tính bằng cách thuận tiện nhất.
a.7/12 cộng 5/24 cộng 5/12 cộng 19/24
b.5/18 cộng 4/15 cộng/7/18 cộng 1/15.
c.1/5 cộng 5/9 cộng 4/5 cộng 1/9 cộng 3/9.
d.1/3 cộng 1/6 cộng 4/3 cộng 2/6 cộng 2/3 cộng 5/6.
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6 2/7 + 7 3/5 + 8 6/9 + 9 1/4 + 2/5 + 5/7 + 1/3 x 3/4 + 1967
= 44/7 + 38/5 + 78/9 + 37/4 + 2/5 + 5/7 + 1/3 + 1967
= ( 44/7 + 5/7 ) + ( 38/5 + 2/5 ) + ( 26/3 + 1/3 ) + ( 37/4 + 3/4 ) +1967
= 7 + 8 + 9 + 10 + 1967
= 15 + 9 + 10 + 1967
= 24 + 10 + 1967
= 34 + 1967
= 2001
a: \(100+98+96+...+2-97-95-...-1\)
\(=100+\left(98-97\right)+\left(96-95\right)+...+\left(2-1\right)\)
\(=100+1+...+1\)
\(=100+49=149\)
b: \(1+2-3-4+5+6-7-8+9+10-11-12+...+...-299-300+301+302\)
\(=\left(1+2-3-4\right)+\left(5+6-7-8\right)+...+\left(297+298-299-300\right)+603\)
\(=603+\left(-4\right)+\left(-4\right)+...+\left(-4\right)\)
\(=603-4\cdot75=603-300=303\)
a: \(A=\dfrac{5}{7}-\dfrac{2}{7}+\dfrac{8}{11}+\dfrac{3}{11}+\dfrac{1}{2}=\dfrac{3}{7}+\dfrac{1}{2}+1=\dfrac{6+7+14}{14}=\dfrac{27}{14}\)
b: \(B=\dfrac{11}{17}+\dfrac{6}{17}-\dfrac{8}{19}-\dfrac{30}{19}+\dfrac{-3}{4}=1-2-\dfrac{3}{4}=-1-\dfrac{3}{4}=-\dfrac{7}{4}\)
c: \(C=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}=\dfrac{49}{50}\)
Bài 1:
a: \(\dfrac{25}{42}-\dfrac{20}{63}=\dfrac{75-40}{126}=\dfrac{35}{126}=\dfrac{5}{18}\)
b: \(\dfrac{9}{20}-\dfrac{13}{75}-\dfrac{1}{6}=\dfrac{135}{300}-\dfrac{52}{300}-\dfrac{50}{300}=\dfrac{33}{300}=\dfrac{11}{100}\)
a) 7/12 + 5/24 + 5/12 + 19/24
= (7/12 + 5/12) + (5/24 + 19/24)
= 1 + 1
= 2
b) 5/18 + 4/15 + 7/18 + 1/15
= (5/18 + 7/18) + (4/15 + 1/15)
= 2/3 + 1/3
= 1
c) 1/5 + 5/9 + 4/5 + 1/9
= (1/5 + 4/5) + (5/9 + 1/9)
= 1 + 1/3
= 4/3
d) 1/3 + 1/6 + 4/3 + 2/6 + 2/3 + 5/6
= (1/3 + 4/3 + 2/3) + (1/6 + 1/6 + 5/6)
= 7/3 + 7/6
= 7/2
a) \(\dfrac{7}{12}+\dfrac{5}{24}+\dfrac{5}{12}+\dfrac{19}{24}\\ =\left(\dfrac{7}{12}+\dfrac{5}{12}\right)+\left(\dfrac{5}{24}+\dfrac{19}{24}\right)\\ =\dfrac{7+5}{12}+\dfrac{5+19}{24}\\ =\dfrac{12}{12}+\dfrac{24}{24}\\ =1+1=2\)
b) \(\dfrac{5}{18}+\dfrac{4}{15}+\dfrac{7}{18}+\dfrac{1}{15}\\ =\left(\dfrac{5}{18}+\dfrac{7}{18}\right)+\left(\dfrac{4}{15}+\dfrac{1}{15}\right)\\ =\dfrac{5+7}{18}+\dfrac{4+1}{15}\\ =\dfrac{12}{18}+\dfrac{5}{15}\\ =\dfrac{1}{3}+\dfrac{1}{3}=\dfrac{1+1}{3}=\dfrac{2}{3}\)