Division de Fractions

Arithmétique Aide aux Devoirs : Division de Fractions

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L'inverse (ou l'inverse multiplicatif) d'un nombre entier (nombre non nul) x est 1/x. L'inverse de la fraction p/q est la fraction q/p.
Exemple : L'inverse de 7 est 1/7, et l'inverse de 3/5 est 5/3.

Tout nombre peut être divisé par une fraction simplement en multipliant le nombre par l'inverse de la fraction.

Exemple : Pour diviser 15 par 4/7, en premier il faut multiplier 15 apr 7/4. Ainsi, 15 ÷ 4/7 = 15 x 7/4 = (15 x 7)/4 = 105/4.
Exemple : Pour diviser 7/9 par 5/6, en premier il faut multiplier 7/9 par 6/5. Ainsi, 7/9 ÷ 5/6 = 7/9 x 6/5 = 7/3 x 2/5 = (7 x 2)/(3 x 5) = 14/15.
Cliquer ici pour savoir plus sur multiplication de fractions.

DIVISION DE FRACTION	RÉSULTAT	EXPLICATION
2/19 ÷ 9 =	2/171	L'inverse de 9 = 1/9. Donc, 2/19 x 1/9 = (2 x 1)/(19 x 9) = 2/171.
3/29 ÷ 1/8 =	24/29	L'inverse de 1/8 = 8. Donc, 3/29 x 8 = (3 x 8)/(29 x 1) = 24/29.
14/31 ÷ 7 =	2/31	L'inverse de 7 = 1/7. Donc, 14/31 x 1/7 = 2/31 x 1/1 = 2/31.
6/37 ÷ 1/6 =	36/37	L'inverse de 1/6 = 6. Donc, 6/37 x 6 = (6 x 6)/(37 x 1) = 36/37.
4/45 ÷ 1/9 =	4/5	L'inverse de 1/9 = 9. Donc, 4/45 x 9 = 4/5 x 1 = 4/5.
5/56 ÷ 1/8 =	5/7	L'inverse de 1/8 = 8. Donc, 5/56 x 8 = 5/7 x 1 = 5/7.
8/21 ÷ 7 =	8/147	L'inverse de 7 = 1/7. Donc, 8/21 x 1/7 = (8 x 1)/(21 x 7) = 8/147.
5/48 ÷ 1/6 =	5/8	L'inverse de 1/6 = 6. Donc, 5/48 x 6 = 5/8 x 1 = 5/8.
7/40 ÷ 5 =	7/200	L'inverse de 5 = 1/5. Donc, 7/40 x 1/5 = (7 x 1)/(40 x 5) = 7/200.
3/16 ÷ 1/4 =	3/4	L'inverse de 1/4 = 4. Donc, 3/16 x 4 = 3/4 x 1 = 3/4.
7/25 ÷ 1/3 =	21/25	L'inverse de 1/3 = 3. Donc, 7/25 x 3 = (7 x 3)/25 = 21/25.
3/16 ÷ 2 =	3/32	L'inverse de 2 = 1/2. Donc, 3/16 x 1/2 = (3 x 1)/(16 x 2) = 3/32.
2/81 ÷ 1/18 =	4/9	L'inverse de 1/18 = 18. Donc, 2/81 x 18 = 2/9 x 2 = 4/9.
3/64 ÷ 1/24 =	9/8	L'inverse de 1/24 = 24. Donc, 3/64 x 24 = 3/8 x 3 = 9/8.
5/84 ÷ 1/28 =	5/3	L'inverse de 1/28 = 28. Donc, 5/84 x 28 = 5/3 x 1 = 5/3.
7/66 ÷ 1/18 =	21/11	L'inverse de 1/18 = 18. Donc, 7/66 x 18 = 7/11 x 3 = 21/11.
4/95 ÷ 1/30 =	24/19	L'inverse de 1/30 = 30. Donc, 4/95 x 30 = 4/19 x 6 = 24/19.
1/36 ÷ 1/32 =	8/9	L'inverse de 1/32 = 32. Donc, 1/36 x 32 = 1/9 x 8 = 8/9.
2/81 ÷ 1/15 =	10/27	L'inverse de 1/15 = 15. Donc, 2/81 x 15 = 2/27 x 5 = 10/27.
1/22 ÷ 1/18 =	9/11	L'inverse de 1/18 = 18. Donc, 1/22 x 18 = 1/11 x 9 = 9/11.
1/2 ÷ 9 =	1/18	L'inverse de 9 = 1/9. Donc, 1/2 x 1/9 = (1 x 1)/(2 x 9) = 1/18.
1/3 ÷ 8 =	1/24	L'inverse de 8 = 1/8. Donc, 1/3 x 1/8 = (1 x 1)/(3 x 8) = 1/24.
1/4 ÷ 6 =	1/24	L'inverse de 6 = 1/6. Donc, 1/4 x 1/6 = (1 x 1)/(4 x 6) = 1/24.
