Order of Operations - ACT Math

Order of operations means we start with parentheses, then move on to exponents, then multiplication, then division, then addition and subtraction.

Thus,

Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"

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

(9 + 1) * (42 + 2) * (72 + 1) / 2 =

(10) * (16 + 2) * (49 + 1) / 2 =

(10) * (18) * (50) / 2 =

9000/2 = 4500

Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"

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

(4 * 12) / (5 + 6 + 1) + 72 + (2 * 1 + 2)3 =

(48)/(12) + 72 + (2 + 2)3 =

(48)/(12) + 72 + (4) 3 =

(48)/(12) + 72 + 64 =

4 + 72 + 64 = 140

To solve you must use the order of operations PEMDAS.
Multiplication comes first 4 * 2 = 8. Then add 4 + 8 = 12.

Because the "is" represents the equals sign, we must look at everything before "is" and set that equal to everything after.

The first part of the sentence requires us to represent four times the sum of a number and one. This means we must find the sum of the number and one, then multiply this entire quantity by four. The sum of a number and one can be represented as

If we were to then multiply by four, we would write this as , because the entire quantity must be multiplied.

The second part of the sentence asks us to find four greater than the square of the difference between the number and six. This means we must first find the difference between the number and six, and then we must square this quantity. After we do that, we must increase that quantity by four.

The difference between a number and six is represented by

If we were to find the square of this quantity, we could write this as

Because we want to write an expression that is four greater than this, we could write

Thus, the final equation would be:

Starting inside the parentheses, cube the number to the right of the symbol, which is 1, and then subtract that from the number to the left of the symbol, 5, to get 4. Then we perform the same operation by cubing 4 to get 64, and then subtracting that from 100 to get 36.

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)

Let's start with the first expression:

Substitute in our values for the x- and y-variables.

Step 1: Since there are no parentheses we will start with exponents.

Step 2: Multiplication

Step 3: Subtraction

For the second expression, we will proceed in a similar fashion. Let's start with the first expression:

Substitute in our values for the x- and y-variables.

Step 1: Since there are no parentheses we will start with exponents.

Step 2: Multiplication

Step 3: Subtraction

Last, the difference between the first expression and the second is as follows:

The correct choice is

Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"

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

5 * (482 – 82) + 100 / (3 + 2)2 = ?

5 * (400) + 100 / (5) 2 =

2000 + 100 / 25 =

2000 + 4 = 2004

First you perform multiplication 2 * –3 = –6

Then you add –1 which gives you -7.

Evaluate the exponent, then distribute, then add.

First you perform the operation in the parentheses and then you multiply the exponent; after that, subtract one.

First you evaluate the exponent. Then you multiply it by (–3) which gives you –12. Add –1 makes it –13.

In order to find the equivalent expression, distribute to get .

We begin with

We follow the order of P.E.M.D.A.S.

Parenthesis:

Exponents:

Multiplication:

No division needed, so addition:

Finally, subtraction:

To evaluate an expression use PEMDAS to dictate the order of operations. Thus we simplify the parentheses first:

and
next we move on to exponents so:

Next multiplication and division from left to right:

and finally we add:

To correctly solve this expression, you must follow the correct order of operations: Parentheses- ,

Exponents-,

Multplication/ Division-,

and Addition/Subtraction-.

This is an order of operations, PEMDAS problem. PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction.

First we evaluate the parentheses. .

Then, we evaluate the exponent. , since everything raised to the zeroth power equals .

Then, we do the division.

Lastly, we add the .

Putting it all together, we have .

To correctly solve this expression, you must follow the correct order of operations:

Parentheses (starting with parenthesis inside other parenthesis)-

,

Exponents-

,

Multplication/ Division-

,

and Addition/Subtraction-

.

When we evaluate the function at , we can first plug in for to get

.

Since the power is even, we know that , since any negative number to an even power is always a positive number.

Since the function is , we first compute the exponent before mulitplying by .

So the final answer is

Use order of operations (PEMDAS) in order to simplify the expression:

PEMDAS means to do calculations in the following order.

P: Parentheses

E: Exponents

M: Multiplication

D: Division

Substituting in the above values we get our new equation to be:

.

A: Addition

S: Subtraction

From here we add and subtract from left to right