Question

How do you simplify `8-(-5)-4(-7)`?

Answer 1

41

Explanation:

Using PEMDAS

Parentheses `larr" brackets"`
Exponents `larr" powers"`
Multiply
Divide
Add
Subtract

(work left to right)

Brackets
We have 2 bracketed parts and they are both of multiply type
`-(-5) -> -1(-5)->+5`
`-4(-7) ->+28`

`8+5+28`

Add/Subtract `larr" left to right"`

`41`

Answer 2

`8 - (-5) - 4(-7) = 41`

Explanation:

Given the following expression to simplify:

`8 - (-5) - 4(-7)`

Minuses

First note that minus signs are used for two different purposes here:

• The minus sign in "`-5`" combines with the following `5` to denote the negative number "minus five". In some contexts a minus sign used in this way is called "unary minus".

• The minus sign between "`8`" and "`(-5)`" denotes subtraction. It describes taking "`(-5)`" away from "`8`". in some contexts a minus sign used in this way is called "binary minus".

If we colour the numbers in the expression blue and the subtractions red then we have:

`color(blue)(8) color(red)(-) (color(blue)(-5)) color(red)(-) color(blue)(4)(color(blue)(-7))`

The next thing that is useful to know about binary and unary minuses is that when they occur together, they combine into a plus.

So for example:

`color(blue)(8) color(red)(-) color(blue)(-5) = color(blue)(8) color(red)(+) color(blue)(5)`

`color(white)()`
PEMDAS

To help remember in what order you should evaluate expressions there is a mnemonic PEMDAS:

P Parentheses (i.e. brackets).

E Exponents (i.e. powers).

MD Multiplication and Division.

AS Addition and Subtraction.

This is commonly taught in the USA. In other countries you may come across BODMAS or BIDMAS, but they are very similar.

So you should evaluate anything in parentheses first, followed by any exponents, followed by any multiplications and divisions (evaluated left to right), followed by any additions and subtractions (evaluated left to right).

`color(white)()`
Putting it all together

`color(blue)(8) color(red)(-) (color(blue)(-5)) color(red)(-) color(blue)(4)(color(blue)(-7))`

Evaluate the contents of the parentheses first to get:

`color(blue)(8) color(red)(-) color(blue)(-5) color(red)(-) color(blue)(4) color(red)(*) color(blue)(-7)`

There are no exponents, so next is multiplication and division.

Multiply `color(blue)(4)` by `color(blue)(-7)` to get `color(blue)(-28)`

`color(blue)(8) color(red)(-) color(blue)(-5) color(red)(-) color(blue)(-28)`

Finally we have two subtractions to evaluate (both of which become additions), starting with the left one:

`color(blue)(8) color(red)(-) color(blue)(-5) color(red)(-) color(blue)(-28)= color(blue)(8) color(red)(+) color(blue)(5) color(red)(-) color(blue)(-28) = color(blue)(13) color(red)(-) color(blue)(-28) = color(blue)(13) color(red)(+) color(blue)(28) = color(blue)(41)`