When solving an order of operations question use the GEMDAS method.

G = Grouping Symbols

E = Exponets

M/D = Multiplication OR Division from left to right.

A/S = Addition OR Subtraction from left to right.

\(\displaystyle 8 + 4 * 6 - 12 =\)

\(\displaystyle 4 * 6 = 24\)

\(\displaystyle 8 + 24 - 12 =\)

\(\displaystyle 32 - 12 =\) \(\displaystyle 20\)

The order of operations is the order in which you must solve a problem.  The order is defined as

PARENTHESES

EXPONENTS

MULTIPLICATION

DIVISION

ADDITION

SUBTRACTION

where we solve parentheses first, followed by exponents, and so on.  Following the order of operations, we get

\(\displaystyle 9 \cdot 3^2 + 12 \div 3\)

\(\displaystyle 9 \cdot 9 + 12 \div 3\)

\(\displaystyle 81 + 12 \div 3\)

\(\displaystyle 81 + 4\)

\(\displaystyle 85\)

The order of operations is a specific order in which you must solve a problem.  It is defined as

PARENTHESES

EXPONENTS

MULTIPLICATION

DIVISION

ADDITION

SUBTRACTION

where you solve parentheses first, followed by exponents, and so on.  

So, following this order, we get

\(\displaystyle 4(3^2 + 5^2) - 24 \div 2\)

PARENTHESES

\(\displaystyle 4(9 + 25) - 24 \div 2\)

\(\displaystyle 4(34) - 24 \div 2\)

MULTIPLICATION

\(\displaystyle 136-24 \div 2\)

DIVISION

\(\displaystyle 136 - 12\)

SUBTRACTION

\(\displaystyle 124\)

This problem requires proper order of operations. Remember the acronym for the order of operations: PEMDAS. This acronym will help you to remember the proper order for solving problems:

1. Parentheses
2. Exponents
3. Multiplication and Division (whichever comes first as you read the problem from left to right)
4. Addition and Subtraction (whichever comes first as you read the problem from left to right)

Step 1: Parentheses

\(\displaystyle 2(4-3)^{2}+14\)

\(\displaystyle 2(1)^{2}+14\)

Step 2: Exponents

\(\displaystyle 2(1)^{2}+14=2(1\cdot 1)+14=2(1)+14\)

Step 3: Multiplication

\(\displaystyle 2(1)+14=2+14\)

Step 4: Addition

\(\displaystyle 2+14=16\)

First, let's write an equation that will calculate the cost for each person.

\(\displaystyle \textup{Cost}=\frac{\$315+(\$25\times h\textup{ hours})}{50 \textup{ students}}\)

We need to calculate the number of hours that the students plan to rent the venue from \(\displaystyle 8:00$ AM\) to \(\displaystyle 5:00 $ PM\).

\(\displaystyle \textup{8:00 AM to 12:00 PM=4 hours}\)

\(\displaystyle \textup{12:00 PM to 5:00 PM=5 hours}\)

Let's add these values together to calculate our x-variable (i.e. the number of hours that the students will rent the venue).

\(\displaystyle 4+5=9\textup{ hours}\)

Now, we can substitute in the number of hours that the students will rent the venue and calculate the cost that each student should expect to pay.

\(\displaystyle \textup{Cost}=\frac{\$315+(\$25\times 9\textup{ hours})}{50 \textup{ students}}\)

\(\displaystyle \textup{Cost}=\frac{\$315+\$225}{50 \textup{ students}}\)

\(\displaystyle \textup{Cost}=\frac{\$540}{50 \textup{ students}}\)

Last, we need to divide this total cost by the number of students. 

\(\displaystyle \textup{Cost}=\$10.80\)

Since we are converting from Celsius to Fahrenheit, we need to use the following formula:

 \(\displaystyle ^{\circ}\textup{F} = \frac{9}{5} ^{\circ}\textup{C} + 32\).

Substitute the value for the melting point of nickel in degrees Celsius and solve. 

\(\displaystyle ^{\circ}\textup{F} = \frac{9}{5} \cdot \textup{1,455} ^{\circ } \textup{C} + 32\)

According to the order of operations, we need to perform the multiplication/division operations first.

\(\displaystyle ^{\circ}\textup{F} = \frac{9\times\textup{1,455} ^{\circ } \textup{C}}{5}+32\)

\(\displaystyle ^{\circ}\textup{F} = \frac{\textup{13,095}}{5}+32\)

Simplify.

\(\displaystyle ^{\circ}\textup{F} =\textup{2,619}+32\)

Solve.

\(\displaystyle ^{\circ}\textup{F} = \textup{2,651}\)

Because we want to subtract 28 and 17 first, we need to set that off into parentheses due to the order of operation rules. Remember: without parentheses, division would come before subtraction.  The parentheses around (28 - 17) tells you that the subtraction comes first, then we can do the division by 3.

Because we want to add \(\displaystyle 8\) and \(\displaystyle 9\) first, we need to set that off into parentheses due to the order of operation rules. Then we can multiply by \(\displaystyle 2\). 

\(\displaystyle 6x+7y-3x+2y\)

Re-write the expression to group like terms together.

\(\displaystyle (6x-3x)+(7y+2y)\)

Simplify.

\(\displaystyle 3x+9y\)

To simplify a problem like the example above we must combine the like-termed variables.

Like terms are the terms that share the same variable(s) to the same power. In this example the like term is \(\displaystyle x^{2}\).

To combine like terms the variable \(\displaystyle x^{2}\) stays the same and you add the numbers in front.

Perform the necessary addition, \(\displaystyle 2+3=5\), to get \(\displaystyle 5x^{2}\).

We have the simplified version of the equation, \(\displaystyle 5x^{2}\).