Tính một cách hợp lí: \(1,2.\frac{{15}}{4} + \frac{{16}}{7}.\frac{{ - 85}}{8} - 1,2.5\frac{3}{4} - \frac{{16}}{7}.\frac{{ - 71}}{8}\)
Tính một cách hợp lí: 1,2×15/4+16/7×-85/8-1,2 × 5 3/4 - 16/7 × -71/8
`1,2×15/4+16/7×-85/8-1,2 × 5 3/4 - 16/7 × -71/8`
`=6/5xx15/4+16/7xx(-85)/8-6/5xx23/4-16/7xx(-71)/8`
`=6/5xx(15/4-23/4)+16/7xx[(-85/8)-(-71/8)]`
`=6/5xx(-8/4)+16/7xx(-14/8)`
`=-32/5`
Tính bằng cách hợp lí :
\(B=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.......\frac{99}{100}\)
B = 1.3/2.2 . 2.4/3.3 . 3.5/4.4 . ...... . 9.11/10.10
= 1.2.3 . ..... . 9/2.3.4 . ..... . 10 . 3.4.5 . ...... . 11/2.3.4 . ..... . 10
= 1/10 . 11/2
= 11/20
Tk mk nha
\(B=\frac{3}{4}.\frac{8}{9}...\frac{99}{100}\)
\(B=\frac{1\cdot3}{2^2}.\frac{2\cdot4}{3^3}...\frac{9\cdot11}{10^2}\)
\(B=\frac{1.3.2.4...9.11}{2^2.3^3...10^2}\)
\(B=\frac{11}{2.10}\)
\(B=\frac{11}{20}\)
Bài 12 : Thực hiện phép tính một cách hợp lí:
p) \(\frac{-5}{9}+\frac{8}{15}+\frac{-2}{11}+\frac{4}{-9}+\frac{7}{15}\) q) \(\frac{5}{13}+\frac{-5}{17}+\frac{-20}{41}+\frac{8}{13}+\frac{-21}{41}\) r) \(\frac{1}{5}+\frac{-2}{9}+\frac{-7}{9}+\frac{4}{5}+\frac{16}{17}\)
p) \(\frac{-5}{9}+\frac{8}{15}+\frac{-2}{11}+\frac{4}{-9}+\frac{7}{15}\)
\(=\left(\frac{-5}{9}+\frac{-4}{9}\right)+\left(\frac{8}{15}+\frac{7}{15}\right)+\frac{-2}{11}\)
\(=-1+1+\frac{-2}{11}\)
\(=-\frac{2}{11}\)
q) \(\frac{5}{13}+\frac{-5}{17}+\frac{-20}{41}+\frac{8}{13}+\frac{-21}{41}\)
\(=\left(\frac{5}{13}+\frac{8}{13}\right)+\left(\frac{-20}{41}+\frac{-21}{41}\right)+\frac{-5}{17}\)
\(=1+\left(-1\right)+\frac{-5}{17}=\frac{-5}{17}\)
r) \(\frac{1}{5}+\frac{-2}{9}+\frac{-7}{9}+\frac{4}{5}+\frac{16}{17}\)
\(=\left(\frac{1}{5}+\frac{4}{5}\right)+\left(\frac{-2}{9}+\frac{-7}{9}\right)+\frac{16}{17}\)
\(=1+\left(-1\right)+\frac{16}{17}=\frac{16}{17}\)
Câu 1: Thực hiện phép tính bằng cách hợp lí
\(\frac{15}{35}+\frac{7}{21}+\frac{19}{34}-1\frac{15}{17}+\frac{2}{3}\)
\(\left(-2\right)^3.\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)
\(16\frac{2}{7}:\left(-\frac{3}{5}\right)+28\frac{2}{7}:\left(-\frac{3}{5}\right)\)
Câu 2: Tìm x biết
\(2.x-\frac{5}{4}=\frac{20}{15}\)
\(1,5:0,3=x:-15\)
\(|2x-1|=2\)
Câu 3: Thực hiện phép tính hợp lí
\(\frac{11}{12}.\frac{15}{33}+\frac{11}{12}.\frac{2}{22}\)
\(3/3\frac{1}{8}.11\frac{17}{19}-3\frac{1}{8}.13\frac{17}{19}\)
\(28\frac{2}{7}:\left(-\frac{3}{5}\right)+16\frac{2}{7}:\left(-\frac{3}{5}\right)\)
bài 1 : tính phân số:
a) \(\frac{5}{7}+\frac{4}{9}=?;\frac{4}{5}-\frac{2}{3}=?;\frac{9}{11}+\frac{3}{8}=?;\frac{16}{25}-\frac{2}{5}=?\)=?
