Question

Type the correct answer in each box. If necessary, use / for the fraction bar(s).

Answer 1

ab = 1/2 and a/b = 8/9

Explanation:

took test

Answer 2

Given:

The values are
`a=0.\overline{6},b=0.75`.

To find:

The values of
`ab` and
`(a)/(b)`.

Solution:

We have,

`a=0.\overline{6}`

`a=0.666...` ...(i)

Multiply both sides by 10.

`10a=6.666...` ...(ii)

Subtracting (i) from (ii), we get

`10a-a=6.666...-0.666...`

`9a=6`

`a=(6)/(9)`

`a=(2)/(3)`

And,

`b=0.75`

`b=(75)/(100)`

`b=(3)/(4)`

Now, the product of a and b is:

`ab=(2)/(3)* (3)/(4)`

`ab=(1)/(2)`

The quotient of a and b is:

`(a)/(b)=((2)/(3))/((3)/(4))`

`(a)/(b)=(2)/(3)* (4)/(3)`

`(a)/(b)=(8)/(9)`

Therefore, the required values are
`ab=(1)/(2)` and
`(a)/(b)=(8)/(9)`.