Solve: (36-20)÷8 - 6 Using Order of Operations

Order of Operations with Fractions

Solve the following:


36−(4⋅5)8−3⋅2= \frac{36-(4\cdot5)}{8}-3\cdot2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:04 Always solve the parentheses first
00:13 Calculate the numerator
00:25 Multiplication precedes subtraction
00:31 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:


36−(4⋅5)8−3⋅2= \frac{36-(4\cdot5)}{8}-3\cdot2=

2

Step-by-step solution

Let's first address the fraction. We must begin by solving the exercise within the parentheses due to the rules of the order of arithmetic operations. Parentheses come before everything else:

36−(20)8−3×2= \frac{36-(20)}{8}-3\times2=

Let's continue by simplifying the fraction, we subtract the exercise in the numerator and divide by 8:

36−208=168=2 \frac{36-20}{8}=\frac{16}{8}=2

We then arrange the exercise accordingly:

2−3×2= 2-3\times2=

Finally we solve the multiplication exercise and then subtract:

2−6=−4 2-6=-4

3

Final Answer

-4

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always solve parentheses first, then multiplication/division left to right
  • Technique: Simplify numerator 36−20=16 36-20=16 , then divide: 168=2 \frac{16}{8}=2
  • Check: Substitute back: 36−208−3×2=2−6=−4 \frac{36-20}{8}-3\times2 = 2-6 = -4 ✓

Common Mistakes

Avoid these frequent errors
  • Solving multiplication before parentheses
    Don't solve 3×2 first and get 2-6 = -4! This ignores parentheses priority and can give wrong results in more complex problems. Always follow PEMDAS: solve parentheses in the fraction first, then division, then multiplication.

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 in the fraction first?

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PEMDAS rules say parentheses come first, even when they're in a fraction! In 36−(4⋅5)8 \frac{36-(4\cdot5)}{8} , you must solve 4⋅5=20 4\cdot5=20 before anything else.

Can I solve 3×2 before working on the fraction?

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No! Even though multiplication and division have equal priority, you work left to right. The fraction 36−208 \frac{36-20}{8} comes before 3×2 3\times2 , so solve it first.

What if I get confused about the order?

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Write out PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Follow this order step by step!

How do I handle the fraction bar?

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The fraction bar acts like grouping symbols! Solve everything in the numerator first: 36−20=16 36-20=16 , then divide by the denominator: 16÷8=2 16÷8=2 .

Why is my answer negative?

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Don't worry! Negative answers are common. Here we get 2−6=−4 2-6=-4 because we're subtracting a larger number from a smaller one.

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