Parentheses and brackets: Evaluate 2³[1/4+4(36÷12)]

  • MHB
  • Thread starter Dnichol016
  • Start date
I hope this helps with your grandson's homework. In summary, the expression 2[1/4 + 4(36 divided by 12)] can be simplified to 98.
  • #1
Dnichol016
4
0
2[1/4 + 4(36 divided by 12)]

its 2 to the 3rd power. How do you solve this?
 
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  • #2
Hello, and welcome to MHB! :)

As written, the expression evaluates to:

\(\displaystyle \frac{49}{2}\)

Are you certain you have copied it correctly?
 
  • #3
Dnichol016 said:
2[1/4 + 4(36 divided by 12)]

its 2 to the 3rd power. How do you solve this?
The "deepest" parentheses are "(36 divided by 12)" which is 3 so
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
MarkFL said:
Hello, and welcome to MHB! :)

As written, the expression evaluates to:

\(\displaystyle \frac{49}{2}\)

Are you certain you have copied it correctly?
Yes it’s in my grandsons homework
 
  • #5
2833EABD-6C42-4473-808B-9E229704D990.jpeg
 
  • #6
Okay, we are given to evaluate:

\(\displaystyle 2^3\left[\frac{1}{4}+4(36\div12)\right]\)

Do the division within the innermost brackets:

\(\displaystyle 2^3\left[\frac{1}{4}+4(3)\right]\)

Do the indicated multiplication within the brackets:

\(\displaystyle 2^3\left[\frac{1}{4}+12\right]\)

Do the indicated addition within the brackets:

\(\displaystyle 2^3\left[\frac{49}{4}\right]\)

Rewrite \(2^3\) as \(8\):

\(\displaystyle 8\left[\frac{49}{4}\right]\)

Do the indicated multiplication:

\(\displaystyle 8\left[\frac{49}{4}\right]=2\cdot49=98\)
 
  • #7
Thank yo so much
 

Related to Parentheses and brackets: Evaluate 2³[1/4+4(36÷12)]

1. What is the difference between parentheses and brackets?

Parentheses and brackets are both symbols used in mathematical expressions to indicate the order of operations. Parentheses are typically used to group terms together and indicate that those terms should be evaluated first. Brackets are used to enclose terms or expressions that need to be evaluated as a single unit.

2. How do you evaluate an expression with both parentheses and brackets?

When evaluating an expression with both parentheses and brackets, first simplify the expression inside the parentheses, then simplify the expression inside the brackets. Finally, use the order of operations to evaluate the remaining terms in the expression.

3. What is the order of operations when evaluating an expression with parentheses and brackets?

The order of operations when evaluating an expression with parentheses and brackets is to first simplify the expression inside the parentheses, then simplify the expression inside the brackets. Finally, use the order of operations to evaluate the remaining terms in the expression.

4. Can parentheses and brackets be used interchangeably in an expression?

No, parentheses and brackets cannot be used interchangeably in an expression. They have different meanings and serve different purposes in mathematical expressions. Using the wrong symbol can result in an incorrect answer.

5. How do you solve an expression with exponents and fractions?

To solve an expression with exponents and fractions, first simplify the fraction by finding the common denominator. Then, use the exponent rules to simplify the expression. Finally, use the order of operations to evaluate the remaining terms in the expression.

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