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\(A=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{9801}\right)\)
\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\left(1-\dfrac{1}{99}\right)\left(1+\dfrac{1}{99}\right)\)
\(=\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{98}{99}\right)\cdot\left(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}\right)\)
\(=\dfrac{1}{99}\cdot\dfrac{100}{2}=\dfrac{50}{99}\)
\(\frac{75}{100}+\frac{3}{4}\times29+75\%\times30+0,75\times40\)
\(=0,75+0,75\times29+\frac{75}{100}\times30+0,75\times40\)
\(=0,75\times1+0,75\times29+0,75\times30+0,75\times40\)
\(=0,75\times\left(1+29+30+40\right)\)
\(=0,75\times100\)
\(=75\)
1000 - (45,7 x 2,5 + 8,5 x 45,7 - 45,7)
= 1000 - (45,7 x 2,5 + 8.5 x 45,7 -45,7 x 1)
= 1000 - (45,7 x ( 2,5 +8,5 -1))
= 1000 - (45,7 x 10)
= 1000 - 457
= 553.
Chúc bạn học tốt
3/25 x ( 15/7 - 2/7 ) + 3/7 x 1/25
= 3/25 x 13/7 + 3/7 x 1/25
= (3 x 13/7 + 3/7 ) x 1/25
= 42/7 x 1/25
= 6 x 1/25
= 6/25
\(\dfrac{3}{25}\times\dfrac{15}{7}+\dfrac{3}{7}\times\dfrac{1}{25}-\dfrac{2}{7}\times\dfrac{3}{25}\)
\(=\dfrac{3}{25}\times\left(\dfrac{15}{7}-\dfrac{2}{7}\right)+\dfrac{3}{7}\times\dfrac{1}{25}\)
\(=\dfrac{3}{25}\times\dfrac{13}{7}+\dfrac{3}{7}\times\dfrac{1}{25}\)
\(=\dfrac{3\times13}{25\times7}+\dfrac{3\times1}{7\times25}\)
\(=\dfrac{39}{175}+\dfrac{3}{175}\)
\(=\dfrac{39+3}{175}\)
\(=\dfrac{42}{175}\)
\(=\dfrac{6}{25}\)
a) 22 giờ 48 phút - 3giờ 25 phút x 5=5 giờ 43 phút
b) 45 ngày - 15 ngày 16 giờ : 4= 41 ngày 11 giờ
\(\dfrac{45.21.25}{7.15.36}=\dfrac{3.3.3.5.7.5.5}{7.5.3.3.2.3.2}=\dfrac{25}{4}\)
45\7 x 21\15 x 25/36
=45x21x25/7x15x36
=15x3x7x3x25/7x15x3x12
=3x25/12
=75/12
=25/4
=25(24+48)+75(16+56)
=72*25+72*75
=72*100
=7200
\(25.24+25.48+75.16+75.56\)
\(=25.\left(24+48\right)+75.\left(16+56\right)\)
\(=25.72+75.72\)
\(=\left(25+75\right).72\)
\(=100.72\)
\(=7200\)