Bài 8 : Tính chất cơ bản của phép cộng phân số

1: \(-\dfrac{1}{2}< \dfrac{x}{18}< \dfrac{-1}{3}\)

=>\(-\dfrac{9}{18}< \dfrac{x}{18}< -\dfrac{6}{18}\)

=>-9<x<-6

2: \(\dfrac{4}{7}x-\dfrac{2}{4}=\dfrac{1}{5}\)

=>\(\dfrac{4}{7}x=\dfrac{1}{5}+\dfrac{2}{4}=\dfrac{7}{10}\)

=>\(x=\dfrac{7}{10}:\dfrac{4}{7}=\dfrac{49}{40}\)

3: \(-\dfrac{2}{5}+\dfrac{4}{5}x=\dfrac{3}{5}\)

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

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

4: \(-\dfrac{3}{6}-\dfrac{4}{7}:x=-2\)

=>\(\dfrac{4}{7}:x=-\dfrac{3}{6}+2=2-\dfrac{1}{2}=\dfrac{3}{2}\)

=>\(x=\dfrac{4}{7}:\dfrac{3}{2}=\dfrac{4}{7}\cdot\dfrac{2}{3}=\dfrac{8}{21}\)

5: \(\dfrac{2}{5}+\dfrac{3}{4}:x=-\dfrac{1}{2}\)

=>\(\dfrac{3}{4}:x=-\dfrac{1}{2}-\dfrac{2}{5}=\dfrac{-9}{10}\)

=>\(x=-\dfrac{3}{4}:\dfrac{9}{10}=-\dfrac{3}{4}\cdot\dfrac{10}{9}=\dfrac{-30}{36}=-\dfrac{5}{6}\)

9: \(\dfrac{5}{7}-\dfrac{2}{3}x=\dfrac{4}{5}\)

=>\(\dfrac{2}{3}x=\dfrac{5}{7}-\dfrac{4}{5}=\dfrac{-3}{35}\)

=>\(x=-\dfrac{3}{35}:\dfrac{2}{3}=\dfrac{-9}{70}\)

Sửa đề: so sánh với 1/2

1/3^2<1/2*3

1/4^2<1/3*4

...

1/80^2<1/79*80

=>1/3^2+1/4^2+...+1/80^2<1/2-1/3+1/3-1/4+...+1/79-1/80=39/80<1/2

\(\dfrac{-5}{7}+\dfrac{3}{4}+\dfrac{-1}{5}+\dfrac{-2}{7}+\dfrac{1}{4}\\ =\left(\dfrac{-5}{7}+\dfrac{-2}{7}\right)+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)-\dfrac{1}{5}\\ =-1+1-\dfrac{1}{5}\\ =0-\dfrac{1}{5}\\ =\dfrac{-1}{5}\)

-3/31 +-6/17 +1/25 + -28/31 + -11/17 + -1/5

`(-1/6 + 5/12 )+7/12`

`= ( -2/12 + 5/12 )+7/12`

`= 3/12 + 7/12`

`= 1/4 + 7/12`

`= 3/12 + 7/12`

`= 10/12`

`=5/6`

(-1/6 + 5/12) + 7/12

\(\left(\dfrac{-1}{6}+\dfrac{5}{12}\right)+\dfrac{7}{12}\\ =\dfrac{-1}{6}+\dfrac{5}{12}+\dfrac{7}{12}\\ =\dfrac{-1}{6}+1\\ =\dfrac{5}{6}\)

\(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + .....+\(\dfrac{1}{n.(n+1)}\) = \(\dfrac{3}{10}\)

\(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\) +......+ \(\dfrac{1}{n}-\dfrac{1}{n+1}\) = \(\dfrac{3}{10}\)

\(\dfrac{1}{3}-\dfrac{1}{n+1}\) = \(\dfrac{3}{10}\)

         \(\dfrac{1}{n+1}\) = \(\dfrac{1}{3}-\dfrac{3}{10}\)

          \(\dfrac{1}{n+1}\) = \(\dfrac{1}{30}\)

           n + 1 = 30

           n = 30 - 1

           n = 29

Kết luận n = 29 là giá  trị thỏa mãn yêu cầu đề bài.

Bạn xem bài dưới nek

Số phần công việc mà 3người làm trong1 giờ là:

1/5+1/4+1/6=37/60(công việc)

37/60

B

B

B

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