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# 特殊的分数除法

2012年10月9日

5 1 5 ′1 5 = ′ = 9 2 9 ′ 2 18
2
3 1 1

16 9 16 9 2 ′ = ′ = 27 8 27 8 3

2

1

14 7 14 5 2 ? = ′ = 15 5 15 7 3
3 1

14 3 14 ? 3 = ? = 11 5 11? 5 14 3 14 5 70 ? = ′ = 11 5 11 3 33

3 3 1 (1) ? = 2 8 4 3 3 1 (3) ? = 2 10 5 4 2 2 ( 2) ? = 3 9 3 9 3 3 ( 4) ? = 2 10 5

5 5 1 ( 5) ? = 2 12 6 8 2 4 ( 7) ? = 5 15 3 4 2 2 ( 6) ? = 3 15 5 5 1 5 (8) ? = 8 16 2

5 3 5 (1) ? = 16 4 4 9 3 3 ( 2) ? = 20 5 4 10 5 2 (3) ? = 21 7 3 12 4 3 ( 4) ? = 25 5 5 16 8 2 ( 5) ? = 27 9 3 15 5 3 ( 6) ? = 28 14 2

1 5 1 6 1 (1) ? = ′ = 12 6 12 5 10 4 2 4 5 2 ( 2) ? = ′ = 15 5 15 2 3 5 1 5 ?1 5 = (3) ? = 26 13 26 ?13 2

24 12 24 ?12 2 ( 4) ? = = 35 5 35 ? 5 7 3 9 3 4 2 ( 5) ? = ′ = 10 4 10 9 15 4 1 4 12 16 ( 6) ? = ′ = 9 12 9 1 3

13 7 13? 7 13 = (1) ? = 24 24 24 ? 24 7 18 17 18 ?17 18 = ( 2) ? = 35 35 35 ? 35 17 25 19 25?19 25 (3) ? = 18 ?18 = 19 18 18

11 22 22 ?11 2 ? = = 15 5 15? 5 3 1 1 1?1 3 ? = = 3 4 3? 4 4 1 7 1? 7 1 ? = = 15 15 15?15 7

×

×

1 1 1 (1) ? ? 12 3 4 1?1?1 = 12 ? 3? 4 14 7 7 ( 2) ′ ? 15 2 5 14 7 7 = ? ′ 15 5 2 2 7 = ′ 3 2 7 = 3

=1

1 1 1 ′ = 2 3 6

1 1 1 ? = 6 3 2

1 1 1 + = 6 3 2

1 1 1 ′ = 3 4 12

1 1 1 1 1 1 ? = + = 12 4 3 12 4 3

1 1 1 1 1 1 1 1 1 ′ = ? = + = 4 5 20 20 5 4 20 5 4

1 1 1 ′ = 5 6 30

1 1 1 1 1 1 ? = + = 30 6 5 30 6 5

(1)

1 1 1 ′ = 2 3 6

1 1 1 ? = 6 3 2

1 1 1 + = 6 3 2

1 1 1 1 ? = + 6 3 6 3

( 2)

1 1 1 ′ = 3 4 12

1 1 1 ? = 12 4 3

1 1 1 + = 12 4 3

1 1 1 1 ? = + 12 4 12 4

( 3)

1 1 1 ′ = 4 5 20

1 1 1 ? = 20 5 4

1 1 1 + = 20 5 4

1 1 1 1 ? = + 20 5 20 5

( 4)

1 1 1 ′ = 5 6 30

1 1 1 ? = 30 6 5

1 1 1 + = 30 6 5

1 1 1 1 ? = + 30 6 30 6

1 1 1 ′ = 2 3 6 1 1 1 ′ = 3 4 12 1 1 1 ′ = 4 5 20 1 1 1 ′ = 5 6 30

1 1 1 ? = 6 3 2 1 1 1 ? = 12 4 3 1 1 1 ? = 20 5 4 1 1 1 ? = 30 6 5

1 1 1 ? = 2 6 3 1 1 1 ? = 12 4 3 1 1 1 ? = 20 5 4 1 1 1 ? = 30 6 5

1 1 1 + = 2 6 3

1 1 1 + = 12 4 3 1 1 1 + = 20 5 4 1 1 1 + = 30 6 5

1 1 1 1 1 1 1 1 1 ′ = （ ）÷（ ）= （ ）+（ ）= 7 6 42 7 6 6 7 42 42 1 1 1 1 1 1 1 1 1 ′ =

（ ）÷（ ）= （ ）+（ ）= 8 7 56 8 7 7 8 56 56

1 1 1 1 1 1 1 1 1 ′ = （ ）÷（ ）= （ ）+（ ）= 8 72 9 9 8 8 9 72 72 1 1 1 1 1 1 1 1 1 ′ = （ ）÷（ ）= （ ）+（ ）= 10 9 90 10 9 9 10 90 90

1 1 1 ′ = 2 3 6 1 1 1 ′ = 3 4 12 1 1 1 ′ = 4 5 20 1 1 1 ′ = 5 6 30

1 1 1 ? = 2 6 3 1 1 1 ? = 12 4 3 1 1 1 ? = 20 5 4 1 1 1 ? = 30 6 5

1 1 1 + = 2 6 3 1 1 1 + = 12 4 3 1 1 1 + = 20 5 4 1 1 1 + = 30 6 5

1 1 1 ′ = 6 7 42 1 1 1 ′ = 7 8 56 1 1 1 ′ = 8 9 72 1 1 1 ′ = 9 10 90

1 1 1 ? = 42 7 6 1 1 1 ? = 56 8 7 1 1 1 ? = 72 9 8 1 1 1 ? = 90 10 9

1 1 1 + = 6 42 7

1 1 1 + = 56 8 7 1 1 1 + = 72 9 8 1 1 1 + = 90 10 9

1 1 1 ′ = 11 12 132 1 1 1 ? = 132 11 12 1 1 13 + =( ) 132 11 132

a c 如果在分数 和 中，a 能被 c b d b 整除， 能被 d 整除，那么

a c a ?c ? ? b d b?d

1 1 如果在分数 和 中， a 和 b 是 a b 两个相邻的自然数，且 b ? a

1 1 1 ? ? a b c

1 1 1 1 ? ? ? c b c b

1 1 1 ′ = 2 3 6

1 1 1 - = 2 3 6
1 1 1 - = 3 4 12 1 1 1 - = 4 5 20 1 1 1 - = 5 6 30

1 1 1 ′ = 3 4 12
1 1 1 ′ = 4 5 20 1 1 1 ′ = 5 6 30