# How do you simplify 49\div 7+ 10[ 3( 9- 2) - 2( 17- 8) ]?

Apr 28, 2018

The answer is $37$.

#### Explanation:

Work the problem with PEMDAS

$\frac{49}{7} + 10 \left[3 \left(9 - 2\right) - 2 \left(17 - 8\right)\right]$

Take care of the inner parenthesis first:

$49 \div 7 + 10 \left[3 \cdot 7 - 2 \cdot 9\right]$

Now deal with the brackets:

$49 \div 7 + 10 \left[21 - 18\right]$

$49 \div 7 + 10 \cdot 3$

Left to right, do the multiplication and division:

$7 + 30$

$37$

Apr 29, 2018

$37$

#### Explanation:

When doing calculations with multiple operations:

Identify the different terms first. (Separated by $+ \mathmr{and} -$ signs)

Within each term, use the order:

• brackets
• powers and roots
• multiply and divide (in any order)

Then re-arrange the terms so the additions are at the front.

• then add and do the subtractions last.

color(blue)(49\div 7) " "color(red)(+" " 10[ 3( 9- 2) - 2( 17- 8) ])" "larr inner brackets
$\textcolor{w h i t e}{\times} \downarrow \textcolor{w h i t e}{\times \times \times \times \times} \downarrow \textcolor{w h i t e}{\times \times \times x} \downarrow$
$= \textcolor{b l u e}{7} \textcolor{w h i t e}{\times \times} \textcolor{red}{+ \textcolor{w h i t e}{x . x} 10 \left[3 \left(7\right) \textcolor{w h i t e}{\times} - \textcolor{w h i t e}{\times} 2 \left(9\right)\right]} \text{ } \leftarrow$ multiply brackets
$\textcolor{w h i t e}{\times} \downarrow \textcolor{w h i t e}{\times \times \times \times \times} \downarrow \textcolor{w h i t e}{\times \times \times x} \downarrow$
$= \textcolor{b l u e}{7} \textcolor{w h i t e}{\times \times} \textcolor{red}{+ \textcolor{w h i t e}{x . . x} 10 \left[21 \textcolor{w h i t e}{x . x} - \textcolor{w h i t e}{x . x} 18\right]} \text{ } \leftarrow$ subtract
$\textcolor{w h i t e}{\times} \downarrow \textcolor{w h i t e}{\times \times \times \times \times \times \times} \downarrow$
$= \textcolor{b l u e}{7} \textcolor{w h i t e}{\times \times} \textcolor{red}{+ \textcolor{w h i t e}{x \ldots . \times \times x} 10 \left[3\right]} \text{ } \leftarrow$ multiply the bracket
$\textcolor{w h i t e}{\times} \downarrow \textcolor{w h i t e}{\times \times \times \times x . \times \times} \downarrow$
$= \textcolor{b l u e}{7} \textcolor{w h i t e}{\times \times} \textcolor{red}{+ \textcolor{w h i t e}{x \ldots . \times \times \times} 30} \text{ } \leftarrow$ add the two terms

$= 37$