Tính:
a) 1 3 + 4 7 + 5 21 - 1 = . . . . . . . . .
b) 2 2 7 + 1 6 × 1 2 5 - 3 = . . . . . . . . .
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18 tháng 1
a: \(\dfrac{16}{15}\cdot\dfrac{-5}{14}\cdot\dfrac{54}{24}\cdot\dfrac{56}{21}\)
\(=\dfrac{16}{24}\cdot\dfrac{-5}{15}\cdot\dfrac{54}{21}\cdot\dfrac{56}{14}\)
\(=\dfrac{2}{3}\cdot\dfrac{-1}{3}\cdot\dfrac{18}{7}\cdot4\)
\(=\dfrac{-2\cdot2\cdot4}{7}=-\dfrac{16}{7}\)
b: \(\dfrac{7}{3}\cdot\dfrac{-5}{2}\cdot\dfrac{15}{21}\cdot\dfrac{4}{-5}\)
\(=\dfrac{7}{3}\cdot\dfrac{5}{7}\cdot\dfrac{5}{2}\cdot\dfrac{4}{5}\)
\(=\dfrac{5}{3}\cdot\dfrac{4}{2}=\dfrac{5}{3}\cdot2=\dfrac{10}{3}\)
c: \(\left(-\dfrac{2}{5}+\dfrac{1}{3}\right)\left(\dfrac{3}{2}-\dfrac{3}{7}\right)\)
\(=\dfrac{-2\cdot5+3}{15}\cdot\dfrac{3\cdot7-3\cdot2}{14}\)
\(=\dfrac{-7}{15}\cdot\dfrac{15}{14}=\dfrac{-7}{14}=-\dfrac{1}{2}\)
d: \(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)\left(5-\dfrac{1}{4}\right)\)
\(=\dfrac{3-2}{6}\cdot\dfrac{20-1}{4}\)
\(=\dfrac{1}{6}\cdot\dfrac{19}{4}=\dfrac{19}{24}\)
e: \(\left(\dfrac{4}{5}\right)^2=\dfrac{4^2}{5^2}=\dfrac{16}{25}\)
LT
1
18 tháng 1
a: \(\left(-\dfrac{3}{7}\right)^2=\dfrac{\left(-3\right)^2}{7^2}=\dfrac{9}{49}\)
b: \(\dfrac{5}{17}+\dfrac{-15}{34}\cdot\dfrac{2}{5}\)
\(=\dfrac{5}{17}-\dfrac{15}{5}\cdot\dfrac{2}{34}\)
\(=\dfrac{5}{17}-\dfrac{1}{17}\cdot3=\dfrac{2}{17}\)
c: \(\dfrac{-7}{21}+\left(1+\dfrac{1}{3}\right)\)
\(=-\dfrac{1}{3}+1+\dfrac{1}{3}\)
=1
d: \(\left(-\dfrac{1}{5}+\dfrac{3}{12}\right)+\dfrac{-3}{4}\)
\(=\dfrac{-1}{5}+\dfrac{1}{4}-\dfrac{3}{4}\)
\(=\dfrac{-1}{5}-\dfrac{2}{4}\)
\(=\dfrac{-1}{5}-\dfrac{1}{2}=\dfrac{-7}{10}\)
27 tháng 7 2021
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
HQ
Hà Quang Minh
Giáo viên
19 tháng 9 2023
a)
\(\begin{array}{l}0,75 - \frac{5}{6} + 1\frac{1}{2} = \frac{3}{4} - \frac{5}{6} + \frac{3}{2}\\ = \frac{9}{{12}} - \frac{{10}}{{12}} + \frac{{18}}{{12}} = \frac{{17}}{{12}}\end{array}\)
b)
\(\begin{array}{l}\frac{3}{7} + \frac{4}{{15}} + \left( {\frac{{ - 8}}{{21}}} \right) + \left( { - 0,4} \right) = \frac{3}{7} + \frac{4}{{15}} - \frac{8}{{21}} - \frac{2}{5}\\ = \left( {\frac{3}{7} - \frac{8}{{21}}} \right) + \left( {\frac{4}{{15}} - \frac{2}{5}} \right)\\ = \left( {\frac{9}{{21}} - \frac{8}{{21}}} \right) + \left( {\frac{4}{{15}} - \frac{6}{{15}}} \right)\\ = \frac{1}{{21}} + \left( {\frac{{ - 2}}{{15}}} \right)\\ = \frac{5}{{105}} - \frac{{14}}{{105}}\\ = \frac{{ - 9}}{{105}} = \frac{{ - 3}}{{35}}\end{array}\)
c)
\(\begin{array}{l}0,625 + \left( {\frac{{ - 2}}{7}} \right) + \frac{3}{8} + \left( {\frac{{ - 5}}{7}} \right) + 1\frac{2}{3}\\ = \frac{5}{8} + \left( {\frac{{ - 2}}{7}} \right) + \frac{3}{8} - \frac{5}{7} + \frac{5}{3}\\ = \left( {\frac{5}{8} + \frac{3}{8}} \right) + \left( {\frac{{ - 2}}{7} - \frac{5}{7}} \right) + \frac{5}{3}\\ = 1 - 1 + \frac{5}{3} = \frac{5}{3}\end{array}\)
d)
