(b,\frac{-7}{21}+\left(1+\frac{1}{3}\right)\) \(c,\frac{2}{15}+\left(\frac{5}{9}+\frac{-6}{9}\right)\)
\(d,\left(\frac{-1}{5}+\frac{3}{12}\right)+\frac{-3}{4}\)
\(e,\frac{4}{20}+\frac{16}{42}+\frac{6}{15}+\frac{-3}{5}+\frac{2}{21}+\frac{-10}{21}+\frac{3}{20}\)
thực hiện các phép tính sau:
A =\(\frac{5.2^{30}.3^{18}-4.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
B = 1 - 3 + 5 - 7 + 9 - 11 + ..... + 2017 - 2019
C =\(\left(\frac{151515}{606060}+\frac{151515}{121212}+\frac{151515}{202020}+\frac{151515}{303030}+\frac{151515}{424242}\right).\frac{28}{15}\)
Bài 1: Tính (hợp lý nếu có thể)
a) \(\frac{8}{40}+\frac{-4}{20}-\frac{3}{5}\)
b) \(\frac{-7}{12}+\frac{-2}{12}-\frac{-3}{36}\)
c) \((\frac{1}{6}+\frac{-4}{13})-(\frac{-17}{6}-\frac{30}{13})\)
d) \(-\frac{-5}{4}+\frac{7}{4}-\frac{-11}{7}+\frac{2}{7}\)
e) \(-\frac{1}{8}+\frac{-7}{9}+\frac{-7}{8}+\frac{6}{7}+\frac{2}{14}\)
f) \(\frac{-2}{9}-\frac{11}{-9}+\frac{5}{7}-\frac{-6}{-7}\)
Tính Nhanh.
a.45-12-5-23
b.2534-150-834
c.\(\frac{34}{13}-\frac{19}{28}-\frac{3}{31}\)
d.\(\frac{7}{3}-\frac{11}{5}-\frac{4}{5}\)
e.\(\frac{18}{13}+\frac{55}{46}+\frac{5}{13}\)
f.\(\left(\frac{27}{25}-\frac{4}{9}\right)-\left(\frac{2}{25}-\frac{5}{9}\right)\)
g.21,567-9,248-7,752
h.8,275-1,56-3,215
i.56,04-31,5-10,15
j.18,72-9,6-3,72-0,4
k.46,55+20,33+25,67
l.20-0,5-1,5-2,5-3,5-4,5-6,5
Tính nhanh :
a) 17 x 8 + 51 x 4
b) 2 x 2 x 3 x 5 x 19
c) 54 x 275 + 825 x 15 + 275
d) 100 - 99 + 98 - 97 + 96 - 95 + 94 - 93 + ... + 4 - 3 + 2
e) \(\frac{167x198+98}{198x168-100}\)
g) \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{2019x2020}\)
h)\(\frac{4}{2x4}+\frac{4}{4x6}+\frac{4}{6x8}+...+\frac{4}{16x18}\)
k) 1,5 + 2,5 + 3,5 + 4,5 + 5,5 + 6,5 + 7,5 + 8,5
m) \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)
n) \(\frac{13}{50}+9\%+\frac{14}{100}+24\%\)
