Solve Complex Fraction: ((32×4+8)÷(35-27))÷(-2) Step-by-Step

Order of Operations with Negative Fractions

Solve the following equation:

(32×4+8) ⁣:(−27+35)−2= \frac{(32\times4+8)\colon(-27+35)}{-2}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:04 Always solve the parentheses first
00:23 Multiplication and division precede addition and subtraction
00:49 Let's continue calculating the parentheses
00:56 Continue to solve the expression according to the correct order of operations
01:03 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

(32×4+8) ⁣:(−27+35)−2= \frac{(32\times4+8)\colon(-27+35)}{-2}=

2

Step-by-step solution

We begin by solving the two parentheses in the numerator of the fraction:

(32×4+8)=128+8=136 (32\times4+8)=128+8=136

(−27+35)=8 (-27+35)=8

We obtain the following exercise:

136:8−2= \frac{136:8}{-2}=

17−2=−8.5 \frac{17}{-2}=-8.5

3

Final Answer

-8.5

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Solve parentheses first, then division and multiplication left-to-right
  • Technique: Calculate (32×4+8)=136 (32×4+8) = 136 and (−27+35)=8 (-27+35) = 8 first
  • Check: Verify 1368=17 \frac{136}{8} = 17 , then 17−2=−8.5 \frac{17}{-2} = -8.5 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing by -2 before solving the complex fraction
    Don't divide by -2 first = wrong order and confusing negatives! This violates PEMDAS and makes tracking signs much harder. Always solve the complex fraction completely first, then divide by -2 as the final step.

Practice Quiz

Test your knowledge with interactive questions

\( 20\div(4+1)-3= \)

FAQ

Everything you need to know about this question

Why do I solve the parentheses before the division?

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PEMDAS order requires parentheses first! You must calculate (32×4+8) (32×4+8) and (−27+35) (-27+35) before any division operations.

How do I handle the negative sign in -27+35?

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Think of it as adding a negative number: 35+(−27)=35−27=8 35 + (-27) = 35 - 27 = 8 . The result is positive because 35 is larger than 27.

Why is my final answer negative?

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Because you're dividing a positive number (17) by a negative number (-2). Remember: positive ÷ negative = negative result.

Can I write the answer as a fraction instead?

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Yes! −8.5=−172 -8.5 = -\frac{17}{2} . Both forms are correct, but -8.5 is often preferred for final answers unless fractions are specifically requested.

What if I accidentally do 136÷8÷(-2) from left to right?

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You'd get the same answer! Since 136÷8−2=1368×(−2) \frac{136÷8}{-2} = \frac{136}{8×(-2)} , the order doesn't matter here, but always follow PEMDAS to avoid confusion in other problems.

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