# How do you evaluate \frac { 1} { 3} ( 2\frac { 1} { 4} \cdot 1\frac { 1} { 5} - \frac { 17} { 20} )?

Jun 21, 2017

$\frac{1}{3} \left(2 \frac{1}{4} \cdot 1 \frac{1}{5} - \frac{17}{20}\right) = \frac{37}{60}$

#### Explanation:

To evaluate $\frac{1}{3} \left(2 \frac{1}{4} \cdot 1 \frac{1}{5} - \frac{17}{20}\right)$

we should follow the order of operations PEMDAS i.e. first parentheses, then exponents, multiplication, division, addition and subtraction. Here we do not have exponents, but have parentheses and within the parentheses, we should first solve multiplication.

Most importantly we should convert mixed fractions to improper fractions. As $2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$ and $1 \frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5}$, the above expression becomes

$\frac{1}{3} \left(\frac{9}{4} \cdot \frac{6}{5} - \frac{17}{20}\right)$ and performing multiplication first, we get

$\frac{1}{3} \left(\frac{54}{20} - \frac{17}{20}\right)$

= $\frac{1}{3} \times \frac{54 - 17}{20}$

= $\frac{1}{3} \times \frac{37}{20}$ - parentheses has been simplified and now carrying out multiplication we get

$\frac{1}{3} \left(2 \frac{1}{4} \cdot 1 \frac{1}{5} - \frac{17}{20}\right) = \frac{37}{60}$

Jun 27, 2017

color(magenta)(37/60

#### Explanation:

$\frac{1}{3} \left(2 \frac{1}{4} \cdot 1 \frac{1}{5} - \frac{17}{20}\right)$

$\therefore = \frac{1}{3} \left(\frac{9}{4} \cdot \frac{6}{5} - \frac{17}{20}\right)$

$\therefore = \frac{1}{3} \left(\frac{54}{20} - \frac{17}{20}\right)$

$\therefore = \frac{1}{3} \left(\frac{37}{20}\right)$

$\therefore = \frac{1}{3} \times \frac{37}{20}$

:.color(magenta)(=37/60