How do you solve this problem?  (-9 x 4) - (8- -3) x 2   

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kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

In order to answer to this problem, you need to know the order of operations.  If you apply math operators (+, -, x, /, ^, etc) in different orders, you get different answers. So we have to know in which order to use them, and always do it the same way. You can remember the order using the mnemonic phrase "Please Excuse My Dear Aunt Sally". The order of operations is:

-Parentheses

-Exponents

-Multiply

-Divide

-Add

-Subtract

(-9 x 4) - (8- -3) x 2

Parenthesis first, so do whatever you see inside the parentheses:

(-36) - (11) x 2

You can remove the parenthesis once there are no more operations to do within them. No exponents here, so we move on to multiplication:

-36 - 22

Now we can do addition and subtraction:

-36 - 22 = -58

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

(-9 x 4) - (8- -3) x 2

To solve this problem the rule of BODMAS/ PEMDAS is to be followed (Parenthesis Exponents Multiplication Division Addition Subtraction)

First solve within the brackets then remove parenthesis,

(-9 x 4) - (8- -3) x 2

-36 - (11) x 2

-36 -11 x 2                      

Then multiplication 

-36 - 22

Since there are similar signs we add the numbers and take the sign of the bigger number

-58 Answer.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

(-9*4)-(8- -3)*2

There are  two terms here. (-9*4) and (8- -3)*2. The second term is to be subtracted from the first.Each term is simplified by order priority rules: BODMAS Or BOMDAS.

In equal priority operations, go from left to right , 'the first- come- first- serve' way.

First term:

(-9*4)=-9*4= -36.

Second term:

(8- -3)*2= (8+3)*2, as 8--3=8+3, the - -3 equals +3

=11*2

=22.

Therefore, First term - second term = -36-22=-58. The sum of two terms of the same sign is equal to adding them by pure magnitudes and keeping the same sign.

Alternate way by opening the brackets:

Use this method if you are well versed with sign rules and group theory.

(-9*4)-(8--3)*2

-9*4-(8)*2-(--3)*2 , as mutiplication of (8--3) by 2 is ditributive.

=-36-16-(3)*2 as --3 =3 as  3-3 =0 therfore, +3 =--3, being the additive inverse of -3 and 0 being the additive identity.

=-36-16-6

= -58, as lke sign numbers could be added by their magnitudes and the same could be retained .

 

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