Question

Calculati
a)-1intreg 4/5-(-3intreg7/10)-(+2intreg8/15)

b)(-1intreg4/21)-(-2intreg2/7)-(+3intreg3/14)

c)(-16/45)-(+8/27)-(+25/36)-(-41/54)

d)(-13/42)-(-9/56)-(+8/63)-(-5/84)

Answer 1

a)   - 9 / 5  +  37 / 10 -  38 / 15 =   ( - 54 + 111 - 76 ) /   30 =  - 19 / 30

→ cmmmc al numitorilor ( 5;  10   si 15 ) = 2 x 3 x 5 = 30

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b)   -  25 / 21  +  16 / 7  -  45 / 14  = (  - 25 × 2 + 16 × 6 - 45 × 3 ) / 42 =

= ( - 50 + 96 - 135 ) / 42 = 89 / 42 = 2 intregi si 5 / 42

→ cmmmc al numitorilor  21;  7   si 14 =  2 x 3 x 7 = 42

→ aduc fractiile la acelasi numitor

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c)   - 16 / 45 -  8 / 27  - 25 / 36 + 41 / 54 =  ( - 16 × 12  - 8 × 20 - 25 × 15  + 41 × 10 ) / 540 =

= ( - 192 - 160 - 375 + 410 ) / 540 =

= ( - 727 + 410 ) / 540 =

=  -  317 /  540

45 = 3² × 5

27 = 3³

36 = 2² × 3²

54 = 2 × 3³

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cmmmc = 2² × 3³× 5 = 4 × 27 × 5 = 540

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d)

- 13 / 42 + 9 / 56 - 8 / 63 + 5 / 84 =

= ( - 13 × 12 + 9 × 9 - 8 × 8 + 5 × 6 ) / 504 =

= ( - 156 + 81 - 64 + 30 ) / 504 =

= - 109 / 504

42 = 6 x 7 = 2 x 3 x 7

56 = 8 x 7 = 2³ x 7

63 = 7 x 9 = 7 × 3²

84 =7 x 4 x 3 = 2² ×  3 × 7

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cmmmc al numitorilor ( 42;   56;    63;  84 ) = 7 x 8 x 9 = 504