To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

For this problem, we solve the exponents before completing addition and subtraction to get our final answer of 88:

$\displaystyle 15^{2}-12^{2}+7$

$\displaystyle 225-12^{2}+7$

$\displaystyle 225-144+7$

$\displaystyle 81+7=88$

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

For this problem, we need to solve what is inside the parentheses first. In order to do this, solve the multiplication before the addition and subtraction. Complete the multiplication outside the parentheses, then solve the addition between that answer and the answer from the parentheses to get a final answer of 24:

$\displaystyle 6\cdot2+(7-2\cdot 3+11)$

$\displaystyle 6\cdot2+(7-6+11)$

$\displaystyle 6\cdot2+(1+11)$

$\displaystyle 6\cdot2+12$

$\displaystyle 12+12=24$

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

For this problem, we need to solve the inside of each set of parentheses first. Once we get these answers, multiply them together to get the final answer of 99:

$\displaystyle (12-3)\cdot (5+6)$

$\displaystyle 9\cdot (5+6)$

$\displaystyle 9\cdot11=99$

The order of operations is the order in which you must solve problems.  The order is

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

where you start with parentheses and follow the order until you reach subtraction. So we will follow the order for this problem

$\displaystyle 8 \cdot 4 + 12 \div 6-(9-4)$

Parentheses

$\displaystyle 8 \cdot 4 + 12 \div 6-5$

Multiplication

$\displaystyle 32 + 12 \div 6-5$

Division

$\displaystyle 32 + 2-5$

Addition

$\displaystyle 34-5$

Subtraction

$\displaystyle 29$

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.

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