Tính nhanh
3/4×5/7+3/2×2/7+5/4×3/
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= 51/20
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= 3/14
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= 4/7 - 2/7
= 2/7
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= 17/45
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= 2/3
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= 2 x 1/4
= 1/2
11211 - 1 - 1 - 1 - 2 - 2 - 2 - 2 - 3 - 3 - 3 - 4 - 4 - 4 - 5 - 5 - 5 - 6 - 7 - 7 - 65 - 4 - 3 - 2 - 34 - 5 - 3 - 3 - 4
= 11211 - (1 + 1 + 1 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 7 + 65 + 4 + 3 + 2 + 34 + 5 + 3 + 3 + 4)
= 11211 - 190
= 11021
a: \(=\dfrac{4}{5}\cdot\dfrac{7}{3}\cdot\dfrac{3}{7}\cdot\dfrac{5}{4}+2011=2011+1=2012\)
b: \(=\dfrac{1}{3}\cdot\dfrac{9}{7}\cdot\dfrac{7}{9}=\dfrac{1}{3}\)
a)
\(11\dfrac{3}{13}-\left(2\dfrac{4}{7}+5\dfrac{3}{13}\right)\)
\(=\dfrac{146}{13}-\left(\dfrac{18}{7}+\dfrac{68}{13}\right)\)
\(=\dfrac{146}{13}-\dfrac{18}{7}-\dfrac{68}{13}\)
\(=\left(\dfrac{146}{13}-\dfrac{68}{13}\right)-\dfrac{18}{7}\)
\(=6-\dfrac{18}{7}\)
\(=\dfrac{24}{7}\)
b)
\(\dfrac{2}{7}\times5\dfrac{1}{4}-\dfrac{2}{7}\times3\dfrac{1}{4}\)
\(=\dfrac{2}{7}\times\dfrac{21}{4}-\dfrac{2}{7}\times\dfrac{13}{4}\)
\(=\dfrac{2}{7}\times\left(\dfrac{21}{4}-\dfrac{13}{4}\right)\)
\(=\dfrac{2}{7}\times2\)
\(=\dfrac{4}{7}\)
\(a,11\dfrac{3}{13}-\left(2\dfrac{4}{7}+5\dfrac{3}{13}\right)\)
\(=\dfrac{146}{13}-\left(\dfrac{18}{7}+\dfrac{68}{13}\right)\)
\(=\dfrac{146}{13}-\dfrac{68}{13}-\dfrac{18}{7}\)
\(=6-\dfrac{18}{7}\)
\(=\dfrac{24}{7}\)
\(b,\dfrac{2}{7}\times5\dfrac{1}{4}-\dfrac{2}{7}\times3\dfrac{1}{4}\)
\(=\dfrac{2}{7}\times\dfrac{21}{4}-\dfrac{2}{7}\times\dfrac{13}{4}\)
\(=\dfrac{2}{7}\times\left(\dfrac{21}{4}-\dfrac{13}{4}\right)\)
\(=\dfrac{2}{7}\times2\)
\(=\dfrac{4}{7}\)
a)2/3*4/7+1/3*4/7=(2/3+1/3)*4/7=1*4/7=4/7
b)5/8*3/7*7/3=5/8*1=5/8
c)(4/5+2)*5/4=4/5*5/4+2=1+2=3
x-7=-5
=>x=-5+7=2
x+2=0
=>x=0-2=-2
\(\left(3x-2^4\right)\cdot7^3=2\cdot7^4\)
=>\(3x-16=\frac{2\cdot7^4}{7^3}=2\cdot7=14\)
=>3x=16+14=30
=>x=30/3=10
|x-5|=|-7|
=>x-5=7 hoặc x-5=-7
=>x=12 hoặc x=-2
x-[42+(-28)]=-8
=>x-14=-8
=>x=-8+14
=>x=6
128-3(x+4)=23
=>3(x+4)=128-23=105
=>x+4=35
=>x=35-4=31
4-(7-x)=x-(13-4)
=>4-7+x=x-9
=>x-3=x-9
=>-3=-9(vô lý)
=>x∈∅
Bài 2:
S1=1+2+...+999
\(=\frac{999\left(999+1\right)}{2}=999\cdot\frac{1000}{2}\)
\(=999\cdot500=499500\)
S1=10+12+...+2010
Số số hạng của dãy là:
(2010-10):2+1=2000:2+1=1001(số)
Tổng của dãy số là:
\(S_1=\left(2010+10\right)\cdot\frac{1001}{2}=2020\cdot\frac{1001}{2}=1001\cdot1010=1011010\)
\(=\dfrac{3}{4}\times\left(\dfrac{5}{7}+\dfrac{4}{7}+5\right)\)
\(=\dfrac{3}{4}\times\dfrac{44}{7}=\dfrac{33}{7}\)