Question

ajutati-ma va rog frumos 11111

Answer 1

5 intregi si 1/2 = ( 5 x 2 + 1) / 2 = 11/ 2 

2 intregi si 1/4 = ( 2 x 4 + 1) / 4 = 9/4 

11/2 + 9/4 - 5/8 = 44 / 8 + 18 / 8 - 5/8 = 62/8 - 5/8 = 57/8 = 7 intregi si 1/8 
  → le aduc la acelasi numitor comun 8, amplific pe 11/2 cu 4, pe 9/4 cu 2 

7/21 + 5/35 - 1/14 = 

21 = 3 x 7 
35 = 5 x 7 
14 = 2 x 7
__________
cmmmc al numerelor ( 21, 35, 14  ) = 2 x 3 x 5 x 7 = 210 

= 70/210 +  30 / 210  - 15/210 = 100/210 - 15/210 = 85/210 = 17/42

→ am amplificat prima fractie cu 10, a doua fractie cu 6, iar a treia fractie cu 15 

1 intreg si 1/9 = ( 1 x 9 + 1) /9 = 10/9 

2 intregi si 3/8 = ( 2 x 8 + 3) = 19/8 

9 = 3²
8 = 2³ 
36 = 2² x 3² 
___________
cmmmc al numerelor ( 9, 8, 36) = 2³ x 3³ = 72 
→ amplific fractia 10/9 cu 8,  fractia 19/8 cu 9, iar fractia 1/36 cu 2 

80/72 + 171/72 - 2/72 = 251/72 - 2/72 = 249/72 = 83/24 = 3 intregi si 11/24 

5/2 - 7/8 + 3/10 =
cmmmc al numerelor ( 2, 8, 10) = 8 x 5 = 40 


= ( 5 x 20) /40 - ( 7 x 5) / 40 + ( 3 x 4) / 40 =  100/40 - 35/40 + 12/40 = 

= 65/40 + 12/40 = 77/40 = 1 intreg si 37/40 

8 intregi si 1/2 = ( 8 x 2 + 1) / 2 = 17/2 

17/2 x ( 3/4 - 1/6) = 17/2 x ( 9/12 - 2/12) =  17/2  x  7/12 = 119/24 =
= 4 intregi si  23/24

1 + 2 + 3+ 4+.........+ 10 = 10 x ( 1 + 10) : 2 = 5 x 11 = 55 ( formula sumei lui Gauss) 

55/5 + ( 1 x 4 + 3) / 4 = 11 + 7/4 = 44/4 + 7/4 = 51/4 = 12 intregi si 3/4