Order of operations to simplify expressions .

In summary, the conversation discusses a fraction with a potential incorrect answer of 11/14 or 5.5, but the correct answer is actually -29/14. The conversation also clarifies the meanings of "2^2" and "SQRoot".
  • #1
rachealfarr
1
0
Hi, I have worked the problem but I am not sure that this is the correct answer, Please help.

3(-3) - (5)2^2
____________

8- SQRoot(36) +12 I got an answer of 11/14
but When I check on an online calculator to see if it is correct I am getting 5.5 ...

2^2 = TWO SQUARED
SQRoot = Square root of

Thank you :)
 
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  • #2
Welcome, rachealfarr. (Wave)

The fraction

$$\frac{3(-3) - (5)2^2}{8 - \sqrt{36} + 12}$$

cannot be equal to either $11/14$ or $5.5$. It's a negative number: $3(-3) - (5)2^2 = -9 - (5)4 = -9 - 20 = -29$ and $8 - \sqrt{36} + 12 = 8 - 6 + 12 = 2 + 12 = 14$, hence the fraction is $-29/14$.

Could you check again to make sure you have the right fraction?
 
  • #3
\(\displaystyle \frac{3(-3)-(5)2^2}{8-\sqrt{36}+12}=\frac{3(-3)-(5)4}{8-6+12}=\frac{-9-20}{8-6+12}=-\frac{29}{14}\)
 

FAQ: Order of operations to simplify expressions .

What is the order of operations to simplify expressions?

The order of operations is a set of rules used to determine the sequence in which mathematical operations should be performed in an expression. The acronym PEMDAS is commonly used to remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Why is it important to follow the order of operations?

Following the order of operations ensures that expressions are evaluated consistently and accurately. Without following the order, different people may arrive at different answers for the same expression.

Can the order of operations be changed?

No, the order of operations is a fundamental rule in mathematics and cannot be changed. It is universally accepted and used by mathematicians and scientists.

What happens if parentheses are not used in an expression?

If parentheses are not used in an expression, the other operations should be performed according to the order of operations. However, the use of parentheses can change the order of operations, as anything inside parentheses should be evaluated first.

Are there any exceptions to the order of operations?

Yes, there are some exceptions to the order of operations. For example, in some cases, exponents may be evaluated before multiplication and division. It is important to always follow the specific rules for the order of operations in a given expression.

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