Solve the Expression: 20 - (16-10)/2 Using Order of Operations

Order of Operations with Fraction Division

20−16−102=? 20-\frac{16-10}{2}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 When there's a fraction, we'll treat the numerator and denominator as if they're in parentheses
00:09 Multiplication and division precede addition and subtraction, so we'll start with them
00:15 We're left with a simple subtraction exercise
00:17 That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

20−16−102=? 20-\frac{16-10}{2}=\text{?}

2

Step-by-step solution

According to the order of operations, we will first solve the fraction exercise:

16−102=62=3 \frac{16-10}{2}=\frac{6}{2}=3

20−3=17 20-3=17

3

Final Answer

17 17

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then division before subtraction
  • Technique: Solve numerator 16-10=6, then divide: 62=3 \frac{6}{2}=3
  • Check: Substitute back: 20-3=17 matches our answer ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without following order of operations
    Don't calculate 20-16=4 first and then continue left to right = wrong answer of 7! This ignores the fraction that must be solved completely first. Always solve the entire fraction 16−102 \frac{16-10}{2} before subtracting from 20.

Practice Quiz

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\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why can't I just work from left to right like reading?

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Mathematics has a special order called PEMDAS! Unlike reading, math operations must follow this sequence: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. This ensures everyone gets the same answer.

Do I solve the numerator 16-10 before dividing by 2?

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Yes! The fraction bar acts like invisible parentheses around the numerator. So 16−102 \frac{16-10}{2} means (16-10)÷2. Always solve the top completely first: 16-10=6, then divide: 6÷2=3.

What if I got a different answer like 14 or 15?

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You likely worked left to right or made an arithmetic error. Double-check by following PEMDAS carefully: First 16−102=3 \frac{16-10}{2}=3 , then 20-3=17. The correct answer is always 17.

How do I remember to do fractions before subtraction?

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Think of the fraction as one complete unit that must be solved first! In PEMDAS, division comes before subtraction, so 16−102 \frac{16-10}{2} gets solved completely before subtracting from 20.

Can I use a calculator for this type of problem?

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Yes, but be careful with parentheses! Enter it as: 20 - ((16-10)÷2). The extra parentheses ensure your calculator follows the correct order of operations.

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