Question

HELP FAST FAST FAST FAST FAST

Answer 1

`(4)/(11)`

Explanation:

the first step is to convert the repeating decimals into fractions

the dots above the digits indicate they are being repeated, that is

0.141414... and 0.222...

We require 2 equations with the repeating digits, placed after the decimal point

let x = 0.1414 → (1)

multiply both sides by 100

100x = 14.1414 → (2)

subtract (1) from (2) on both sides

99x = 14 ( divide both sides by 99 )

x =
`(14)/(99)`

similarly

let x = 0.2222 → (1)

multiply both sides by 10

10x = 2.2222 → (2)

subtract (1) from (2) on both sides

9x = 2 ( divide both sides by 9 )

x =
`(2)/(9)`

Now we add the 2 fractions

`(14)/(99)` +
`(2)/(9)`

multiply the numerator/ denominator of the second fraction by 11 to obtain a common denominator

=
`(14)/(99)` +
`(2(11))/(9(11))`

=
`(14)/(99)` +
`(22)/(99)`

=
`(36)/(99)`

=
`(4)/(11)` ← in simplest form