Solve (5+4-3)² ÷ (5×2-10×1): Order of Operations Practice

Division by Zero with Order of Operations

(5+43)2:(5×210×1)= (5+4-3)^2:(5\times2-10\times1)=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:03 Always solve the parentheses first
00:06 Multiplication precedes subtraction
00:19 We obtained division by 0
00:24 We cannot divide by 0 therefore there is no solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(5+43)2:(5×210×1)= (5+4-3)^2:(5\times2-10\times1)=

2

Step-by-step solution

This simple rule is the order of operations which states that exponentiation precedes multiplication and division, which precede addition and subtraction, and that operations enclosed in parentheses precede all others,

In the given expression, the establishment of division between two sets of parentheses, note that the parentheses on the left indicate strength, therefore, in accordance to the order of operations mentioned above, we start simplifying the expression within those parentheses, and as we proceed, we obtain the result derived from simplifying the expression within those parentheses with given strength, and in the final step, we divide the result obtained from the simplification of the expression within the parentheses on the right,

We proceed similarly with the simplification of the expression within the parentheses on the left, where we perform the operations of multiplication and division, in strength, in contrast, we simplify the expression within the parentheses on the right, which, according to the order of operations mentioned above, means multiplication precedes division, hence we first perform the operations of multiplication within those parentheses and then proceed with the operation of division:

(5+43)2:(52101)=(2)2:(1010)=4:0 (5+4-3)^2:(5\cdot2-10\cdot1)= \\ (-2)^2:(10-10)= \\ 4:0\\ We conclude that the sequence of operations within the expression that is within the parentheses on the left yields a smooth result, this result we leave within the parentheses, these we raised in the next step in strength, this means we remember that every number (positive or negative) in dual strength gives a positive result,

As we proceed, note that in the last expression we received from establishing division by the number 0, this operation is known as an undefined mathematical operation (and this is the simple reason why a number should never be divided by 0 parts) therefore, the given expression yields a value that is not defined, commonly denoted as "undefined group" and use the symbol :

{} \{\empty\} In summary:

4:0={} 4:0=\\ \{\empty\} Therefore, the correct answer is answer A.

3

Final Answer

No solution

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then exponents, then multiplication and division left to right
  • Calculate Step-by-Step: (5+43)2=62=36 (5+4-3)^2 = 6^2 = 36 and (5×210×1)=0 (5×2-10×1) = 0
  • Check Division: When denominator equals zero, the expression is undefined, not solvable ✓

Common Mistakes

Avoid these frequent errors
  • Trying to divide by zero and getting an answer
    Don't calculate 36 ÷ 0 and write down a number like 0 or infinity = mathematically impossible! Division by zero is undefined in mathematics because no number times 0 equals 36. Always recognize when the denominator becomes zero and conclude the expression has no solution.

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 can't I divide by zero?

+

Division asks "what number times 0 gives me 36?" But any number times 0 equals 0, never 36! That's why division by zero is undefined - there's no answer that works.

What does 'no solution' mean exactly?

+

When we get division by zero, the mathematical expression cannot be solved. It's like asking "What's the color of silence?" - the question itself doesn't make sense mathematically.

Did I make a calculation error if I got zero in the denominator?

+

Not necessarily! Double-check your arithmetic: 5×210×1=1010=0 5×2-10×1 = 10-10 = 0 . If your math is correct and you get 0 in the denominator, then no solution is the right answer.

How do I write 'no solution' on a test?

+

You can write "No solution," "Undefined," or "Does not exist." Some teachers accept the symbol \emptyset (empty set). Check what your teacher prefers!

Is this different from getting zero as an answer?

+

Yes, very different! Getting 0 as an answer means x=0 x = 0 . Getting division by zero means the problem cannot be solved at all - there's no value that works.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Order of Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations