loulakar

Verified answer

Bonsoir,

IV) a) décompose :

8400 = 2 x 4200
4200 = 2 x 2100
2100 = 3 x 700
700 = 7 x 100
100 = 2 x 50
50 = 2 x 25
25 = 5 x 5

8400 = 2^4 x 3 x 5 x 7

2160 = 2 x 1080
1080 = 2 x 540
540 = 2 x 270
270 = 3 x 90
90 = 3 x 30
30 = 3 x 10
10 = 2 x 5

2160 = 2^4 x 3^3

3360 = 2 x 1680
1680 = 2 x 830
830 = 2 x 415
415 = 5 x 83

3360 = 2^3 x 5 x 83

b) déduire :

2160/8400 = (2^4 x 3^3)/(2^4x3x5x7)
2160/8400 = 2^4/2^4 x 3^3/3 x 1/35
2160/8400 = 3^2/35
2160/8400 = 9/35

3360/8400 = (2^3x5x83)/(2^4x3x5x7)
3360/8400 = 2^3/2^4 x 5/5 x 83/21
3360/8400 = 1/2 x 83/21
3360/8400 = 83/42

3360/2160 = (2^3x5x83)/(2^4x3^3)
3360/2160 = 2^3/2^4 x 415/27
3360/2160 = 1/2 x 415/27
3360/2160 = 415/54

c) calcul

2160/8400 + 3360/2160 =
9/35 + 415/54 =
(9x54)/(35x54) + (415x35)/(54x35) =
486/1890 + 14525/1890 =
15011/1890

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