Bài 10: Phép nhân phân số

`1/3 xx 4/5 + 1/3 xx 6/5 - 1/3`

`=1/3 xx 4/5 + 1/3 xx 6/5 - 1/3xx1`

`= 1/3 xx ( 4/5 + 6/5 -1)`

`= 1/3 xx 1`

`=1/3`

\(\dfrac{1}{3}\times\dfrac{4}{5}+\dfrac{1}{3}\times\dfrac{6}{5}-\dfrac{1}{3}=\dfrac{1}{3}\times\left(\dfrac{4}{5}+\dfrac{6}{5}-1\right)=\dfrac{1}{3}\times1=\dfrac{1}{3}\)

\(\dfrac{1}{3}.\dfrac{4}{5}+\dfrac{1}{3}.\dfrac{6}{5}-\dfrac{1}{3}\)

\(=\dfrac{1}{3}.\left(\dfrac{4}{5}+\dfrac{6}{5}\right)-\dfrac{1}{3}\)

\(=\dfrac{1}{3}.2-\dfrac{1}{3}\)

\(=\dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}\)

`1/3 xx 1/4 + 1/3 xx 6/5 - 1/3`

`=1/3 xx 1/4 + 1/3 xx 6/5 - 1/3xx1`

`=1/3 xx (1/4 + 6/5 -1)`

`=1/3xx 9/20`

`= 9/60`

`= 3/20`

\(\dfrac{1}{3}\times\dfrac{1}{4}+\dfrac{1}{3}\times\dfrac{6}{5}-\dfrac{1}{3}\)

\(=\dfrac{1}{12}+\dfrac{6}{15}-\dfrac{1}{3}=\dfrac{15}{180}+\dfrac{72}{180}-\dfrac{1}{3}=\dfrac{87}{180}-\dfrac{1}{3}=\dfrac{29}{60}-\dfrac{1}{3}=\dfrac{29}{60}-\dfrac{20}{60}=\dfrac{9}{60}=\dfrac{3}{20}\)

`1/3xx1/4+1/3xx6/5 -1/3`

`=1/3xx1/4+1/3xx6/5-1/3.1=1/3xx(1/4+6/5-1)`

`=1/3xx9/20`

`=3/20`

`@Nae`

\(\dfrac{8}{5}+\dfrac{1}{10}:3-\dfrac{2}{15}\)

\(=\dfrac{8}{5}+\dfrac{1}{10}\times\dfrac{1}{3}-\dfrac{2}{15}\)

\(=\dfrac{1}{30}+\dfrac{8}{5}-\dfrac{2}{15}\)

\(=\dfrac{1}{30}+\dfrac{24}{15}-\dfrac{2}{15}\)

\(=\dfrac{1}{30}+\dfrac{22}{15}\)

\(=\dfrac{3}{2}\)

`8/5+1/10:3-2/15`

`=8/5+1/10xx1/3-2/15`

`=8/5+1/30-2/15`

`=48/30+1/30-4/30`

`=45/30=3/2

\(\dfrac{8}{5}+\dfrac{1}{10}:3-\dfrac{2}{15}\)

\(=\dfrac{8}{5}+\dfrac{1}{10}.\dfrac{1}{3}-\dfrac{2}{15}\)

\(=\dfrac{8}{5}+\dfrac{1}{30}-\dfrac{2}{15}\)

\(=\dfrac{48}{30}+\dfrac{1}{30}-\dfrac{4}{30}\)

\(=\dfrac{45}{30}=\dfrac{3}{2}\)

\(a,\dfrac{11}{12}x+\dfrac{3}{4}=-\dfrac{1}{6}\)

\(\Leftrightarrow\dfrac{11}{12}x=-\dfrac{1}{6}-\dfrac{3}{4}\)

\(\Leftrightarrow\dfrac{11}{12}x=-\dfrac{11}{12}\)

\(\Leftrightarrow x=-\dfrac{11}{12}:\dfrac{11}{12}\)

\(\Leftrightarrow x=-\dfrac{11}{12}.\dfrac{12}{11}\)

\(\Leftrightarrow x=-1\)

\(b,3-\left(\dfrac{1}{6}-x\right).\dfrac{2}{3}=\dfrac{2}{3}\)

\(\Leftrightarrow3-\dfrac{2}{3}.\left(\dfrac{1}{6}-x\right)=\dfrac{2}{3}\)

\(\Leftrightarrow3-\dfrac{1}{9}+\dfrac{2}{3}x=\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{2}{3}x=\dfrac{2}{3}-3+\dfrac{1}{9}\)

\(\Leftrightarrow\dfrac{2}{3}x=-\dfrac{20}{9}\)

\(\Leftrightarrow x=-\dfrac{20}{9}:\dfrac{2}{3}\)

\(\Leftrightarrow x=-\dfrac{10}{3}\)

`6/13 *5/18 + (-7/24) +5/18*7/13 + (-5/24)`

`= 5/18(6/13 +7/13) +(-7/24-5/24)`

`= 5/18+ (-1/2)`

` = 5/18 -9/18 = -4/18 = -2/9`

Đề :

`6/13`.`5/18+(-7/24)`+`5/18`.`7/13+(-5/24)`

`=` `5/18.(6/14+7/13)+(-7/24-5/24)`

`=` `5/18+(-1/2)`

`=` `5/18-9/18`

`=` `(-4/18)`

`=` `(-2/9)`

@Nae

`a, -21/15 . (-10)/14 = 210/210=1`

`b, (-2/3)^2= 4/9`

`c, (-3)/4 . (-4)/5 . 16/9= 192/180=16/15`

`d, (-8)/3 . 5/6= -40/18=-20/9`

`e, 16/30 . 5/12= 8/15 . 5/12=40/180=2/9`

`f, 13/30 . (-1)/5= -13/150`

`g, 2/21 . 3/28= 6/588= 1/98`

`h, (-3/4)^3= -27/64`

1: \(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)\)

=1/2*10/39

=5/39

2: \(=\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)=\dfrac{5}{2}\cdot\dfrac{10}{11}=\dfrac{50}{22}=\dfrac{25}{11}\)

13/47 . 1/8 + 13/2 . 1/47 +13/47 . -13/8 -34/47=13/47 . 1/8 + 13/47 . 1/2 + 13/47 . -13/8 -34/47=13/47 . [1/8 + 1/2 +(-13/8)] -34/47=13/47 .[1/8 + 4/8 + (-13/8)] -34/47=13/47.(-8/8) -34/47= -13/47 - 34/47=(-13/47)+(-34/47)=-47/47=-1 xong

Chỗ .- là sao bạn nhỉ? Bạn xem lại đề.

Thời gian trong ngày Mai đã dành cho công việc cá nhân khác:
\(1-\dfrac{1}{3}-\dfrac{1}{24}-\dfrac{7}{16}=\dfrac{3}{16}\left(ngày\right)\)

Lời giải:

$S=(100+99-98-97)+(96+95-94-93)+...+(4+3-2-1)$

$=\underbrace{4+....+4}_{25}=4.25=100$