Tính bằng 2 cách: a/ \(4\frac{3}{7}.2\) b/ \(5\frac{1}{2}.3\)
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=\(\frac{36-4+3}{6}-\frac{30+10-9}{6}-\frac{18-14+15}{6}\)
=\(\frac{35}{6}-\frac{31}{6}-\frac{19}{6}=\frac{35-31-19}{6}-\frac{15}{6}=-\frac{5}{2}\)
bài này thì dễ:
\(\left(6-\frac{2}{3}+\frac{1}{2}\right)-\left(5+\frac{5}{3}-\frac{3}{2}\right)-\left(3-\frac{7}{3}+\frac{5}{2}\right)\)
Cách 1:
\(\frac{35}{6}-\frac{31}{6}-\frac{19}{6}=\frac{35-31-19}{6}=-\frac{15}{6}=-\frac{5}{2}\)
Cách 2:
\(6-\frac{2}{3}+\frac{1}{2}-5-\frac{5}{3}+\frac{3}{2}-3+\frac{7}{3}-\frac{5}{2}=-2\frac{1}{2}=-\frac{5}{2}\)
a)
Cách 1
3/4*1/2*2
=3/8*2
=3/4
Cách 2
3/4*1/2*2
=3/4*(1/2*2)
=3/4*1
=3/4
b)
Cách 1
(3/4+1/2)*5/7
=5/4*5/7
=25/28
Cách 2
(3/4+1/2)*5/7
=3/4*5/7+5/7*1/2
=15/28+5/14
=25/28
c)
Cách 1
5/7*13/21+2/7*13/21
=65/147+26/147
=13/21
cách 2
5/7*13/21+2/7*13/21
=13/21*(2/7+5/7)
=13/21*1
=13/21
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{10}}\right)\)\(\Leftrightarrow A=1-\frac{1}{2^{10}}=\frac{2^{10}-1}{2^{10}}\)
nhân A với 1/2
ta có: A= 1/2+1/2^2+1/2^3+...+1/2^10
1/2.A= 1/2^2+1/2^3+...+1/2^11
lấy A-1/2.A= 1/2-1/2^11
1/2.A=1/2-1/2^11
A= (...-...):1/2
a, \(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}=\frac{1\cdot2\cdot3\cdot4\cdot5}{2\cdot3\cdot4\cdot5\cdot6}=\frac{1}{6}\)
b, 10,3 x 37,5 - 37,5 x 10,2
= 37,5 x ( 10,3 - 10,2 )
= 37,5 x 0,1
= 3,75
a) \(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\)
\(=\frac{1\times2\times3\times4\times5}{2\times3\times4\times5\times6}\)
\(=\frac{1}{6}\)
b) 10,3 x 37,5 - 37,5 x 10,2
= 37,5 x ( 10,3 - 10,2 )
= 37,5 x 0,1
= 3,75
a, C1: \(4\frac{3}{7}.2=\frac{31}{7}.2=\frac{31.2}{7}=\frac{62}{7}=8\frac{6}{7}\)
C2: \(4\frac{3}{7}.2=\left(4+\frac{3}{7}\right).2=\left(4.2\right)+\left(\frac{3}{7}.2\right)=8+\frac{6}{7}=8\frac{6}{7}\)
b, C1: \(\frac{11}{2}.3=\frac{11.3}{2}=\frac{33}{2}=16\frac{1}{2}\)
C2: \(5\frac{1}{2}.3=\left(5+\frac{1}{2}\right).3=\left(5.3\right)+\left(\frac{1}{2}.3\right)=15+1\frac{1}{2}=16\frac{1}{2}\)