\(a,\dfrac{2}{3}+\dfrac{2}{7}=\dfrac{14}{21}+\dfrac{6}{21}=\dfrac{20}{21}\)

\(b,8-\dfrac{2}{3}=\dfrac{24}{3}-\dfrac{2}{3}=\dfrac{22}{3}\)

\(c,\dfrac{3}{8}\times4=\dfrac{3}{2}\)

\(d,\dfrac{3}{4}:\dfrac{1}{2}=\dfrac{3}{4}\times2=\dfrac{3}{2}\)

a) 20/21

b) 22/3

c) 3/2

d) 3/2

a) 20/21

b) 22/3

c) 3/2

d) 3/2

C

a: \(2^2\cdot5-\dfrac{\left(1^{10}+8\right)}{3^2}\)

\(=4\cdot5-\dfrac{1+8}{3}\)

=20-3

=17

b: \(5^8:5^6+4\left(3^2-1\right)\)

\(=5^2+4\left(9-1\right)\)

=25+4*8

=25+32

=57

c: \(400-\left\{36-20:\left[3^3-\left(8-3\right)\right]\right\}\)

\(=400-36+20:\left[27-5\right]\)

\(=364+\dfrac{20}{22}\)

\(=364+\dfrac{10}{11}=\dfrac{4014}{11}\)

A) 2².5 - (1¹⁰ + 8) : 3²

= 4.5 - (1 + 8) : 9

= 20 - 9 : 9

= 20 - 1

= 19

B) 5⁸ : 5⁶ + 4.(3² - 1)

= 5² + 4.(9 - 1)

= 25 + 4.8

= 25 + 32

= 57

C) 400 - {36 - 20 : [3³ - (8 - 3)]}

= 400 - [36 - 20 : (27 - 5)]

= 400 -(36 - 20 : 22)

= 400 - (36 - 10/11)

= 400 - 386/11

= 4014/11

a, 4/9 +1/2 = 17/18

b, 3/8 + 1/2 = 7/8

c, 9/8 + 3/5 = 69/40

d, 5 - 3/4 = 17/4

a. 4/9 + 1/2 = 17/18

b. 3/8 + 1/2 = 7/8

c. 9/8 + 3/5 = 69/40

d. 5 - 3/4 = 17/4

a: \(=\left(\dfrac{5}{8}-\dfrac{28}{8}\right)\cdot\dfrac{5}{6}=\dfrac{-23}{8}\cdot\dfrac{5}{6}=\dfrac{-115}{48}\)

b: \(=\dfrac{4}{7}\cdot\dfrac{24+25}{15}=\dfrac{4}{7}\cdot\dfrac{49}{15}=\dfrac{28}{15}\)

c: \(=\dfrac{7}{2}:\dfrac{24-10}{15}=\dfrac{7}{2}\cdot\dfrac{15}{14}=\dfrac{15}{4}\)

2:

a: =4+3/8+5+2/3

=9+3/8+2/3

=216/24+9/24+16/24

=216/24+25/24

=241/24

b; =2+3/8+1+1/4+3+6/7

=6+3/8+1/4+6/7

=6+5/8+6/7

=419/56

c: \(=2+\dfrac{3}{8}-1-\dfrac{1}{4}+5+\dfrac{1}{3}\)

=6+3/8-1/4+1/3

=6+1/8+1/3

=6+11/24

=155/24

d: \(=3+\dfrac{5}{6}+6\cdot\dfrac{13}{6}\)

=3+13+5/6

=16+5/6

=101/6

e: =3+1/2+4+5/7-5-5/14

=3+4-5+1/2+5/7-5/14

=2+7/14+10/14-5/14

=2+12/14

=2+6/7=20/7

f: =9/2+1/2:11/2

=9/2+1/11

=99/22+2/22=101/22

2:

a: =4+3/8+5+2/3

=9+3/8+2/3

=216/24+9/24+16/24

=216/24+25/24

=241/24

b; =2+3/8+1+1/4+3+6/7

=6+3/8+1/4+6/7

=6+5/8+6/7

=419/56

c: \(=2+\dfrac{3}{8}-1-\dfrac{1}{4}+5+\dfrac{1}{3}\)

