Question

VĂ ROG AJUTAȚIMĂ LA EXERCIȚILE 4 ȘI 5
DAU COROANA

Answer 1

Răspuns

Explicație pas cu pas:

Answer 2

Răspuns

Explicație pas cu pas:

4)

a) → introduc intregii in fractie

1 intreg si 3 / 4 = ( 1 x 4 + 3 ) / 4 = 7 / 4

2 intregi si 7 / 9 = ( 2 x 9 + 7 ) / 9 = 25 / 9

= 7 / 4 + 25 / 9 =  → le aducem la acelasi numitor comun 36

=( 63 + 100 ) / 36 =

= 163 / 36 =

= 4 intregi si  19 / 36

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b) 3 intregi si 5 / 6 = 23 / 6   si  1 intreg si 2 / 5 = 7 / 5

= 23 / 6 + 7 / 5 =

= 115 / 30 + 42 / 30 =

= 157 / 30 =

= 5 intregi si 7 / 30

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c)  4 intregi si 1 / 15 = 61 / 15;    3 intregi si 2 / 30 = 46 / 15

= 61 / 15 + 46 / 15 =

= 107 / 15 =

= 7 intregi si 2 / 15

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d) 2 intregi si 1 / 21 = 43 / 21,  iar   3 intregi si 1 / 7 = 22 / 7

= 43 / 21 + 22 / 7 =

= ( 43 + 66 ) 21 =

= 109 / 21 =

= 5 intregi si 4 / 21

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e)   65 / 16 + 11 / 8 = ( 65 + 22 ) / 16 = 87 / 16 = 5 intregi si 7 / 16

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f)    2 intregi si 3 / 5 = 13 / 5  si   1 intreg si 2 / 15 = 17 / 15

= 13 / 5 + 17 / 15 =

= ( 13 × 3 + 17 ) / 15 =

= ( 39 + 17 ) / 15 =

= 56 / 15 =

= 3 intregi si 11 / 15

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g) 3 intregi si 1 / 24 = 73 / 24;   2 intregi si 3 / 18 = 39 / 18

= 73 / 24 + 39 / 18 =

→ c.m.m.m.c. al numitorilor ( 24 si 18 ) = 72

= ( 73 × 3 + 39 × 4 ) / 72 =

= ( 219 + 156 ) / 72 =

= 375 / 72 = → simplific cu 3

= 125 / 24 =

= 5 intregi si 5 / 24

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h) 4 intregi si 1 / 25 = 101 / 25;    1 intreg si 2 / 20 = 22 / 20

= 101 / 25 + 22 / 20 =

= 101 / 25 + 11 / 10 =

= → c.m.m.m.c al numitorilor 25 si 10 = 50

= ( 101 × 2 + 11 × 5 ) / 50 =

= ( 202 + 55 ) / 50 =

= 257 / 50 =

= 5 intregi si 7 / 50

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5)

a) 3 / 5 + 1 / 10 + 7 / 6 + 4 / 5 =

→ c.m.m.m.c al numitorilor ( 5;  10;  6 ) = 30

= ( 3 × 6 + 3 + 7 × 5 + 4 × 6 ) / 30 =

= ( 18 + 3 + 35 + 24 ) / 30 =

= 80 / 30 =

= 8 / 3 =

= 2 intregi si 2 / 3

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b)    2 / 3 + 1 / 6 + 5 / 8 + 11 / 12 =

→ c.m.m.m.c. al numitorilor ( 3;  6;  8  si 12 ) = 24  

= ( 2 × 8 + 4 + 5 × 3 + 11 × 2 ) / 24 =

= ( 16 + 4 + 15 + 22 ) / 24 =

= 57 / 24 =

= 19 / 8 =

= 2 intregi si 3 / 8

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c)   4 / 18 + 3 / 4 + 1 / 9 + 5 / 6 =

→ c.m.m.m.c al numitorilor ( 18;  4;   9  si 6 ) = 36

= ( 4 × 2 + 3 × 9 + 4 + 5 × 6 ) / 36 =

= ( 8 + 27 + 4 + 30 ) / 36 =

= 69 / 36 = → simplific cu 3

= 23 / 12 =

= 1 intreg si 11 / 12

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d)  5 / 21 + 6 / 7 + 5 / 42 + 9 / 14 =

→ c.m.m.m.c. al numitorilor ( 21;  7;  42;  14 ) = 42

= ( 5 × 2 + 6 × 6 + 5  + 9 × 3 ) / 42 =

= ( 10 + 36 + 5 + 27 ) / 42 =

= 78 / 42 = → simplific cu 6

= 13 / 7 =

= 1 intreg si 6 / 7

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e) 1 / 10 + 7 / 12 + 1 / 15 + 4 / 30 =

→ c.m.m.m.c al numitorilor ( 10, 12,  15  si 30 ) = 60

= ( 6 + 7 × 5 + 4 + 4 × 2 ) / 60 =

=  ( 10 + 35 + 8 ) / 60 =

= 53 / 60

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f)    5 / 36 + 1 / 18 + 3 / 24 + 1 / 4 =

→ c.m.m.m.c al numitorilor ( 36;  18;   24 si 4 ) = 72

= ( 5 × 2 + 4 + 3 × 3 + 18 ) / 72 =

= ( 10 + 4 + 9 + 18 ) / 72 =

= 41 / 72