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\(2\frac{3}{4}.\frac{1}{2}-\frac{1}{2}.\frac{3}{7}+\frac{1}{3}\)
\(=\frac{11}{4}.\frac{1}{2}-\frac{1}{2}.\frac{3}{7}+\frac{1}{3}\)
\(=\frac{11}{8}-\frac{3}{14}+\frac{1}{3}\)
\(=\frac{251}{168}\)
Bài 1 : a, thực hiện phép tính :
\(2\frac{3}{4}×\frac{1}{2}-\frac{1}{2}×\frac{3}{7}+\frac{1}{3}\)
\(=\frac{11}{4}×\frac{1}{2}-\frac{1}{2}×\frac{3}{7}+\frac{1}{3}\)
\(=\frac{1}{2}×\left(\frac{11}{4}-\frac{3}{7}\right)+\frac{1}{3}\)
\(=\frac{1}{2}×\frac{65}{28}+\frac{1}{3}\)
\(=\frac{65}{56}+\frac{1}{3}\)
\(=\frac{251}{168}\)
b , Tìm x biết :
a, 435- ( x + 16 ) = 425 : 17
435 - ( x + 16 ) = 25
x + 16 = 435 - 25
x + 16 = 410
x = 410 - 16
x = 394
Vậy x = 394
b, ( x + 3/4 ) × 7/4 = 5 - 7/6
( x + 3/4 ) × 7/4 = 23/6
x + 3/4 = 23/6 : 7/4
x + 3/4 = 23/6 × 4/7
x + 3/4 = 46/21
x = 46/21 - 3/4
x = 121/84
Vậy x = 121/84
\(100\times2:1\times3:2\times4:3\times5:4\times...\times100:99\)
\(=100\times\frac{2}{1}\times\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times...\times\frac{100}{99}\)
\(=100\times\frac{100}{1}\)
\(=10000\)
Chúc bạn học tốt !!!
100 x 2 : 1 x 3 : 2 x 4 : 3 x ... x 100 : 99
= 100 x 2/1 x 3/2 x 4/3 x ... x 100/99
= 100 x 100/1
= 100 x 100
= 10000
a) \(\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6}=\frac{2}{6}=\frac{1}{3}\)
b) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}=\frac{1}{4}\)
\(a)\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}\)
\(\Rightarrow\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{6}\)
\(\Rightarrow\frac{1}{3}\)
\(b)\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\)
\(=\frac{1\times2\times3}{2\times3\times4}\)
\(=\frac{1}{4}\)
\(b)\left(1-\frac{1}{2}\right)\div\left(1-\frac{1}{3}\right)\div\left(1-\frac{1}{4}\right)\)
\(=\frac{1}{2}\div\frac{2}{3}\div\frac{3}{4}\)
\(=\frac{1}{2}\times\frac{3}{2}\times\frac{4}{3}\)
\(=\frac{1\times3\times2\times2}{2\times2\times3}\)
\(=1\)
\(\frac{4}{5}x\frac{1}{4}+\frac{1}{2}x\frac{4}{5}\)
\(\frac{4}{5}x\left(\frac{1}{4}+\frac{1}{2}\right)\)
\(\frac{4}{5}x\frac{3}{4}=\frac{3}{5}\)
\(\frac{3}{4}x\frac{4}{5}+\frac{5}{6}x\frac{6}{7}x\frac{7}{8}\)
\(\frac{3}{5}+\frac{5}{8}=\frac{49}{40}\)
A) 4/5 x 1/4 + 1/2 x 4/5
= 4/5 x (1/4 + 1/2)
= 4/5 x (1/4 + 2/4)
= 4/5 x 3/4
= 3/5
Đặt A = 1 - 1/2 + 1 - 1/6 + 1 - 1/12 + 1 - 1/20 + 1 - 1/30 + 1 - 1/42 + 1 - 1/56 + 1 - 1/72 + 1 - 1/89
= (1 + 1 + 1 + .... 1 + 1) + (1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90)
= 9 - (1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7 + 1/7x8 + 1/8x9 + 1/9x10)
Mỗi phân số thành phần trong biểu thức () ta tách được như sau:
1/1 x 2 = 1- 1/2
1/2 x 3 = 1/2 - 1/3
1/3 x 4 = 1/3 - 1/4
........
1/9 x 10 = 1/9 - 1/10
Như vậy:
A = 9 - (1-1/2 + 1/2-1/3 + 1/3-1/4 + 1/4-1/5 + 1/5-1/6 + 1/6-1/7 + 1/7-1/8 + 1/8-1/9 + 1/9-1/10)
= 9 - (1 - 1/10)
= 9 - 9/10
= 81/10
Đáp số: 81/10
5,5 + \(\dfrac{3}{4}\) - 5 + \(\dfrac{1}{4}\)
(5,5 - 5) + (\(\dfrac{3}{4}\) + \(\dfrac{1}{4}\))
= 0,5 + 1
= 1,5
\(\dfrac{5}{2}\) x \(\dfrac{2}{3}\) + \(\dfrac{1}{4}\) : \(\dfrac{3}{2}\)
= \(\dfrac{5}{2}\) x \(\dfrac{2}{3}\) + \(\dfrac{1}{4}\) x \(\dfrac{2}{3}\)
= (\(\dfrac{5}{2}\) + \(\dfrac{1}{4}\)) x \(\dfrac{2}{3}\)
= (\(\dfrac{10}{4}\) + \(\dfrac{1}{4}\)) x \(\dfrac{2}{3}\)
= \(\dfrac{11}{4}\) x \(\dfrac{2}{3}\)
= \(\dfrac{11}{6}\)
Tính \(x\):
435 - [\(x\) + 16] = 425 : 17
435 - [\(x\) + 16] = 25
[\(x\) + 16] = 435 - 25
\(x\) + 16 = 410
\(x\) = 410 - 16
\(x\) = 394