Question

-Efectuați calculele, folosind ordinea efectuării operațiilor:
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Answer 1

Răspuns:

a)

2/9 × ( - 3/4 + 27/8) = 2/9 × ( - 6/8 + 27/8) = 2/9 × ( 21/8) = 7/(3×4) = 7/12

->  am amplificat fractia 3/4 cu 2 = (3×2)/(4×2) = 6/8

-> am aflat diferenta parantezei ( - 6+27)/8 = 21/8

-> am simplificat pe 2 cu 8 = 1/4, dar si pe 21 cu 9 cu 3 =(21:3)/(9:3)=7/3

-> am inmultit fractiile 1/4 cu 7/3 =7/12 ( se inmultesc numaratorii intre ei si numitorii intre ei)

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b)

- 1/7 × 8 + ( - 1/7) = - 8/7 - 1/7 = (-8-1)/7 = - 9/7 = - 1 intreg si 2/7

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c)

- 3/10 × ( - 5/9) + ( - 1/6) = 1/6

= + (3×5)/(10×9) =

= (15/90)⁽¹⁵ =

= 1/6

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d) ( - 1 intreg si 1/5) = - ( 1×5+1)/5 = - 6/5 -> am introdus intregii in fractie

( - 3/4 + 1/8) × ( - 6/5) - ( - 5/2) × ( - 7 - 1/5) =

-> amplific fractia 3/4 cu 2 , dar si - 7/1 cu 5

= ( - 6/8 + 1/8) × ( - 6/5) - (- 5/2) × ( - 35/5 - 1/5) =

= ( - 5/8) × ( - 6/5) - ( - 5/2) × ( - 34/5) =

= 3/4 - ⁴⁾17 =

= 3/4 - (17×4)/4 =

= 3/4 - 68/4 =

= - 65/4 =

= - 16 intregi si 1/4

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e) 1 intreg si 1/3 = ( 1×3+1)/3 = 4/3 -> am introdus intregii in fractie

( - 5/6 + 1/12) × 4/3 =

= ( - 10/12 + 1/12) × 4/3=

= ( - 9/12) × 4/3 =

= - 36/36 =

= - 1

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f)

1 intreg si 1/7 = (1×7+1)/7 = 8/7

2 intregi si 1/7 = (2×7+1)/7 = 15/7 -> am introdus intregii in fractie

- 7/5 × ( 4/49 + ⁷⁾8/7) - ( - 1/18 - ²⁾1/9) × ( - 15/7) =

= - 7/5 × ( 4/49 + 56/49) - ( - 1/18 - 2/18 )×( - 15/7) =

= - 7/5 × (60/49) - ( - 3/18) × ( - 15/7) =

= - (7/49) × 60/5 - ( 1/6 ) × 15/7 =

= - ²⁾12/7 - 5/14 =

= -  24/14 - 5/14 =

= - 29/14 =

= - 2 intregi si 1/14

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g)

- 3/8 - ( - 14/25 ) × ( + 75/28) = 9/8

= - 3/8 - ( - 14/28) × ( 75/25) =

= - 3/8 + (1/2) × 3 =

= - 3/8 + ⁴⁾3/2 =

= - 3/8 + 12/8 =

= 9/8 =

= 1 intreg si 1/8

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h)

0,5 = (5/10)⁽⁵ = 1/2

0,25 = (25/100)⁽²⁵ = 1/4

13 intregi si 1/2 = (13×2+1)/2 = 27/2

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= 1/2 + 4/33 × ( - 1/4 + ²⁾27/2) =

= 1/2 + 4/33 × ( - 1/4 + 54/4 ) =

= 1/2 + 4/33 × ( 53/4) =

= ³³⁾1/2 + ²⁾53/33 =

= 33/66 + 106/66 =

= 139/66 =

= 2,1(06)

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i)

3,(2) = (32-3)/9 = 29/9

=( - 1/- 2 ) × [ 3,(2) - 5/27] =

= 1/2 × ( ³⁾29/9 - 5/27) =

= 1/2 × ( 87/27- 5/27) =

= 1/2 × ( 82/27) =

= ( 82/2) × 1/27 =

= 41/27 =

= 1,(518)

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j)

2³ = 8

3 intregi si 1/5 = ( 3×5+1)/5 = 16/5

0,625 = (625/1000)⁽¹²⁵ = 5/8

1,2 = (12/10)⁽² = 6/5

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= [ ( 2³ - 16/5 ) × 0,625 + 1,2 ] × 5/7 = 3

= [ (⁵⁾8 - 16/5) × 5/8 + 12/10 ] × 5/7 =

= [ ( 40/5 - 16/5) × 5/8 + 6/5 ] × 5/7 =

= ( 24/5 × 5/8 + 6/5) × 5/7 =

=( ⁵⁾3 + 6/5) × 5/7 =

= ( 15/5 + 6/5 ) × 5/7 =

= ( 21/5) × 5/7 =

= ( 21/7) × ( 5/5) =

= 3 × 1 =

= 3