Solve (0/(5+4÷2))-(5+3)÷4: Order of Operations Challenge

Order of Operations with Division Zero

05+4:2(5+3):4= \frac{0}{5+4:2}-(5+3):4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following problem
00:03 0 divided by any other number that is not 0, is always equal to 0
00:06 In our fraction the numerator is 0
00:09 and the denominator is different from 0 therefore the entire expression equals 0
00:14 Always solve the parentheses first
00:18 Continue to solve the expression according to the proper order of operations
00:23 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

05+4:2(5+3):4= \frac{0}{5+4:2}-(5+3):4=

2

Step-by-step solution

This simple rule is the foundation of 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,

First, we pay special attention to the given rule, the first break from the left is the number 0, remember that dividing the number 0 by any number always yields the result 0, (except dividing by the number 0 itself, which is generally forbidden, even though this simple rule that breaks in the given rule, in accordance with the order of operations mentioned, means that this break is worth nothing) therefore the value of this break is 0 and therefore we can simply omit it entirely (as if - the entire break) from the given rule, as this is a common practice that does not contribute anything in terms of numerical value,

05+4:2(5+3):4=0(5+3):4=(5+3):4= \frac{0}{5+4:2}-(5+3):4= \\ \downarrow\\ 0-(5+3):4= \\ -(5+3):4= As usual we should not forget to keep the negative sign after the break, as this minus sign indicates multiplication by negative one,

We will continue and simplify this rule,

In accordance with the order of operations mentioned we will start with the multiplication and division operations, next we will calculate the result of the division operation:

(5+3):4=8:4=2 -(5+3):4=\\ -8:4=\\ -2 In the last step we did not forget that dividing a positive number by a negative number yields a negative result,

We received that the correct answer is answer c.

3

Final Answer

2 -2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Any number divided by zero equals zero (0÷n=0)
  • Technique: Simplify parentheses first: (5+3)÷4 = 8÷4 = 2
  • Check: Substitute back: 0 - 2 = -2 matches our answer ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the zero in division
    Don't skip calculating 0÷(5+4÷2) thinking it's complicated = wrong final answer! Zero divided by any non-zero number always equals zero, which is crucial for the subtraction step. Always evaluate every part of the expression following order of operations.

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 does zero divided by any number equal zero?

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Think of division as 'how many groups?' If you have 0 items to divide into groups, you'll always have 0 in each group. So 07=0 \frac{0}{7} = 0 because 0 ÷ 7 = 0.

Do I really need to calculate what's in the denominator?

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Yes! Even though the numerator is 0, you must verify that the denominator isn't zero. If it were zero, the division would be undefined, not zero.

Why is the final answer negative?

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The expression becomes 0(5+3)÷4=02=2 0 - (5+3) ÷ 4 = 0 - 2 = -2 . The subtraction sign makes the result negative since we're subtracting a positive number from zero.

Can I just ignore the first part since it's zero?

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Not immediately! First verify the denominator isn't zero, then you can simplify. The expression 05+4÷2 \frac{0}{5+4÷2} becomes 0 only after confirming 5+4÷2 ≠ 0.

What if I calculated the denominator wrong?

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Double-check using order of operations: 5+4÷2=5+2=7 5 + 4 ÷ 2 = 5 + 2 = 7 . Division comes before addition, so calculate 4÷2 first, then add 5.

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