- #1
Dnichol016
- 4
- 0
2[1/4 + 4(36 divided by 12)]
its 2 to the 3rd power. How do you solve this?
its 2 to the 3rd power. How do you solve this?
Parentheses and brackets: Evaluate 2³[1/4+4(36÷12)]
- Context: MHB
- Thread starter Dnichol016
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Discussion Overview
The discussion revolves around evaluating the expression 2³[1/4 + 4(36 ÷ 12)], with participants exploring different interpretations and calculations of the expression. The focus includes mathematical reasoning and clarification of the order of operations.
Discussion Character
- Mathematical reasoning
- Debate/contested
Main Points Raised
- One participant suggests that the expression evaluates to 49/2, questioning the accuracy of the original problem statement.
- Another participant provides a step-by-step evaluation, leading to the conclusion that the expression simplifies to 98, while also confirming the original problem is as stated.
- There is a suggestion that the expression might have been miswritten, proposing an alternative interpretation that would change the outcome significantly.
Areas of Agreement / Disagreement
Participants express differing views on the evaluation of the expression, with no consensus reached on the correct interpretation or final value.
Contextual Notes
There are indications of potential misinterpretation of the expression, particularly regarding the placement of parentheses and the order of operations, but these remain unresolved.
- #2
MarkFL
Gold Member
MHB
- 13,284
- 12
Hello, and welcome to MHB! :)
As written, the expression evaluates to:
$$\frac{49}{2}$$
Are you certain you have copied it correctly?
As written, the expression evaluates to:
$$\frac{49}{2}$$
Are you certain you have copied it correctly?
- #3
HallsofIvy
Science Advisor
Homework Helper
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The "deepest" parentheses are "(36 divided by 12)" which is 3 soDnichol016 said:
that reduces to "2[1/4+ 4(3)]= 2[1/4+ 12]. Now 1/4+ 12= 1/4+ 48/4= 49/4
so we can reduce further to 2[49/4]= 49/2. That is NOT 2^3= 8.
It is possible that you intended the "4+ 4(36 divided by 23)" to all be in the denominator, not just the 4. That would require one more set of brackets:
2[1/{4+ 4(36 divided by 23)}]= 2[1/{4+ 4(3)}]= 2[1/(4+ 12)]= 2[1/16]= 2/16= 1/8.
But 1/8 is still not 8!
- #4
Dnichol016
- 4
- 0
Yes it’s in my grandsons homeworkMarkFL said:
- #5
Dnichol016
- 4
- 0
- #6
MarkFL
Gold Member
MHB
- 13,284
- 12
Okay, we are given to evaluate:
$$2^3\left[\frac{1}{4}+4(36\div12)\right]$$
Do the division within the innermost brackets:
$$2^3\left[\frac{1}{4}+4(3)\right]$$
Do the indicated multiplication within the brackets:
$$2^3\left[\frac{1}{4}+12\right]$$
Do the indicated addition within the brackets:
$$2^3\left[\frac{49}{4}\right]$$
Rewrite \(2^3\) as \(8\):
$$8\left[\frac{49}{4}\right]$$
Do the indicated multiplication:
$$8\left[\frac{49}{4}\right]=2\cdot49=98$$
$$2^3\left[\frac{1}{4}+4(36\div12)\right]$$
Do the division within the innermost brackets:
$$2^3\left[\frac{1}{4}+4(3)\right]$$
Do the indicated multiplication within the brackets:
$$2^3\left[\frac{1}{4}+12\right]$$
Do the indicated addition within the brackets:
$$2^3\left[\frac{49}{4}\right]$$
Rewrite \(2^3\) as \(8\):
$$8\left[\frac{49}{4}\right]$$
Do the indicated multiplication:
$$8\left[\frac{49}{4}\right]=2\cdot49=98$$
- #7
Dnichol016
- 4
- 0
Thank yo so much
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