Solve the Expression: 20/(2+3) + 6 Using Order of Operations

Order of Operations with Complex Fractions

202+3+6=? \frac{20}{2+3}+6=\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 are in parentheses
00:10 Multiplication and division precede addition and subtraction, so we'll start with them
00:15 We're left with a simple addition problem
00:18 That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

202+3+6=? \frac{20}{2+3}+6=\text{?}

2

Step-by-step solution

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

203+2=205=4 \frac{20}{3+2}=\frac{20}{5}=4

4+6=10 4+6=10

3

Final Answer

10 10

Key Points to Remember

Essential concepts to master this topic
  • Rule: Solve operations inside parentheses before division
  • Technique: Calculate 2+3=5 first, then 205=4 \frac{20}{5}=4
  • Check: Substitute back: 205+6=4+6=10 \frac{20}{5}+6=4+6=10 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing 20 by 2 first instead of solving parentheses
    Don't calculate 20÷2=10 first and get 10÷3+6=9.33! This ignores parentheses and breaks PEMDAS order. Always solve what's inside parentheses (2+3=5) before dividing 20÷5=4.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( 12+3\cdot0= \)

FAQ

Everything you need to know about this question

Why do I solve 2+3 first instead of 20÷2?

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The parentheses in the denominator must be solved first according to PEMDAS! The fraction bar acts like parentheses around the entire denominator (2+3), so you calculate this before dividing.

What if I accidentally did 20÷2 first?

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You'd get 103+6≈9.33 \frac{10}{3}+6 \approx 9.33 , which is wrong! Remember that everything in the denominator must be calculated as one unit before division.

Is there a difference between 20/(2+3) and 20/2+3?

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Absolutely! The first gives 205+6=10 \frac{20}{5}+6=10 , while the second gives 10+3=13 10+3=13 . Parentheses completely change the order of operations.

How do I remember to do parentheses first in fractions?

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Think of the fraction bar as a grouping symbol just like parentheses. Whatever is below the line must be calculated as one complete unit before you can divide.

What comes after solving the parentheses?

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After getting 205 \frac{20}{5} , perform the division to get 4, then add 6. Follow PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

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