\(\begin{array}{l}\left( { - 3} \right).\left( {\frac{{ - 38}}{{21}}} \right).\left( {\frac{{ - 7}}{6}} \right).\left( { - \frac{3}{{19}}} \right)\\ = \frac{{ - 3.\left( { - 38} \right).\left( { - 7} \right).\left( { - 3} \right)}}{{21.6.19}}\\ = \frac{{3.38.7.3}}{{21.6.19}}\\ = \frac{{3.2.19.7.3}}{{3.7.3.2.19}}\\ = 1\end{array}\)
e)
\(\begin{array}{l}\left( {\frac{{11}}{{18}}:\frac{{22}}{9}} \right).\frac{8}{5} = \left( {\frac{{11}}{{18}}.\frac{9}{{22}}} \right).\frac{8}{5}\\ = \frac{{11.9.4.2}}{{9.2.2.11.5}} = \frac{2}{5}\end{array}\)
g)
\(\left[ {\left( {\frac{{ - 4}}{5}} \right).\frac{5}{8}} \right]:\left( {\frac{{ - 25}}{{12}}} \right) = \frac{{ - 20}}{{40}}:\left( {\frac{{ - 25}}{{12}}} \right)\\ = \frac{{ - 1}}{2}.\frac{{ - 12}}{{25}} = \frac{6}{{25}}\)
26 tháng 6 2023
`@` `\text {Ans}`
`\downarrow`
`a.`
\(0,3-\dfrac{4}{9}\div\dfrac{4}{3}\cdot\dfrac{6}{5}+1\)
`=`\(0,3-\dfrac{1}{3}\cdot\dfrac{6}{5}+1\)
`=`\(0,3-0,4+1\)
`= -0,1 + 1`
`= 0,9`
`b.`
\(1+2\div\left(\dfrac{2}{3}-\dfrac{1}{6}\right)\cdot\left(-2,25\right)\)
`=`\(1+2\div\dfrac{1}{2}\cdot\left(-2,25\right)\)
`=`\(1+4\cdot\left(-2,25\right)\)
`= 1+ (-9) = -8`
`c.`
\(\left[\left(\dfrac{1}{4}-0,5\right)\cdot2+\dfrac{8}{3}\right]\div2\)
`=`\(\left(-\dfrac{1}{4}\cdot2+\dfrac{8}{3}\right)\div2\)
`=`\(\left(-\dfrac{1}{2}+\dfrac{8}{3}\right)\div2\)
`=`\(\dfrac{13}{6}\div2\)
`=`\(\dfrac{13}{12}\)
`d.`
\(\left[\left(\dfrac{3}{8}-\dfrac{5}{12}\right)\cdot6+\dfrac{1}{3}\right]\cdot4\)
`=`\(\left(-\dfrac{1}{24}\cdot6+\dfrac{1}{3}\right)\cdot4\)
`=`\(\left(-\dfrac{1}{4}+\dfrac{1}{3}\right)\cdot4\)
`=`\(\dfrac{1}{12}\cdot4=\dfrac{1}{3}\)
`e.`
\(\left(\dfrac{4}{5}-1\right)\div\dfrac{3}{5}-\dfrac{2}{3}\cdot0,5\)
`=`\(-\dfrac{1}{5}\div\dfrac{3}{5}-\dfrac{1}{3}\)
`=`\(-\dfrac{1}{3}-\dfrac{1}{3}=-\dfrac{2}{3}\)
`f.`
\(0,8\div\left\{0,2-7\left[\dfrac{1}{6}+\left(\dfrac{5}{21}-\dfrac{5}{14}\right)\right]\right\}\)
`=`\(0,8\div\left[0,2-7\left(\dfrac{1}{6}-\dfrac{5}{42}\right)\right]\)
`=`\(0,8\div\left(0,2-7\cdot\dfrac{1}{21}\right)\)
`=`\(0,8\div\left(0,2-\dfrac{1}{3}\right)\)
`= 0,8 \div (-2/15)`
`=-6`
`@` `yHGiangg.`
HQ
Hà Quang Minh
Giáo viên
27 tháng 11 2023
a) $\frac{5}{9}:\frac{7}{3} = \frac{5}{9} \times \frac{3}{7} = \frac{{15}}{{63}} = \frac{5}{{21}}$
b) $\frac{2}{7}:\frac{8}{5} = \frac{2}{7} \times \frac{5}{8} = \frac{{10}}{{56}} = \frac{5}{{28}}$
c) $\frac{4}{{15}}:\frac{2}{5} = \frac{4}{{15}} \times \frac{5}{2} = \frac{{20}}{{30}} = \frac{2}{3}$
d) $\frac{7}{9}:\frac{{21}}{9} = \frac{7}{9} \times \frac{9}{{21}} = \frac{{63}}{{189}} = \frac{1}{3}$
HP
3
T
13 tháng 8 2023
a) \(\dfrac{6}{7}+\dfrac{7}{8}=\dfrac{48}{56}+\dfrac{49}{56}=\dfrac{97}{56}\)
b) \(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\)
c) \(\dfrac{2}{3}.\dfrac{4}{9}=\dfrac{8}{27}\)
d) \(\dfrac{1}{5}:\dfrac{2}{7}=\dfrac{1}{5}.\dfrac{7}{2}=\dfrac{7}{10}\)
13 tháng 8 2023
a: =48/56+49/56
=97/56
b: =12/15-10/15
=2/15
c: =(2*4)/(3*9)=8/27
d: =1/5*7/2=7/10
28 tháng 9 2023
1.
