Question

Express $1.3\overline{2}+0.\overline{35}$ as a fraction in the simplest form.

• A. $\frac{553}{331}$
• B. $\frac{331}{553}$
• C. $\frac{553}{330}$
• D. $\frac{330}{553}$

Answer 1

The correct option is C $\frac{553}{330}$

Let $x=1.32=1.3222$...(i)

Multiplying eq.(i) by $10$, we have
$10x=\mathrm{13.222..}$

Again, multiplying eq.(i) by $100$, we have
$100x=\mathrm{132.222...}$.....(iii)
Subracting eq.(ii) from (iii), we have
$100x-10x=\left(\mathrm{132.222...}\right)-\left(\mathrm{13.222...}\right)$

$90x=119$
$\Rightarrow x=\frac{119}{90}$
Again, $y=0.35=\mathrm{0.353535...}$

Multiply (iv) by $100$, we have...(iv)
$100y=\mathrm{35.353535...}\left(v\right)$

Subracting (iv) from (v), we have
$100y-y=\left(\mathrm{35.353535...}\right)-\left(\mathrm{0.353535...}\right)$
$99y=35$
$y=\frac{35}{90}$

Now, $1.3\overline{2}+0.\overline{35}=x+y=\frac{119}{90}+\frac{35}{99}$
$=\frac{1309+350}{990}=\frac{1659}{990}=\frac{553}{330}$