1. Să se afle x eQ din proporţiile:
a)4/3=x/9 b)2/3=10/x c)4/x=8 d)2/x=10/15 e)x/3=5 f)3/x=2,4 g)x/18=4/9 h)2=9/x i)0,(15)/x=2,5
Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
a) 4/3 = x/9 => 3 x = 4 × 9 → produsul mezilor = produsul extremilor
3 x = 36
x = 36 : 3
x = 12
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b) 2/3 = 10/x => 2 x = 3 × 10
2 x = 30
x = 30 : 2
x = 15
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c) 4/x = 8 ⇒ 8 x = 4 ⇒ x = 4/8 ⇒ x = 1/2 ∈ Q
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d) 2/x = 10/15 ⇒ 10 x = 2 × 15
10 x = 30
x = 30 : 10
x = 3
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e) x/3 = 5 ⇒ x = 3 × 5 ⇔ x = 15
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f) 3/x = 2,4 ⇒ x = 3/2,4
x = 3 : 24/10
x = 3 × 10/24
x = 30/24
x = 5/4 ∈ Q
x = 1,25
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g) x/18 = 4/9 ⇒ 9 x = 18 × 4
x = 72/9
x = 8
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h) 2 = 9/x ⇒ 2 x = 9 ⇒ x = 9/2 ∈ Q ⇔ x = 4,5
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i) 0,(15)/x = 2,5
2,5 x = 15/99
x = (5/33) : 25/10
x = (5/33) × 2/5
x = 2/33 ∈ Q
0,(15) = 15/99 = (15:3)/(99:3) = 5/33
2,5 = 25/10 = (25:5)/(10:5) = 5/2