Gọi số sách của 3 lớp 7A, 7B, 7C lần lượt là x,y,z ( cuốn sách)

- Số sách của 3 lớp 7A, 7B, 7C tỉ lệ với các số 5,6,4

=> x+y+z = 180

Theo bài, ta có:

\(\dfrac{x}{5}=\dfrac{y}{6}=\dfrac{z}{4}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{5}=\dfrac{y}{6}=\dfrac{z}{4}\) = \(\dfrac{x+y+z}{5+6+4}=\dfrac{180}{15}=12\)

\(\dfrac{x}{5}=12=>x=12\cdot5=60\)

\(\dfrac{y}{6}=12=>y=12\cdot6=72\)

\(\dfrac{z}{4}=12=>z=12\cdot4=48\)

Vậy số sách của 3 lớp 7A, 7B, 7C đã quyên góp lần lượt là 60,72,48 cuốn sách

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

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

\(x-\dfrac{2}{3}=\dfrac{3}{4}-\dfrac{4}{3}\)

\(x-\dfrac{2}{3}=\dfrac{-7}{12}\)

\(x=\dfrac{-7}{12}+\dfrac{2}{3}\)

\(x=\dfrac{-7+8}{12}\)

\(x=\dfrac{1}{12}\)

b) \(\left|\dfrac{1}{3}-x\right|=\dfrac{2}{5}\)

\(\left|-\dfrac{2}{5}\right|=\dfrac{2}{5}\)

\(\left|\dfrac{2}{5}\right|=\dfrac{2}{5}\)

=> \(\dfrac{1}{3}-x=\dfrac{2}{5}\)

=> \(\dfrac{1}{3}-x=\dfrac{-2}{5}\)

TH1: \(\dfrac{1}{3}-x=\dfrac{2}{5}\)

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

\(x=\dfrac{-1}{15}\)

TH2: \(\dfrac{1}{3}-x=\dfrac{-2}{5}\)

\(x=\dfrac{1}{3}+\dfrac{2}{5}\)

\(x=\dfrac{11}{15}\)

c) \(\dfrac{x-1}{3}=\dfrac{27}{x-1}\)

\(\left(x-1\right)\left(x-1\right)=3\cdot27\)

\(\left(x-1\right)^2=81\)

\(\left(x-1\right)^2=9^2=\left(-9\right)^2\)

TH1: x-1 = 9

x = 10

TH2: x-1 = -9

x = -9 +1

x= -8

Vậy x ϵ { 10 ; -8}

a) \(\dfrac{7}{2}-\left(\dfrac{3}{4}+\dfrac{1}{5}\right)\)

= \(\dfrac{7}{2}-\dfrac{19}{20}\)

=\(\dfrac{70-19}{20}\)

=\(\dfrac{51}{20}\)

b)\(\dfrac{12}{23}\cdot\dfrac{7}{13}+\dfrac{11}{23}\cdot\dfrac{7}{13}\)

= \(\left(\dfrac{12}{13}+\dfrac{11}{23}\right)\cdot\dfrac{7}{13}\)

= \(1\cdot\dfrac{7}{13}\) = \(\dfrac{7}{13}\)

c) \(\left|-2\right|-\left(\dfrac{5}{9}-\dfrac{2}{3}\right)^2:\dfrac{4}{27}\)

= \(2-\dfrac{1}{81}:\dfrac{4}{27}\)

= \(2-\dfrac{1}{12}\) = \(\dfrac{23}{12}\)

1 người làm xong việc trong số ngày là

            12 x 10 = 120 (ngày)

Muốn làm xong trong 8 ngày cần số người là

            120 : 8 = 15 (người)

Chu vi mảnh vườn đó là:

(5,5 + 3,75) .2 = 18,5 (m)

Số khóm hoa cần trồng là:

18,5 : \(\dfrac{1}{4}\) = 74 (khóm)

Vậy cần trồng 74 khóm hoa

a) \(\dfrac{1}{5}\)+\(\dfrac{4}{5}\):x = 0,75

  \(\dfrac{1}{5}\)+\(\dfrac{4}{5}\):x = \(\dfrac{3}{4}\)

      \(\dfrac{4}{5}\):x = \(\dfrac{3}{4}\)-\(\dfrac{1}{5}\)

      \(\dfrac{4}{5}\):x = \(\dfrac{15}{20}-\dfrac{4}{20}\)

      \(\dfrac{4}{5}\):x = \(\dfrac{11}{20}\)

          x = \(\dfrac{11}{20}\). \(\dfrac{4}{5}\)

         x = \(\dfrac{11}{25}\)

   Vậy x = \(\dfrac{11}{25}\)

b)x+\(\dfrac{1}{2}\)= 1 -x

 x + x = 1 - \(\dfrac{1}{2}\)

2x    = \(\dfrac{1}{2}\)

 x     = \(\dfrac{1}{2}\) : 2

x      = \(\dfrac{1}{4}\)

 Vậy x = \(\dfrac{1}{4}\)

a) \(\dfrac{2}{3}\). \(\dfrac{5}{4}\)-\(\dfrac{3}{4}\).\(\dfrac{2}{3}\)

= \(\dfrac{2}{3}\).( \(\dfrac{5}{4}\)-\(\dfrac{3}{4}\))

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

 ​ b) 2.(\(-\dfrac{3}{2}\))²-\(\dfrac{7}{2}\)

=2. \(\dfrac{9}{4}\)-\(\dfrac{7}{2}\)

=\(\dfrac{9}{2}\)-\(\dfrac{7}{2}\)

= 1

c)\(-\dfrac{3}{4}\).5\(\dfrac{3}{13}\)-0.75.\(\dfrac{36}{13}\)

= \(-\dfrac{3}{4}\).\(\dfrac{63}{13}\)-\(\dfrac{3}{4}\).\(\dfrac{36}{13}\)

= \(\dfrac{3}{4}\).\(-\dfrac{63}{13}\)-\(\dfrac{3}{4}\).​​\(\dfrac{36}{13}\)

=\(\dfrac{3}{4}\).(\(-\dfrac{63}{13}\)-\(\dfrac{36}{13}\))

= \(\dfrac{3}{4}\). (-8)

= -6

​​

a) \(\dfrac{2}{3}\). \(\dfrac{5}{4}\)-\(\dfrac{3}{4}\).\(\dfrac{2}{3}\)

= \(\dfrac{2}{3}\).( \(\dfrac{5}{4}\)-\(\dfrac{3}{4}\))

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

 ​ b) 2.(\(-\dfrac{3}{2}\))²-\(\dfrac{7}{2}\)

=2. \(\dfrac{9}{4}\)-\(\dfrac{7}{2}\)

=\(\dfrac{9}{2}\)-\(\dfrac{7}{2}\)

= 1

c)\(-\dfrac{3}{4}\).5\(\dfrac{3}{13}\)-0.75.\(\dfrac{36}{13}\)

= \(-\dfrac{3}{4}\).\(\dfrac{63}{13}\)-\(\dfrac{3}{4}\).\(\dfrac{36}{13}\)

= \(\dfrac{3}{4}\).\(-\dfrac{63}{13}\)-\(\dfrac{3}{4}\).​​\(\dfrac{36}{13}\)

=\(\dfrac{3}{4}\).(\(-\dfrac{63}{13}\)-\(\dfrac{36}{13}\))

= \(\dfrac{3}{4}\). (-8)

= -6

​​

s cậu lại nói zị=)))