a, 17 * ( 53 - 43 ) + 43 * ( 53 + 17 )

= 17 x 10 +43 x 70

= 170 + 3010

= 3180

7)

53.(51+4)+53.(49+96)+53

=53.55+53.145+53

=53.(55+145+1)

=53.201

=10653

8)

42.(15+96)+6.(25+4).7

=42.111+(6.7).29

=42.111+42.29

=42.(111+29)

=42.140

=5880

9)

45.(13+78)+9.(87+22).5

=45.91+(9.5).109

=45.91+45.109

=45.(91+109)

=45.200

=9000

10)

16.(27+75)+8.(53+25).2

=16.102+(8.2).78

=16.102+16.78

=16.(102+78)

=16.180

=2880

7)

53.(51+4)+53.(49+96)+53

=53.55+53.145+53

=53.(55+145+1)

=53.201

=10653

8)

42.(15+96)+6.(25+4).7

=42.111+(6.7).29

=42.111+42.29

=42.(111+29)

=42.140

=5880

9)

45.(13+78)+9.(87+22).5

=45.91+(9.5).109

=45.91+45.109

=45.(91+109)

=45.200

=9000

10)

16.(27+75)+8.(53+25).2

=16.102+(8.2).78

=16.102+16.78

=16.(102+78)

=16.180

=2880

Phương pháp giải:

Thực hiện phép tính lần lượt từ trái sang phải.

Lời giải chi tiết:

83 − 7 − 6 = 70         83 − 13 = 70

53 − 9 − 4 = 40         53 − 13 = 40

73 − 5 − 8 = 60         73 − 13 = 60

`2/5+3/5=(2+3)/5=5/5=1`

`3/4+5/4=(3+5)/4=8/4=2`

`3/8+7/8=(3+7)/8=10/8=5/4`

`35/25+7/25=(35+7)/25=42/25`

$`\color{yellow}{Cần cù bù thông minh}`$

\(\left(\frac{3}{4}+\frac{2}{11}-\frac{8}{13}\right)+\left(\frac{1}{4}-\frac{5}{13}\right)\)

\(=\frac{3}{4}+\frac{2}{11}-\frac{8}{13}+\frac{1}{4}-\frac{5}{13}\)

\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{2}{11}-\left(\frac{8}{13}+\frac{5}{13}\right)\)

\(=1+\frac{2}{11}-1\)

\(=\frac{2}{11}\)

\(\left(\frac{9}{53}+\frac{21}{31}\right)+\left(\frac{44}{53}-\frac{16}{7}\right)+\frac{10}{31}\)

\(=\frac{9}{53}+\frac{21}{31}+\frac{44}{53}-\frac{16}{7}+\frac{10}{31}\)

\(=\left(\frac{9}{53}+\frac{44}{53}\right)+\left(\frac{21}{31}+\frac{10}{31}\right)-\frac{16}{7}\)

\(=1+1-\frac{16}{7}\)

\(=2-\frac{16}{7}\)

\(=\frac{14}{7}-\frac{16}{7}\)

\(=\frac{-2}{7}\)

a) \(\left(-4\right)\left(-3\right)\left(-125\right).25.\left(-8\right)=\left[25\left(-4\right)\right]\left[\left(-125\right)\left(-8\right)\right]\left(-3\right)\)

\(=\left(-100\right).1000.\left(-3\right)=300.1000=300000\)

b) \(\left(-4\right).9\left(-125\right).25.\left(-8\right)=\left[25\left(-4\right)\right]\left[\left(-125\right)\left(-8\right)\right].9\)

\(=\left(-100\right).1000.9=\left(-100\right).9000=-900000\)

c) \(7.\left(-25\right)\left(-3\right).2.\left(-4\right)=\left[\left(-25\right)\left(-4\right)\left(-3\right)\right].7.2=-4200\)

d) \(\left[93-\left(20-7\right)\right]\div16=\left(93-13\right)\div16=80\div16=5\)

e) \(53-\left(-51\right)+\left(-53\right)+49=\left(53-53\right)+\left(51+49\right)=100\)

f) \(168-49+\left(-68\right)+4=168-49-68+4=55\)

\(\dfrac{3}{8}+\dfrac{3}{4}=\dfrac{3+3\cdot2}{8}=\dfrac{9}{8}\)

\(\dfrac{3}{4}\cdot12=\dfrac{3\cdot12}{4}=\dfrac{36}{4}=9\)

\(\dfrac{1}{6}-\dfrac{1}{12}=\dfrac{2}{12}-\dfrac{1}{12}=\dfrac{1}{12}\)

\(\dfrac{13}{7}-\dfrac{9}{5}=\dfrac{13\cdot5-9\cdot7}{7\cdot5}=\dfrac{2}{35}\)

\(\dfrac{3}{8}:2=\dfrac{3}{8\cdot2}=\dfrac{3}{16}\)

\(A=\frac{7}{3\times13}+\frac{7}{13\times23}+...+\frac{7}{53\times63}\)

\(A=\frac{7}{10}.\left[\left(\frac{1}{3}-\frac{1}{13}\right)+\left(\frac{1}{13}-\frac{1}{23}\right)+....+\left(\frac{1}{53}-\frac{1}{63}\right)\right]\)

\(A=\frac{7}{10}.\left(\frac{1}{3}-\frac{1}{13}+\frac{1}{13}-\frac{1}{23}+....+\frac{1}{53}-\frac{1}{63}\right)\)

\(A=\frac{7}{10}.\left(\frac{1}{3}-\frac{1}{63}\right)\)

\(A=\frac{7}{10}.\frac{20}{63}\)

\(A=\frac{2}{9}\)

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