\(\frac{5}{12}\times\frac{2}{3}+\frac{2}{3}\times\frac{7}{12}+\frac{1}{3}\)

\(=\frac{2}{3}\times\left(\frac{5}{12}+\frac{7}{12}\right)+\frac{1}{3}\)

\(=\frac{2}{3}\times1+\frac{1}{3}\)

\(=\frac{2}{3}+\frac{1}{3}\)

\(=1\)

\(\frac{5}{12}\times\frac{2}{3}+\frac{2}{3}\times\frac{7}{12}+\frac{1}{3}=\frac{2}{3}\times\left(\frac{5}{12}+\frac{7}{12}\right)+\frac{1}{3}\)

                                                   \(=\frac{2}{3}\times\frac{12}{12}+\frac{1}{3}=\frac{2}{3}\times1+\frac{1}{3}=\frac{2}{3}+\frac{1}{3}=\frac{3}{3}=1\)

5/12 x 2/3 + 2/3 x 7/12 + 1/3

=5/12 x 2/3 + 2/3 x 7/12 + 1/3 x 2

=(5/12 + 7/12 +12/12)x 2/3

=2x2/3

=4/3 

\(a.32,5-3\cdot0,87=32,5-2,61=29,89\)

\(8,5\cdot\left(1\dfrac{1}{2}+\dfrac{4}{4}\right):5=8,5\cdot\left(\dfrac{3}{2}+\dfrac{4}{4}\right):5\\ =8,5\cdot\left(\dfrac{6}{4}+\dfrac{4}{4}\right):5\\ =8,5\cdot\dfrac{10}{4}:5\\ =\dfrac{85}{4}:5\\ =\dfrac{17}{4}\)

\(b.30,96-6,45+14,4:3=30,96-6,45+4,8\\ =29,31\)

\(\dfrac{2}{5}\cdot\left(\dfrac{4}{5}-\dfrac{1}{2}\right)=\dfrac{2}{5}\cdot\left(\dfrac{8}{10}-\dfrac{5}{10}\right)\\ =\dfrac{2}{5}\cdot\dfrac{3}{10}=\dfrac{3}{25}\)

bài 2

\(a.2,5\cdot12,5\cdot8\cdot0,4=\left(2,5\cdot0,4\right)\left(12,5\cdot8\right)\\ =1\cdot100=100\)

b,\(\dfrac{12}{15}\cdot\dfrac{5}{6}\cdot\dfrac{3}{20}\cdot\dfrac{32}{5}=\dfrac{12\cdot5\cdot3\cdot32}{15\cdot6\cdot20\cdot5}\\ =\dfrac{3\cdot4\cdot5\cdot3\cdot4\cdot8}{3\cdot5\cdot2\cdot3\cdot5\cdot4\cdot5}=\dfrac{16}{25}\)

Bài 1: 

a) \(32.5-3\cdot0.87=32.5-2.61=29.89\)

\(8.5\cdot\left(1\dfrac{1}{2}+\dfrac{4}{4}\right):5=8.5\cdot\dfrac{5}{2}:5=\dfrac{17}{2}\cdot\dfrac{5}{2}:5=\dfrac{85}{4}\cdot\dfrac{1}{5}=\dfrac{17}{4}\)

b) \(30.96-6.45+14.4:3=24.51+4.8=29.33\)

\(\dfrac{2}{5}\left(\dfrac{4}{5}-\dfrac{1}{2}\right)=\dfrac{2}{5}\left(\dfrac{8}{10}-\dfrac{5}{10}\right)=\dfrac{2}{5}\cdot\dfrac{3}{10}=\dfrac{6}{50}=\dfrac{3}{25}\)

1/2 + 1/3 + 1/4 + 1/5 + 4/5 + 3/4 + 2/3 + 1/2

= (1/2 + 1/2) + (1/3 + 2/3) + (1/4 + 3/4) + (1/5 + 4/5)

= 1 + 1 + 1 + 1

= 4

\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{4}{5}+\dfrac{3}{4}+\dfrac{2}{3}+\dfrac{1}{2}\)

\(=\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{4}+\dfrac{3}{4}\right)+\left(\dfrac{1}{5}+\dfrac{4}{5}\right)\)

=1+1+1+1

=4

=(12+12)+(13+23)+(14+34)+(15+45)=(12+12)+(13+23)+(14+34)+(15+45)
=(12+12)+(13+23)+(14+34)+(15+45)

=1+1+1+1

=4

\(\frac{1}{3}x\)\(\frac{1}{2}-\frac{1}{5}x\)\(\frac{1}{2}\)

=(\(\frac{1}{3}-\frac{1}{5}\)) x \(\frac{1}{2}\)

=\(\frac{2}{15}x\)\(\frac{1}{2}\)

=\(\frac{1}{15}\)

1/3 * 1/2 - 1/5 * 1/2

= (1/3 + 1/5) * 1/2

=8/15*1/2

=4/15

1\3x1\2-1\5x1\2=1\3 x1\2-1\5x1\2=1\7-1\6=1\1=1

3/5 x 5 + 12 x 3/5 + 3 : 5/3

=3/5 x 5 + 12 x 3/5 + 3 x 3/5

= 3/5 x ( 5 + 12 + 3 ) 

= 3/5 x 20

= 12

\(\dfrac{3}{4}.\dfrac{2}{3}-\dfrac{1}{6}.\dfrac{3}{4}-\dfrac{3}{4}.\dfrac{1}{2}\) 

= \(\dfrac{3}{4}.\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\) 

= \(\dfrac{3}{4}.0\) 

= 0

\(\dfrac{3}{4}\cdot\dfrac{2}{3}-\dfrac{1}{6}\cdot\dfrac{3}{4}-\dfrac{3}{4}\cdot\dfrac{1}{2}\)

\(=\dfrac{3}{4}\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\)

\(=\dfrac{3}{4}\cdot\left(\dfrac{4}{6}-\dfrac{1}{6}-\dfrac{3}{6}\right)\)

=0

a,Ta có \(\frac{x}{6}=\frac{2}{3}\)

\(\Rightarrow3x=12\Rightarrow x=4\)

Vậy x = 4

b, \(\left(\frac{4}{7}+\frac{8}{9}\right)-\frac{5}{9}=\frac{4}{7}+\frac{8}{9}-\frac{5}{9}\)

\(=\frac{4}{7}+\left(\frac{8}{9}-\frac{5}{9}\right)\)

\(=\frac{4}{7}+\frac{1}{3}\)

\(=\frac{19}{21}\)

Bài 1 mình nhầm. x phần 6 = 4 phần 7 mới đúng. Cảm ơn bạn nhé

A = \(\dfrac{1}{2}\)+ \(\dfrac{1}{3}\)+ \(\dfrac{1}{4}\)+ \(\dfrac{1}{2}\)+ \(\dfrac{2}{3}\)+ \(\dfrac{3}{4}\)

A = ( \(\dfrac{1}{2}\)+ \(\dfrac{1}{2}\)) + ( \(\dfrac{1}{4}\)+\(\dfrac{3}{4}\)) +( \(\dfrac{1}{3}\)+ \(\dfrac{2}{3}\))

A = 1 + 1 + 1

A = 3

B = ( \(\dfrac{3}{4}\) + \(\dfrac{5}{7}\)+ \(\dfrac{16}{64}\)+ \(\dfrac{2}{7}\)) - 2

B = ( \(\dfrac{3}{4}\)+ \(\dfrac{1}{4}\)) + ( \(\dfrac{5}{7}\)+ \(\dfrac{2}{7}\)) - 2

B = 1 + 1 - 2

B = 2 - 2

B = 0