Đáp án:

Giải thích các bước giải:

a/

Ta có:
`1212/1414 = {12xx101}/{14xx101} = 12/14`

`121212/141414 = {12xx10101}/{14xx10101} = 12/14`

Nên `12/14 = 1212/1414 = 121212/141414`

b/

Ta có:

`2424/3535 = {24 xx 101}/{35 xx 101} = 24/35`

`242424/353535 = {24 xx 10101}/{35 xx 10101} = 24/35`

Nên `24/35 = 2424/3535 = 242424/353535`

c/

Ta có:

`{abab}/{cdcd} = {abxx101}/{cd×101} = {ab}/{cd}`

`{ababab}/{cdcdcd} = {abxx10101}/{cd×10101} = {ab}/{cd}`

Nên `{ab}/{cd} = {abab}/{cdcd} = {ababab}/{cdcdcd}`

d/

Ta có:

`123123/145145 = {123xx1001}/{145xx1001} = 123/145`

`123123123/145145145 = {123xx1001001}/{145xx1001001} = 123/145`

Nên `123/145 = 123123/145145 = 123123123/145145145`

a ) Ta có :

`12/14 = 12/14` ( giữ nguyên )

`1212/1414 = (1212 : 101)/(1414 : 101) = 12/14`

`121212/141414 = (121212 : 10101)/(141414 : 10101) = 12/14`

Vì `12/14 = 12/12=12/14` nên `12/14 = 1212/1414 = 121212/141414`

b ) Ta có :

`24/35 = 24/35` ( giữ nguyên )

`2424/3535 = (2424 : 101)/(3535 : 101) = 24/35`

`242424/353535 = (242424 : 10101)/(353535 : 10101) = 24/35`

Vì `24/35 = 24/35 =24/35` nên `24/35 = 2424/3535 = 242424/353535`

c ) Ta có :

`(ab)/(cd) = (ab)/(cd)` ( giữ nguyên )

`(abab)/(cdcd) = (abab : 101)/(cdcd : 101) = (ab)/(cd)`

`(ababab)/(cdcdcd) = (ababab : 10101)/(cdcdcd : 10101) = (ab)/(cd)`

Vì `(ab)/(cd) = (ab)/(cd) = (ab)/(cd)` nên `(ab)/(cd) = (abab)/(cdcd) = (ababab)/(cdcdcd)`

d ) Ta có :

`123/145 = 123/145` ( giữ nguyên )

`123123/145145 = (123123 : 1001)/(145145 : 1001) = 123/145`

`123123123/145145145 = (123123123 : 1001001)/(145145145 : 1001001) = 123/145`

Vì `123/145 = 123/145=123/145` nên `123/145 = 123123/145145 = 123123123/145145145`

`#dtkc`