Tham khảo :

Câu hỏi của ๖ۣۜ๖ۣۜHσàηɠ ๖ۣۜTử ๖ۣۜGĭóッ - Toán lớp 7 - Học trực tuyến OLM

a)              75 - 3.(2/13+1/17-1/19)            3.[25-(2/13+1/17-1/19)]

               -------------------------------------- = ---------------------------------------------- = 3/11

                275-11.(2/13+1/17-1/19)            11.[25-(2/13+1/17-1/19)]

a)     \(\frac{75-\frac{6}{13}+\frac{3}{17}-\frac{3}{19}}{275-\frac{22}{13}+\frac{11}{17}-\frac{11}{19}}=\frac{75-3.\left(\frac{2}{13}+\frac{1}{17}-\frac{1}{19}\right)}{275-11.\left(\frac{2}{13}+\frac{1}{17}-\frac{1}{19}\right)}\)

                                                         \(=\frac{75-3}{275-11}\)

                                                         \(=\frac{72}{264}=\frac{3}{11}\)

b)          \(\frac{2}{3.5}+\frac{7}{5.12}+\frac{9}{4.39}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{12}+\frac{3}{52}\)

                                                        \(=\frac{1}{3}-\frac{1}{12}+\frac{3}{52}\)

                                                       \(=\frac{1}{4}+\frac{3}{52}=\frac{4}{13}\)

tử số = 2^10 . 3^8 - 2^10 . 3^9 = 2^10 . 3^8 . (1-3) 

mẫu số = 2^10 . 3^8 + 3^8 . 2^10 . 5 = 2^10 . 3^8 . (1+5)

Đ/S: \(\frac{1-3}{1+5}\)=\(\frac{-1}{3}\)

\(B=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+....+\frac{19}{9^2.10^2}\)

\(B=\frac{3}{1.4}+\frac{5}{4.9}+\frac{7}{9.16}+....+\frac{19}{81.100}\)

\(B=\frac{4-1}{1.4}+\frac{9-4}{4.9}+\frac{16-9}{9.16}+....+\frac{100-81}{81.100}\)

\(B=\frac{4}{1.4}-\frac{1}{1.4}+\frac{9}{4.9}-\frac{4}{4.9}+\frac{16}{9.16}-\frac{9}{9.16}+...+\frac{100}{81.100}-\frac{81}{81.100}\)

\(B=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+....+\frac{1}{81}-\frac{1}{100}\)

\(B=1-\frac{1}{100}< 1\)

=> B < 1 (Đpcm)

B = 3/1².2² + 5/2².3² + 7/3².4² + ... + 19/9².10²

B = 3/1.4 + 5.4.9 + 7/9.16 + ... + 19/81.100

B = 1 - 1/4 + 1/4 - 1/9 + 1/9 - 1/16 + ... + 1/81 - 1/100

B = 1 - 1/100 < 1 ( đpcm)

a, -5/11.7/15.(11/-5)(-30)

=(-5/11.11/-5).(7/15.-30)

=1.7.(-30)/15

=1.7.(-2).15/15

=1.7.(-2)

=-14

b,(11/12):(33/36).3/5

=11/12:(11.3/12.3).3/5

=11/12:11/12.3/5

=1.3/5

=3/5

c,(-5/-9).3/11+(-13/18).3/11

=5/9.3/11+ -13/18.3/11

=3/11.(5/9+ -13/18)

=3/11.(10/18+ -13/18)

=3/11.-3/18

= -9/198

= -1/22

Bài 2:

a,-7/15.5/8.15/7.(-16)

=(-7/15.15/7)(5/8. -16)

= -1.-10

= 10

b,(-1/-2).16/5+(-1/-2)(-11/5)

= 1/2.16/5+1/2. (-11/5)

=1/2.(16/5+ -11/5)

=1/2.5/5

=1/2.1

=1/2

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