How do you simplify #-5+2(8/13)-6times2# using order of operations?

Question

Eva Adamson · Accepted Answer

#-205/13# or #-15 10/13#

The order of operations can be remembered by the mnemonic device PEMDAS (often P lease E xcuse M y D ear A unt S ally). This acronym refers to the order of operations, which is:

You are given

#-5+2(8/13)-6xx2#

Parenthesis You are given parenthesis, but there are no expressions to simplify. You can leave this as it is.

NOTE: You might be tempted to plug #8-:13# in your calculator. Unfortunately, this gives you a fraction which repeats forever as #0.bar615384#. This will give an answer which is not exact and so should be avoided in this problem.

Exponents There are no exponents in this problem. Move on to the next letter.

Multiplication You can now multiply terms #-5+(2xx8)/13-12=-5+16/13-12#

Division If the fraction could be reduced, reducing factions counts as division. However, because the fraction is already in lowest terms, you can move on to the next step.

Addition There are no two numbers you can add. Move on.

Subtraction

#-5+16/13-12=-(5xx13)/13+16/13-12=-65/13+16/13-12#

#=-49/13-12=-49/13-(12xx13)/13=-49/13-156/13#

#=-205/13#

Savannah Anderson · Answer

#=-15 10/13#

Count the number of terms first, before you do any calculations. Simplify each term to a single answer. The answers will be added or subtracted in the last step.

Within each term you do operations in the following order:

Each term will simplify to one answer - add or subtract at the end.

#color(red)(-5) color(blue)( +2(8/13))color(green)( -6xx2)" "larr# there are 3 terms

#=color(red)(-5) color(blue)( +16/13)color(green)( -12)" "larr# add 3 terms

#=color(red)(-5) color(blue)( +1 3/13)color(green)( -12)#

#=1 3/13 -17#

#=-15 10/13#

Savannah Anderson · Answer

undefined To simplify the expression, we follow the order of operations: PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

-5 + 2(8/13) - 6 * 2

= -5 + 2 * (8/13) - 6 * 2

= -5 + (16/13) - 12

= -5 + 1.230769231 - 12

= -5 - 10.76923077

= -15.76923077