a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{3}{4}+...+\frac{1}{9}-\frac{1}{10}\)

= \(1+\left(\frac{-1}{2}+\frac{1}{2}\right)+\left(\frac{-1}{3}+\frac{1}{3}\right)+...+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{10}\)

= \(1-\frac{1}{10}\)

=\(\frac{9}{10}\)

b)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

= \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

=\(1+\left(\frac{-1}{3}+\frac{1}{3}\right)+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{7}+\frac{1}{7}\right)+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{11}\)

=\(1-\frac{1}{11}\)

= \(\frac{10}{11}\)

c) đặt A=\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}\)

     \(\frac{1}{3}A\)=\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)

     \(\frac{2}{3}A\)=\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

      \(\frac{2}{3}A\)=\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

     \(\frac{2}{3}A\)=\(1+\left(\frac{-1}{3}+\frac{1}{3}\right)+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{7}+\frac{1}{7}\right)+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{11}\)

     \(\frac{2}{3}A\)=\(\frac{10}{11}\)

         A= \(\frac{10}{11}:\frac{2}{3}\)

          A= \(\frac{10}{11}.\frac{3}{2}\)=\(\frac{15}{11}\)

d) giả tương tự câu c kết quả \(\frac{25}{11}\)

tổng đặc biệt đó bạn

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{9\times10}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(1-\frac{1}{10}=\frac{9}{10}\)

những câu sau cũng áp dụng như vậy nhé

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{11}\)

\(=1-\frac{1}{11}=\frac{10}{11}\)

\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}\)

\(=\frac{3}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{3}{2}.\left(1-\frac{1}{11}\right)=\frac{3}{2}.\frac{10}{11}=\frac{15}{11}\)

Tính:

2/7 + 5/7=1          

8/15 + 6/15 =14/15         

2/9 + 3/9 + 4/9=9/9=1

[ Không cần làm phép tính ]Điền vào ô trống <,>,= :

3/5 + 1/5 = 1/5 + 3/5

7/9 + 1/9 < 7/9 + 1/9 + 1/9

3/7 + 2/7 < 3/7 + 4/7

1/5 + 3/5 < 2/5 + 3/5

Tính:

2/7 + 5/7=1          

8/15 + 6/15 =14/15         

2/9 + 3/9 + 4/9=9/9=1

[ Không cần làm phép tính ]Điền vào ô trống <,>,= :

3/5 + 1/5 = 1/5 + 3/5

7/9 + 1/9 < 7/9 + 1/9 + 1/9

3/7 + 2/7 < 3/7 + 4/7

1/5 + 3/5 < 2/5 + 3/5

1) Ta có: \(\frac{-4}{7}-\frac{11}{19}+\frac{13}{19}\cdot\frac{-3}{7}+\frac{2}{19}:\frac{-7}{4}\)

\(=\frac{-4}{7}-\frac{11}{19}-\frac{39}{133}-\frac{8}{133}\)

\(=\frac{-76}{133}-\frac{77}{133}-\frac{39}{133}-\frac{8}{133}\)

\(=\frac{-200}{133}\)

2) Ta có: \(\left(\frac{-4}{9}+\frac{3}{5}\right):\frac{1}{\frac{1}{5}}+\left(\frac{1}{5}-\frac{5}{9}\right):\frac{1}{\frac{1}{5}}\)

\(=\left(\frac{-4}{9}+\frac{3}{5}\right)\cdot\frac{1}{5}+\left(\frac{1}{5}-\frac{5}{9}\right)\cdot\frac{1}{5}\)

\(=\frac{1}{5}\left(\frac{-4}{9}+\frac{3}{5}+\frac{1}{5}-\frac{5}{9}\right)\)

\(=\frac{1}{5}\left(-1+\frac{4}{5}\right)\)

\(=\frac{1}{5}\cdot\frac{-1}{5}=\frac{-1}{25}\)

3) Ta có: \(\frac{4}{5}-\left(-\frac{2}{7}\right)-\frac{7}{10}\)

\(=\frac{4}{5}+\frac{2}{7}-\frac{7}{10}\)

\(=\frac{56}{70}+\frac{20}{70}-\frac{49}{70}\)

\(=\frac{27}{70}\)

4) Ta có: \(\frac{2}{7}-\left(-\frac{13}{15}+\frac{4}{9}\right)-\left(\frac{5}{9}-\frac{2}{15}\right)\)

