Question

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

Answer 1

The answer is `37`.

Explanation:

Work the problem with PEMDAS

`49/7+10[3(9-2)-2(17-8)]`

Take care of the inner parenthesis first:

`49 div 7+10[3*7-2*9]`

Now deal with the brackets:

`49 div 7+10[21-18]`

`49 div 7+10*3`

Left to right, do the multiplication and division:

`7+30`

Now do the last addition:

`37`

Answer 2

`37`

Explanation:

When doing calculations with multiple operations:

Identify the different terms first. (Separated by `+ 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
`color(white)(xx)darrcolor(white)(xxxxxxxxxx)darrcolor(white)(xxxxxxx)darr`
`=color(blue)(7)color(white)(xxxx)color(red)(+color(white)(x.x) 10[ 3( 7)color(white)(xx) -color(white)(xx) 2(9) ])" "larr` multiply brackets
`color(white)(xx)darrcolor(white)(xxxxxxxxxx)darrcolor(white)(xxxxxxx)darr`
`=color(blue)(7)color(white)(xxxx)color(red)(+color(white)(x..x) 10[21color(white)(x.x) -color(white)(x.x) 18 ])" "larr` subtract
`color(white)(xx)darrcolor(white)(xxxxxxxxxxxxxx)darr`
`=color(blue)(7)color(white)(xxxx)color(red)(+color(white)(x....xxxxx) 10[3 ])" "larr` multiply the bracket
`color(white)(xx)darrcolor(white)(xxxxxxxxx.xxxx)darr`
`=color(blue)(7)color(white)(xxxx)color(red)(+color(white)(x....xxxxxx) 30)" "larr` add the two terms

`=37`