# How do you use order of operations to simplify 1/7 -: (1/7)^2 - 3/343?

Feb 21, 2017

$\frac{2398}{343}$

#### Explanation:

Follow the order of operations set out in the acronym PEMDAS

{P-parenthesis (brackets) ,E- exponents (powers), M-multiplication, D-division, A- addition and S- subtraction]

rArr1/7÷(1/7)^2-3/343

=1/7÷(1/7xx1/7)-3/343

=1/7÷1/49-3/343larrcolor(red)" bracket/exponent"

[Change division to multiplication and turn dividing fraction upside down.]

$\Rightarrow \left(\frac{1}{\cancel{7}} ^ 1 \times {\cancel{49}}^{7} / 1\right) - \frac{3}{343} \leftarrow \textcolor{red}{\text{ division}}$

$\text{Finally } 7 - \frac{3}{343}$

Change 7 into a fraction with a denominator of 343

$\text{that is } \frac{7}{1} \times \frac{343}{343} = \frac{2401}{343}$

$\Rightarrow \frac{2401}{343} - \frac{3}{243} = \frac{2398}{343} \leftarrow \textcolor{red}{\text{ subtraction}}$

May 27, 2017

$= 6 \frac{340}{343}$

#### Explanation:

In an expression which has different operations, there is a specific order in which they have to be done.

Identify the number of TERMS first. Each term is treated separately and simplified to a single answer.
These are added or subtracted only in the last line.

Within each term, the order to be followed is:

• brackets,
• followed by powers and roots,
• finally multiplication and division

In this case there are two terms. Simplify each separately.

=color(blue)(1/7" " div" " (1/7)^2) -color(red)(3/343)" "larr simplify the brackets
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} \downarrow$
=color(blue)(1/7" " div" " 1/49 -color(red)(3/343)

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \downarrow \textcolor{w h i t e}{\ldots . .} \downarrow \text{ } \leftarrow$multiply by the reciprocal

=color(blue)(1/7 " "xx" " 49/1 -color(red)(3/343)

=color(blue)(1/cancel7 " "xx" " cancel49^7/1 -color(red)(3/343)

$= \text{ "color(blue)(7)" " -" } \textcolor{red}{\frac{3}{343}}$

$= 6 \frac{340}{343}$