\(=\frac{2}{7}+\frac{13}{15}-\frac{4}{9}-\frac{5}{9}+\frac{2}{15}\)

\(=\frac{2}{7}+1-1=\frac{2}{7}\)

5 + 4 = 9     1 + 6 = 7     4 + 2 = 6     9 + 1 = 10     2 + 7 = 9

9 - 5 = 4     7 - 1 = 6     6 - 4 = 2     10 - 9 = 1     9 - 2 = 7

9 - 4 = 5     7 - 6 = 1     6 - 2 = 4     10 - 1 = 9     9 - 7 = 2

5+4 = 9            1 + 6 = 7

5 + 4 = 9        1 + 6 = 7         4 + 2 = 6        9 + 1 = 10         2 + 7 = 9

9 -  5  = 4       7 - 1 = 6          6 - 4 = 2         10 - 9 = 1          9 - 2 =  7

9 - 4 = 5         7 - 6 = 1          6 - 2 = 4          10 - 1 = 9         9 - 7 = 2

Phương pháp giải:

Cộng các số lần lượt từ trái sang phải rồi điền kết quả vào chỗ trống.

Lời giải chi tiết:

8 + 5 = 13          8 + 7 = 15

8 + 4 = 12          8 + 2 + 3 = 13

8 + 2 + 5 = 15    8 + 2 + 2 = 12

9 + 5 = 14          9 + 7 = 16

9 + 8 = 17          9 + 1 + 4 = 14

9 + 1 + 6 = 16    9 + 1 + 7 = 17

13

12

15

14

17

16

15

13

12

16

14

17

a) \(\dfrac{5}{7}\times\dfrac{5}{9}+\dfrac{4}{9}\times\dfrac{5}{7}\)

\(=\dfrac{5}{7}\times\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\)

\(=\dfrac{5}{7}\times1\)

\(=\dfrac{5}{7}\)

b) \(\dfrac{1}{10}+\dfrac{5}{9}+\dfrac{4}{9}+\dfrac{9}{10}-1\)

\(=\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\left(\dfrac{1}{10}+\dfrac{9}{10}-1\right)\)

\(=1+0\)

\(=1\)

c) \(\dfrac{5}{7}\times\dfrac{5}{9}+\dfrac{4}{9}\times\dfrac{5}{7}+\dfrac{2}{7}\)

\(=\dfrac{5}{7}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\dfrac{2}{7}\)

\(=\dfrac{5}{7}+\dfrac{2}{7}\)

\(=1\)

d) \(\dfrac{2}{7}+\dfrac{2}{8}+\dfrac{1}{4}+\dfrac{1}{7}+\dfrac{4}{7}\)

\(=\left(\dfrac{2}{8}+\dfrac{1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{1}{7}+\dfrac{4}{7}\right)\)

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

\(=\dfrac{1}{2}+1\)

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

e) \(\dfrac{4}{5}+\dfrac{3}{10}+\dfrac{2}{10}+0,7\)

\(=\dfrac{4}{5}+\dfrac{5}{10}+\dfrac{7}{10}\)

\(=\dfrac{4}{5}+\dfrac{12}{10}\)

\(=\dfrac{4}{5}+\dfrac{6}{5}\)

\(=\dfrac{10}{5}\)

\(=2\)

g) \(362\times728+326\times272\)

\(=326\times\left(728+272\right)\)

\(=326\times1000\)

\(=326000\) 

14dm5cm=14,5dm;3dm7cm=3,7dm

chu vi hình chữ nhật đó là:

(14,5+3,7)x2=36,4(dm)

ĐS:36,4dm

14 dm 5 cm = 14,5 dm 

3 dm 7 cm = 3,7 dm 

Chiều rộng HCN là :

14,5 - 3,7 = 10,8 ( dm )

chu vi HCN là :

( 14,5 + 10,8 ) x 2 = 50,6 ( dm )

ĐS:..

ban lam sai roi

8 + 1 = 9     7 + 2 = 9     6 + 3 = 9     5 + 4 = 9

1 + 8 = 9     2 + 7 = 9     3 + 6 = 9     4 + 5= 9

9 - 8 = 1     9 - 7 = 2     9 - 6 = 3     9 - 5 = 4

9 - 1 = 8     9 - 2 = 7     9 - 3 = 6     9 - 4 = 5