Question

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

Answer 1

Given:

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

To find:

The values of $ab$ and $\dfrac{a}{b}$.

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

$10a-a=6.666...-0.666...$

$9a=6$

$a=\dfrac{6}{9}$

$a=\dfrac{2}{3}$

And,

$b=0.75$

$b=\dfrac{75}{100}$

$b=\dfrac{3}{4}$

Now, the product of a and b is:

$ab=\dfrac{2}{3}\times \dfrac{3}{4}$

$ab=\dfrac{1}{2}$

The quotient of a and b is:

$\dfrac{a}{b}=\dfrac{\dfrac{2}{3}}{\dfrac{3}{4}}$

$\dfrac{a}{b}=\dfrac{2}{3}\times \dfrac{4}{3}$

$\dfrac{a}{b}=\dfrac{8}{9}$

Therefore, the required values are $ab=\dfrac{1}{2}$ and $\dfrac{a}{b}=\dfrac{8}{9}$.