Solve: 20-(0÷4×3)+1 Using Order of Operations

Order of Operations with Zero Division

Solve the following problem:

20(0:4×3)+1= 20-(0:4\times3)+1=

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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
00:07 0 divided by any number is always equal to 0
00:13 0 multiplied by any number is always equal to 0
00:20 Let's continue to solve the expression according to the correct order of operations
00:25 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 problem:

20(0:4×3)+1= 20-(0:4\times3)+1=

2

Step-by-step solution

Use the order of operations to simplify the following expression. The order of operations states that exponents precede multiplication and division, which in turn precede addition and subtraction, and that parentheses precede all of the above.

Given that multiplication and division precede addition and subtraction, we'll start by calculating the numerical value of the second term from the left. Note that between division and multiplication operations there is no precedence is given according to the order of operations. Therefore we'll perform the operations one after another from left to right - this is considered the natural order of operations. Remember that dividing 0 by any number (except 0) will yield 0, and similarly - multiplying 0 by any number will yield 0:

200:43+1=2003+1=200+1=21 20-0:4\cdot3+1= \\ 20-0\cdot3+1=\\ 20-0+1= \\ 21

Therefore the correct answer is answer A.

3

Final Answer

21

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses, then multiplication and division left to right
  • Technique: Calculate 0÷4×3 as (0÷4)×3 = 0×3 = 0
  • Check: Final calculation: 20-0+1 = 21 matches answer choice A ✓

Common Mistakes

Avoid these frequent errors
  • Working left to right without following PEMDAS
    Don't solve 20-0÷4×3+1 as (20-0)÷4×3+1 = 60! This ignores order of operations and gives wrong results. Always handle operations inside parentheses first, then multiplication and division from left to right.

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 calculate 0÷4×3 before subtracting from 20?

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PEMDAS order of operations says multiplication and division come before addition and subtraction. So you must solve the middle part first: 0÷4×3=0 0÷4×3 = 0 , then do 200+1=21 20-0+1 = 21 .

Does 0÷4×3 equal 0÷12 or does it equal 0×3?

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It equals 0×3! When multiplication and division have equal priority, work left to right. So: 0÷4×3=(0÷4)×3=0×3=0 0÷4×3 = (0÷4)×3 = 0×3 = 0 .

What if I calculated the subtraction first?

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You'd get the wrong answer! If you do (200)÷4×3+1 (20-0)÷4×3+1 , you get 20÷4×3+1=5×3+1=16 20÷4×3+1 = 5×3+1 = 16 . Always follow PEMDAS order strictly.

Why does 0÷4 equal 0 but not the other way around?

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Zero divided by any non-zero number equals zero because 0÷4 0÷4 means "how many 4's fit into 0?" The answer is none, so it's 0. But 4÷0 is undefined!

How do I remember to work left to right with equal operations?

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Think of it like reading a book - when operations have equal priority (like × and ÷), always go left to right just like reading English text!

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