=6+3/8-1/4+1/3

=6+1/8+1/3

=6+11/24

=155/24

d: \(=3+\dfrac{5}{6}+6\cdot\dfrac{13}{6}\)

=3+13+5/6

=16+5/6

=101/6

e: =3+1/2+4+5/7-5-5/14

=3+4-5+1/2+5/7-5/14

=2+7/14+10/14-5/14

=2+12/14

=2+6/7=20/7

f: =9/2+1/2:11/2

=9/2+1/11

=99/22+2/22=101/22

a: Cách 1: \(\left(\frac58-\frac72\right):\frac65\)

\(=\left(\frac58-\frac{28}{8}\right):\frac65\)

\(=-\frac{23}{8}\cdot\frac56=\frac{-115}{48}\)

Cách 2: \(\left(\frac58-\frac72\right):\frac65\)

\(=\left(\frac58-\frac72\right)\cdot\frac56\)

\(=\frac58\cdot\frac56-\frac72\cdot\frac56\)

\(=\frac{25}{48}-\frac{35}{12}\)
\(=\frac{25}{48}-\frac{140}{48}=\frac{-115}{48}\)

b: Cách 1: \(\frac47\left(\frac85+\frac53\right)\)

\(=\frac47\cdot\frac85+\frac47\cdot\frac53\)

\(=\frac{32}{35}+\frac{20}{21}\)

\(=\frac{96}{105}+\frac{100}{105}=\frac{196}{105}=\frac{28}{15}\)

Cách 2: \(\frac47\left(\frac85+\frac53\right)\)

\(=\frac47\left(\frac{24}{15}+\frac{25}{15}\right)\)

\(=\frac47\cdot\frac{49}{15}\)

\(=\frac{49}{7}\cdot\frac{4}{15}=7\cdot\frac{4}{15}=\frac{28}{15}\)

c: Cách 1: \(\frac72:\left(\frac85-\frac23\right)\)

\(=\frac72:\left(\frac{24}{15}-\frac{10}{15}\right)\)

\(=\frac72:\frac{14}{15}=\frac72\cdot\frac{15}{14}=\frac{15}{2\cdot2}=\frac{15}{4}\)

a) 7/15 + 4/5 = 7/15 + 12/15 = 19/15 

b) 4/5 x 5/8= 1/2

c) 2/3 - 3/8= 16/24 - 9/24 = 7/24

d) 1/2 : 2/5= 1/2 x 5/2= 5/4

a) \(\dfrac{7}{15}+\dfrac{4}{5}=\dfrac{7}{15}+\dfrac{12}{15}=\dfrac{19}{15}\)

b) \(\dfrac{4}{5}\times\dfrac{5}{8}=\dfrac{20}{40}=\dfrac{1}{2}\)

c) \(\dfrac{2}{3}-\dfrac{3}{8}=\dfrac{16}{24}-\dfrac{9}{24}=\dfrac{7}{24}\)

d) \(\dfrac{1}{2}:\dfrac{2}{5}=\dfrac{1}{2}\times\dfrac{5}{2}=\dfrac{5}{4}\)

a) 7/15 + 4/5 = 7/15 + 12/15 = 19/15 

b) 4/5 x 5/8= 1/2

c) 2/3 - 3/8= 16/24 - 9/24 = 7/24

d) 1/2 : 2/5= 1/2 x 5/2= 5/4

a) \(3^3 : 3^2\)=\(3^{3-2}=3^1\)

b) \(5^{4} : 5^{2}\)=\(5^{4-2}=5^2\)

c) \(8^{3} . 8^{2}\)=\(8^{3+2}=8^5\)

d) Cách 1:

\(5^{4} . 5^{3}: 5^{2}=5^{4+3}:5^2=5^7:5^2=5^{7-2}=5^5\)

Cách 2: 

\(5^{4} . 5^{3}: 5^{2}=5^{4+3-2}=5^5\)