Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Find the fraction equivalent of each of the following numbers in simplest form.

Answer 1

Answer: they would be

2/3

9/11

8/15

Answer 2

Answer with Step-by-step explanation:

1.Let x=
`0.\bar 6=0.6666...` ..(1)

Multiply by 10 on both side then we get

`10x=6.666...` ...(2)

Subtract equation(1) from equation (2)

`9x=6`

`x=(6)/(9)=(2)/(3)`

`x=(2)/(3)`

2.Let
`x=0.\bar{81}`

`x=0.818181...` ..(1)

Multiply by 100 on both sides then we get

`100x=81.8181...` ..(2)

Subtract equation (1) from equation(2)

`99x=81`

`x=(81)/(99)=(9)/(11)`

`x=(9)/(11)`

3.Let
`x=0.5\bar{3}`

`x=0.5333...`. ..(1)

Multiply by 10 on both sides

`10x=5.333...` ...(2)

Subtract equation (1) from equation(2)

`9x=4.8`

`x=(4.8)/(9)`

`x=(1.6)/(3)=(8)/(15)`

`x=(8)/(15)`