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
