Question

Simplify: $\frac{1}{22}+\frac{8}{11}\times 1\frac{1}{2}$

• A. $\frac{25}{22}$
• B. $1\frac{3}{22}$
• C. $1.1\overline{3}$
• D. $1.1\overline{36}$

Answer 1

Answer: (A), (B), (D)

$1.1\overline{36}$

Using PEMDAS rule, first evaluate the multiplication, followed by division.

$\frac{1}{22}+\frac{8}{11}\times 1\frac{1}{2}$
$=\frac{1}{22}+\frac{8}{11}\times \frac{1\times 2+1}{2}$
$=\frac{1}{22}+\frac{8}{11}\times \frac{3}{2}$
$=\frac{1}{22}+\frac{8\times 3}{11\times 2}$
$=\frac{1}{22}+\frac{24}{22}$
$=\frac{1+24}{22}$
$=\frac{25}{22}$

Now, divide $25$ by $22$ using long division.

$\frac{25}{22}=\mathrm{1.13636...}$
It is a non-terminating and repeating decimal.
Here the digit $3$ and $6$ of hundredths and thousandths place get repeated sequentially.

$\therefore \mathrm{1.13636...}$ can be expressed as $1.1\overline{36}$

Also, $\frac{25}{22}=1\frac{3}{22}$