(3/5+2/5)+(19/13+7/13)+(5/1+16/11)

1+2+5+16/11

8+16/11

TỰ TÍNH

tính = cách hợp lí nhất

g: \(=-457+237+23-123=-220-100=-320\)

h: \(=\left(1-3\right)+\left(5-7\right)+...+\left(41-43\right)+\left(45-47\right)\)

\(=\left(-2\right)+\left(-2\right)+...+\left(-2\right)+\left(-2\right)\)

\(=-2\cdot12=-24\)

i: \(=173+27-46-54-19=200-100-19=100-19=81\)

k: \(=-52+82+49-15+13-36\)

\(=30+34-23\)

=30+11

=41

l: \(=\left(3-5\right)+\left(7-9\right)+\left(11-13\right)+\left(15-17\right)\)

\(=\left(-2\right)+\left(-2\right)+\left(-2\right)+\left(-2\right)\)

=-8

m: \(=\left(1-2\right)+\left(3-4\right)+...+\left(2001-2002\right)+2003\)

\(=2003-1-1-...-1\)

\(=2003-1001=1002\)

n:Số số hạng là:

\(\left[\left(-51\right)-\left(-99\right)\right]:1+1=49\left(số\right)\)

Tổng là \(\left(-51-99\right)\cdot\dfrac{49}{2}=-3675\)

o: \(=-62-38+1523-2523-92\)

\(=-100+1000-92=900-92=808\)

\(K=\frac{3^2-1}{5^2-1}.\frac{7^2-1}{9^2-1}...\frac{43^2-1}{45^2-1}\)

\(=\frac{3^2-1^2}{5^2-1^2}.\frac{7^2-1^2}{9^2-1^2}....\frac{43^2-1^2}{45^2-1^2}\)

\(=\frac{\left(3-1\right)\left(3+1\right)}{\left(5-1\right)\left(5+1\right)}.\frac{\left(7-1\right).\left(7+1\right)}{\left(9-1\right)\left(9+1\right)}....\frac{\left(43+1\right)\left(43-1\right)}{\left(45-1\right)\left(45+1\right)}\)

\(=\frac{2.4}{4.6}.\frac{6.8}{8.10}....\frac{44.42}{44.46}\)

\(=\frac{2.4.6.8...42.44}{4.6.8...44.46}=\frac{2}{46}=\frac{1}{23}\)

Vậy \(K=\frac{1}{23}\)

a) \(\frac{58}{19}+\frac{13}{17}+\frac{35}{43}+\frac{119}{19}+\frac{8}{43}\)

\(=\frac{13}{17}+\left(\frac{58}{19}+\frac{119}{19}\right)+\left(\frac{35}{43}+\frac{8}{43}\right)\)

\(=\frac{13}{17}+\frac{204}{19}+1\)

\(=\frac{1808}{133}\)

b) \(\frac{-5}{7}.\frac{2}{11}+\frac{-5}{7}.\frac{9}{11}+\frac{13}{4}\)

\(=\frac{-5}{7}.\left(\frac{2}{11}+\frac{9}{11}\right)+\frac{13}{4}\)

\(=\frac{-5}{7}.1+\frac{13}{4}\)

\(=\frac{71}{28}\)

c) \(\frac{146}{13}-\left(\frac{21}{7}+\frac{68}{13}\right)\)

\(=\left(\frac{164}{13}-\frac{68}{13}\right)+3\)

\(=\frac{135}{13}\)

d) \(\frac{2}{7}.\frac{21}{4}-\frac{2}{7}.\frac{13}{4}\)

\(=\frac{2}{7}.\left(\frac{21}{4}-\frac{13}{4}\right)\)

\(=\frac{2}{7}.\frac{8}{4}\)

\(=\frac{4}{7}\)

P/s: Mk ko chắc nữa!

b: \(=\dfrac{-5}{7}\left(\dfrac{2}{11}+\dfrac{9}{11}\right)+\dfrac{13}{4}=\dfrac{-5}{7}+\dfrac{13}{4}=\dfrac{-20+91}{28}=\dfrac{71}{28}\)

c: \(=\dfrac{146}{13}-3-\dfrac{68}{13}=6-3=3\)

d: \(=\dfrac{2}{7}\left(\dfrac{21}{4}-\dfrac{13}{4}\right)=\dfrac{4}{7}\)

a: 14/5-7/5=7/5

b: 7/8-1/3+5/4

=21/24-8/24+30/24

=43/24

c; =7/6+5/6+2/15+13/15

=2+1

=3

d: =4*5/3*11=20/33

e: =2/9*1/6*1/4=2/9*1/24=1/108

2:
a: \(=\dfrac{3}{9}\cdot\dfrac{4}{4}\cdot\dfrac{5}{5}\cdot\dfrac{6}{6}\cdot\dfrac{7}{7}=\dfrac{1}{3}\)

b: \(=\dfrac{1}{6}\left(\dfrac{22}{3}-\dfrac{2}{3}\right)=\dfrac{10}{3}\cdot\dfrac{1}{6}=\dfrac{10}{18}=\dfrac{5}{9}\)

c; \(=\dfrac{1}{3}\left(9-\dfrac{2}{5}-\dfrac{3}{5}\right)=\dfrac{8}{3}\)

14/5-7/5=7/5 

7/8-1/3+5/4=13/24+5/4=43/24 

7/6+2/15+5/6+13/15=13/10+5/6+13/15=32/15+13/15=3

4/3*5/11=20/35

2/9:6*1/4=1/27*1/4=1/108

a, ( 1/2 - 13/14 ) : 5/7 - ( -2/21 + 1/7 ) : 5/7

= ( 7/14 - 13/14 ) : 5/7 - ( -2/21 + 3/21 ) : 5/7

= -3/7 : 5/7 - 1/21 : 5/7

= -3/7 . 7/5 - 1/21 . 7/5

= ( -3/7 - 1/21 ) . 7/5

= ( -9/7+ -1/21 ) . 7/5

= -10/21 . 7/5

= -2/3

b, (68/5 + 19/4 ) - 43/5

= 68/5 + 19/4 - 43/5

= ( 68/5 - 43/5 ) + 19/4

= 5 +19/4

= 39/4

c, ( 93/11 + 29/8 ) - 38/11

= 93/11 + 29/8 - 38/11

= ( 93/11 - 38/11 ) + 29/8

= 5 + 29/8

=69/8

d, 4/9 : ( -1/7 ) + 59/9 : ( -1/7 )

= 4/9 . -7 + 59/9 . -7

= ( 4/9 + 59/9 ) . -7

= 7 . -7

= -49