Question

Thực hiện phép tính (Tính hợp lý nếu có thể).

a) $\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}$.

b) $\dfrac{1}{2} \cdot \dfrac{3}{4}+\dfrac{1}{2} \cdot \dfrac{1}{4}+\dfrac{1}{2}$.

c) $\Big(\dfrac{-3}{4}\Big)^2:\Big(\dfrac{-1}{4}\Big)^2+9 \cdot\Big(\dfrac{-1}{9}\Big)+\Big( \dfrac{-3}{2} \Big)$.

d) $\sqrt{0,25} \cdot(-3)^3-\sqrt{\dfrac{1}{81}}:\Big(\dfrac{-1}{3}\Big)^3$.

Answer 1

a) 11/24 - 5/41 + 13/24 + 0,5 - 36/41

= (11/24 + 13/24) - (5/41 + 36/41) + 0,5

= 1 - 1 + 0,5

= 0,5

b) 1/2 . 3/4 + 1/2 . 1/4 + 1/2

= 1/2 . (3/4 + 1/4) + 1/2

= 1/2 . 1 + 1/2

= 1/2 + 1/2

= 1

c) (-3/4)² : (-1/4)² + 9 . (-1/9) + (-3/2)

= 9/16 : 1/16 - 1 - 3/2

= 9 - 1 - 3/2

= 8 - 3/2

= 13/2

d) √0,25 . (-3)³ - √(1/81) : (-1/3)³

= 1/2 . (-27) - 1/9 : (-1/27)

= -27/2 + 3

= -21/2

Answer 2

a) 0,5

b) 1

c) 13/2

d) 27/2

Answer 3

a)\(\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}\)

=\(\left(\dfrac{11}{24}+\dfrac{13}{24}\right)-\left(\dfrac{36}{41}+\dfrac{5}{41}\right)-0,5\)

=\(1-1-0,5\)

=\(0-0,5\)

=\(-0,5\)

b)\(\dfrac{1}{2}.\dfrac{3}{4}+\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{2}\)

=\(\dfrac{1}{2}.\left(\dfrac{1}{4}+\dfrac{3}{4}\right)+\dfrac{1}{2}\)

=\(\dfrac{1}{2}.1+\dfrac{1}{2}\)

=\(\dfrac{1}{2}+\dfrac{1}{2}\)

=1

c)\(\left(-\dfrac{3}{4}\right)^2:\left(-\dfrac{1}{4}\right)^2+9.\left(-\dfrac{1}{9}\right)+\left(-\dfrac{3}{2}\right)\)

=\(\dfrac{9}{16}.\dfrac{16}{1}+9.\left(-\dfrac{1}{9}\right)+\left(-\dfrac{3}{2}\right)\)

=\(9+\dfrac{9}{1}.\left(-\dfrac{1}{9}\right)+\left(-\dfrac{3}{2}\right)\)

=\(9+-1+\left(-\dfrac{3}{2}\right)\)

=\(8+\left(-1,5\right)\)

=\(6,5\)

d)\(\sqrt{0,25}.\left(-3\right)^3-\sqrt{\dfrac{1}{81}}:\left(-\dfrac{1}{3}\right)^3\)

=\(\sqrt{0,25}.-27-\sqrt{\dfrac{1}{81}}.\left(-\dfrac{27}{1}\right)\)

=\(\left(\dfrac{1}{2}-\dfrac{1}{9}\right).\left(-27\right)\)

=\(\dfrac{7}{18}.\left(-27\right)\)

=\(-\dfrac{21}{2}\)

Answer 4

[11/24+13/24]+0,5-[36/41+5/41]=1+0,5-1=0,5

1/2.[3/4+1/4]=1/2.1=1/2

0,5.[-27]-1/9:[-1/27]=-13,5-[-3]=-10,5

Answer 5

a) \(\dfrac{11}{24}-\dfrac{5}{41}+\dfrac{13}{24}+0,5-\dfrac{36}{41}=\left(\dfrac{11}{24}+\dfrac{13}{24}\right)+0,5-\left(\dfrac{36}{41}+\dfrac{5}{41}\right)\)

                                             \(=1+0,5-1\)

                                             \(=0,5\)

b)                                          =\(\dfrac{1}{2}\cdot\left(\dfrac{3}{4}+\dfrac{1}{4}+1\right)\)

                                             =1

Answer 6

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Answer 7

a) 0,5

b) 1

c) 6,5

d) -3

Answer 8

a) 11/24 - 5/41 + 13/24 + 0,5 - 36/41

= (11/24 + 13/24) - ( 36/41 + 5/41) + 0,5

= 1 - 1 + 0,5

= 0,5

b) 1/2 . 3/4 + 1/2 . 1/4 + 1/2

= 1/2. (3/4 + 1/4) + 1/2

= 1/2. 1 + 1/2

= 1

c) (-3/4)² : (-1/4)² + 9 . (-1/9) + (-3/2) 

= 9/16 : 1/16 - 1 - 3/2

= 9 - 1 - 3/2

= 8 - 1,5

= 6,5

d) 0,5 . (-27) - 1/9 : (-1/27)

= -13,5 + 3

= -10,5

Answer 9

a) ​1124−541+1324+0,5−3641=(1124+1324)−(541+3641)+0,5=1−1+0,5=0,5​2411​−415​+2413​+0,5−4136​=(2411​+2413​)−(415​+4136​)+0,5=1−1+0,5=0,5

b) 12⋅34+12⋅14+12=12⋅(34+14+1)=12⋅2=121​⋅43​+21​⋅41​+21​=21​⋅(43​+41​+1)=21​⋅2=1

c) (−34)2:(−14)2+9⋅(−19)+(−32)=916:116−1−32=9−1−32=132.(4−3​)2:(4−1​)2+9⋅(9−1​)+(2−3​)=169​:161​−1−23​=9−1−23​=213​.

d) 0,25⋅(−3)3−181:(−13)3=0,5⋅(−27)−19:−127=−272+3=−2120,25​⋅(−3)3−811​​:(3−1​)3=0,5⋅(−27)−91​:27−1​=2−27​+3=2−21​