1/5 ÷ 7 =	1/35	L'inverse de 7 = 1/7. Donc, 1/5 x 1/7 = (1 x 1)/(5 x 7) = 1/35.
3/5 ÷ 7/4 =	12/35	L'inverse de 7/4 = 4/7. Donc, 3/5 x 4/7 = (3 x 4)/(5 x 7) = 12/35.
5/7 ÷ 8/5 =	25/56	L'inverse de 8/5 = 5/8. Donc, 5/7 x 5/8 = (5 x 5)/(7 x 8) = 25/56.
2/9 ÷ 9/4 =	8/81	L'inverse de 9/4 = 4/9. Donc, 2/9 x 4/9 = (2 x 4)/(9 x 9) = 8/81.
3/23 ÷ 4/3 =	9/92	L'inverse de 4/3 = 3/4. Donc, 3/23 x 3/4 = (3 x 3)/(23 x 4) = 9/92.
5/13 ÷ 3/11 =	55/39	L'inverse de 3/11 = 11/3. Donc, 5/13 x 11/3 = (5 x 11)/(13 x 3) = 55/39.
5/12 ÷ 4/7 =	35/48	L'inverse de 4/7 = 7/4. Donc, 5/12 x 7/4 = (5 x 7)/(12 x 4) = 35/48.
5/7 ÷ 8/3 =	15/56	L'inverse de 8/3 = 3/8. Donc, 5/7 x 3/8 = (5 x 3)/(7 x 8) = 15/56.
7/10 ÷ 8/3 =	21/80	L'inverse de 8/3 = 3/8. Donc, 7/10 x 3/8 = (7 x 3)/(10 x 8) = 21/80.
2/3 ÷ 7/4 =	8/21	L'inverse de 7/4 = 4/7. Donc, 2/3 x 4/7 = (2 x 4)/(3 x 7) = 8/21.
7/81 ÷ 5/18 =	14/45	L'inverse de 5/18 = 18/5. Donc, 7/81 x 18/5 = 7/9 x 2/5 = (7 x 2)/(9 x 5) = 14/45.
5/64 ÷ 11/24 =	15/88	L'inverse de 11/24 = 24/11. Donc, 5/64 x 24/11 = 5/8 x 3/11 = (5 x 3)/(8 x 11) = 15/88.
9/84 ÷ 13/21 =	9/52	L'inverse de 13/21 = 21/13. Donc, 9/84 x 21/13 = 9/4 x 1/13 = (9 x 1)/(4 x 13) = 9/52.
9/66 ÷ 13/12 =	18/143	L'inverse de 13/12 = 12/13. Donc, 9/66 x 12/13 = 9/11 x 2/13 = (9 x 2)/(11 x 13) = 18/143.
3/95 ÷ 7/15 =	9/133	L'inverse de 7/15 = 15/7. Donc, 3/95 x 15/7 = 3/19 x 3/7 = (3 x 3)/(19 x 7) = 9/133.
5/36 ÷ 11/12 =	5/33	L'inverse de 11/12 = 12/11. Donc, 5/36 x 12/11 = 5/3 x 1/11 = (5 x 1)/(3 x 11) = 5/33.
5/27 ÷ 13/15 =	25/117	L'inverse de 13/15 = 15/13. Donc, 5/27 x 15/13 = 5/9 x 5/13 = (5 x 5)/(9 x 13) = 25/117.
9/22 ÷ 19/16 =	72/209	L'inverse de 19/16 = 16/19. Donc, 9/22 x 16/19 = 9/11 x 8/19 = (9 x 8)/(11 x 19) = 72/209.
8/63 ÷ 15/14 =	16/135	L'inverse de 15/14 = 14/15. Donc, 8/63 x 14/15 = 8/9 x 2/15 = (8 x 2)/(9 x 15) = 16/135.
9/22 ÷ 81/121 =	11/18	L'inverse de 81/121 = 121/81. Donc, 9/22 x 121/81 = (1 x 11)/(2 x 9) = 11/18.
7/40 ÷ 21/16 =	2/15	L'inverse de 21/16 = 16/21. Donc, 7/40 x 16/21 = (1 x 2)/(5 x 3) = 2/15.
4/25 ÷ 8/5 =	1/10	L'inverse de 8/5 = 5/8. Donc, 4/25 x 5/8 = (1 x 1)/(5 x 2) = 1/10.
20/21 ÷ 2/33 =	110/7	L'inverse de 2/33 = 33/2. Donc, 20/21 x 33/2 = (10 x 11)/(7 x 1) = 110/7.
6/77 ÷ 72/35 =	5/132	L'inverse de 72/35 = 35/72. Donc, 6/77 x 35/72 = (1 x 5)/(11 x 12) = 5/132.
56/27 ÷ 32/9 =	7/12	L'inverse de 32/9 = 9/32. Donc, 56/27 x 9/32 = (7 x 1)/(3 x 4) = 7/12.
5/24 ÷ 35/36 =	3/14	L'inverse de 35/36 = 36/35. Donc, 5/24 x 36/35 = (1 x 3)/(2 x 7) = 3/14.
8/63 ÷ 52/27 =	6/91	L'inverse de 52/27 = 27/52. Donc, 8/63 x 27/52 = (2 x 3)/(7 x 13) = 6/91.

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