Solve [(4+3)÷7+2÷2-2]÷5: Order of Operations Challenge

Order of Operations with Nested Brackets

[(4+3):7+2:22]:5= \lbrack(4+3):7+2:2-2\rbrack:5=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this problem step by step.
00:11 First, focus on the operations inside the parentheses.
00:19 Remember, division comes before addition and subtraction.
00:29 Now, calculate what's inside the parentheses.
00:33 Keep going! Follow the order of operations to simplify the expression.
00:39 And here's a tip: Zero divided by any number is always zero.
00:44 Great job! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

[(4+3):7+2:22]:5= \lbrack(4+3):7+2:2-2\rbrack:5=

2

Step-by-step solution

Simplifying this expression emphasizes the order of operations, which states that multiplication precedes addition and subtraction, and that division precedes all of them,

In the given expression, the establishment of division operations between the parentheses (the outermost) to a number, therefore according to the order of operations as mentioned, is handled by simplifying the expression in these parentheses, this expression includes division operations that begin on the expression within the parentheses (the innermost), therefore according to the order of operations as mentioned is handled by simplifying the expression in these parentheses and performing the subtraction operations in it, there is no hindrance to calculate the outcome of the division operations in the expression in the outermost parentheses, but for the sake of good order this is done afterwards:

[(4+3):7+2:22]:5=[7:7+2:22]:5 \lbrack(4+3):7+2:2-2\rbrack:5= \\ \lbrack7:7+2:2-2\rbrack:5 Continuing and simplifying the expression in the parentheses we noted, since division precedes addition and subtraction, start with the division operations in the expression and only then calculate the outcome of the addition and subtraction, ultimately perform the division operations on this expression in the parentheses:

[7:7+2:22]:5[1+12]:5=0:5=0 \lbrack7:7+2:2-2\rbrack:5 \\ \lbrack1+1-2\rbrack:5=\\ 0:5=\\0 In the last stage we mentioned that multiplying a number by 0 gives the result 0,

Therefore, this simplifying expression is short so there is no need to elaborate,

And the correct answer here is answer A.

3

Final Answer

0 0

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Solve parentheses first, then division and multiplication left-to-right
  • Technique: Evaluate 7÷7+2÷22 7÷7+2÷2-2 gives 1+12=0 1+1-2=0
  • Check: Final step 0÷5=0 0÷5=0 confirms our bracket calculation ✓

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting before completing all divisions
    Don't calculate 7÷7+2÷2-2 as 7÷(7+2)÷(2-2) = wrong order! This ignores that division happens before addition/subtraction. Always complete all divisions first: 7÷7=1, 2÷2=1, then 1+1-2=0.

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 solve the parentheses first even though division comes before addition?

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Parentheses always come first in PEMDAS! You must solve everything inside each set of brackets completely before moving to operations outside them.

What's the difference between ÷ and : symbols in this problem?

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Both symbols mean division - they're just different notations! The : symbol is commonly used in some countries instead of ÷, but they work exactly the same way.

How do I handle the nested brackets [( )] correctly?

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Work from the innermost brackets outward. First solve (4+3), then solve everything inside the square brackets [ ], finally divide by 5.

Why does anything divided by 5 not always give a whole number?

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You're right that division doesn't always give whole numbers! But in this case, we get 0÷5=0 0÷5=0 because zero divided by any non-zero number equals zero.

Can I solve this problem by working left to right without PEMDAS?

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No! Working left-to-right without following PEMDAS gives wrong answers. You'd get different results that don't follow mathematical rules. Always use the correct order of operations.

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