a) 503 + 120 = 623
b) 1000 - 120 = 880
c) 2 + 18 : 2 = 2 + 9 = 11
d) 21 : 7 - 3 = 3 - 3 = 0
2.
a) x - 3 = 21 => x = 24
b) 15 - x . 3 = 6 => 15 - 3x = 6 => 3x = 15 - 6 = 9 => x = 3
c) x + 21 : 7 = 6 => x + 3 = 6 => x = 3
d) 44 + x : 3 = 50 => x : 3 = 50 - 44 = 6 => x = 18
3.
a) 15 . (21 - 3 . 7) = 15 . (21 - 21) = 15 . 0 = 0
b) (4 : 2 - 2) . 105 = (2 - 2) . 105 = 0 . 105 = 0
c) 376 + 285 + 124 + 715 = 1500
d) 97 + 998 + 9999 + 16 = 11110
e) 252 + 139 - 52 - 39 = 300
4.
a) b - a = 5 - 3 = 2
b) a + b = 3 + 5 = 8
c) 2a + b = 2*3 + 5 = 6 + 5 = 11
d) a . (b + 1) = 3 . (5 + 1) = 3 . 6 = 18
5.
a) 37581 - 9999 = 27582
b) 7345 - 1998 = 5347
c) 485321 - 99999 = 385322
d) 7593 - 1997 = 5596
6.
a) (x - 42) - 110 = 0 => x - 42 = 110 => x = 110 + 42 = 152
b) 2436 : x = 12 => x = 2436 / 12 = 203
c) 74 . (x - 3) = 0 => x - 3 = 0 => x = 3
d) x - 36 : 18 = 2 => x - 2 = 36 => x = 36 + 2 = 38
7.
a) 67 + 135 + 33 = 235
b) 997 + 86 = 1083
c) 37 . 38 + 62 . 37 = 1406
d) 43 . 11 = 473
e) 67 . 99 = 6633
8.
a) 71 - (33 + x) = 26 => 71 - 33 - x = 26 => 38 - x = 26 => x = 38 - 26 = 12
b) 97 - (64 - x) = 44 => 97 - 64 + x = 44 => x = 44 - 97 + 64 => x = 11
c) x - 36 : 18 = 12 => x - 2 = 12 => x = 14
d) 3636 : (12 . x - 91) = 36 => 3636 = 36 * (12 . x - 91) => 3636 = 432 . x - 3276 => 432 . x = 3636 + 3276 => 432 . x = 6912 => x = 6912 / 432 => x = 16
e) ( x : 23 + 45) . 67 = 8911 => (x / 23 + 45) . 67 = 8911 => (x / 23 + 45) = 8911 / 67 => (x / 23 + 45) = 133 => x / 23 = 133 - 45 => x / 23 = 88 => x = 88 . 23 => x = 2024
9.
a) 1 + 2 + 3 + ... + 1998 + 1999 = (1999 . (1999 + 1)) / 2 = 1999 . 2000 / 2 = 1999 . 1000 = 1,999,000
b) Tính tổng tất cả các số tự nhiên có 3 chữ số: Tổng các số từ 100 đến 999 = (100 + 999) / 2 * (999 - 100 + 1) = 1099 / 2 * 900 = 549.5 * 900 = 494550
c) Tính tổng tất cả các số lẻ có 3 chữ số: Các số lẻ từ 101 đến 999 là 101, 103, 105, ..., 999. Số lượng các số này là 450 (900 / 2). Tổng các số này là (101 + 999) / 2 * (450) = 550 * 450 = 247,500
10.
a) 53 . 39 + 47 . 39 - 53 . 21 - 47 . 21 = 2079 + 1833 - 1113 - 987 = 2912
b) 2 . 53 . 12 + 4 . 6 . 87 - 3 . 8 . 40 = 1272 + 1044 - 960 = 1356
c) 47 . 29 - 13 . 29 - 14 . 29 = 1363 - 377 - 406 = 580
d) 1754 : 17 - 74 : 17 + 20 : 17 = 103 - 4 + 1 = 100
e) 26 . 7 - 17 . 9 + 13 . 26 - 17 . 11 = 182 - 153 + 338 - 187 = 180
a) 1 3 + 4 7 + 5 21 − 1 = 7 21 + 12 21 + 5 21 − 21 21 = 3 21 = 1 7
b) 2 2 7 + 1 6 × 1 2 5 − 3 = 16 7 + 1 6 × 7 5 − 3 = 96 42 + 7 42 × 7 5 − 3 = 103 42 × 7 5 − 3 = 103 30 − 90 30 = 13 30