b)\(5+\frac{3}{5}=?;10-\frac{9}{16}=?;\frac{2}{3}-\left(\frac{1}{6}+\frac{1}{8}\right)=?\)
c)\(\frac{5}{7}+\frac{7}{6}=?;\frac{7}{12}+\frac{17}{18}=?;\frac{9}{8}+\frac{15}{32}=?;4+\frac{35}{45}=?\)
d)\(\frac{11}{4}-\frac{15}{16}=?;\frac{5}{6}-\frac{5}{8}=?;\frac{196}{64}-2=?;3-\frac{13}{9}=?\)
e)\(\frac{8}{5}+\frac{7}{6}+\frac{5}{9}-2=?;3-\frac{5}{6}-\frac{4}{9}+\frac{32}{24}=?\)
a)\(\dfrac{5}{7}+\dfrac{4}{9}=\dfrac{45}{63}+\dfrac{28}{63}=\dfrac{73}{63}\) ; \(\dfrac{9}{11}+\dfrac{3}{8}=\dfrac{72}{88}+\dfrac{33}{88}=\dfrac{105}{88}\)
\(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\); \(\dfrac{16}{25}-\dfrac{2}{5}=\dfrac{16}{25}-\dfrac{10}{25}=\dfrac{6}{25}\)
Tính:
\(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+\frac{1}{7}-\frac{1}{8}+.....+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2017}.\)
\(\frac{5-\frac{5}{3}+\frac{5}{9}-\frac{5}{27}}{8-\frac{8}{3}+\frac{8}{9}-\frac{8}{27}}:\frac{15-\frac{15}{11}+\frac{15}{121}}{16-\frac{16}{11}+\frac{16}{121}}.\)
Tính nhanh:
\(\frac{4}{17}-\frac{7}{15}+\frac{13}{17}-\frac{8}{15}+\frac{5}{8}-\frac{7}{16}\)
\(=\left(\frac{4}{17}+\frac{13}{17}\right)-\left(\frac{7}{15}+\frac{8}{15}\right)+\left(\frac{10}{16}-\frac{7}{16}\right)\)
\(=1-1+\frac{3}{16}\)
\(\frac{3}{16}\)
gộp 1,3
2,4
5,6
thì ra 17/17-15/15+3/16=3/16
hk tốt!
Nếu \(\cos a = \frac{1}{4}\) thì \(\cos 2a\) bằng:
A.\(\frac{7}{8}\)
B.\( - \frac{7}{8}\)
C.\(\frac{{15}}{{16}}\)
D.\( - \frac{{15}}{{16}}\)
Ta có \(\cos 2a = 2{\cos ^2}a - 1 = 2.{\left( {\frac{1}{4}} \right)^2} - 1 = \frac{{ - 7}}{8}\)
Chọn B
Tính hợp lí
\(\frac{5-\frac{5}{3}+\frac{5}{9}-\frac{5}{27}}{8-\frac{8}{3}+\frac{8}{9}-\frac{8}{27}}\) : \(\frac{15-\frac{15}{11}+\frac{15}{121}}{16-\frac{16}{11}+\frac{16}{121}}\)
= 5/8:15/16
= .....( sử dụng máy tính đó bạn!)