### All ACT Math Resources

## Example Questions

### Example Question #1071 : Act Math

By how much does the value of exceed the value of when and

**Possible Answers:**

**Correct answer:**

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:

- Parentheses
- Exponents
- Multiplication and Division (whichever comes first as you read the problem from left to right)
- 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 .

### Example Question #1 : How To Find Order Of Operations

5 * (482 – 82) + 100 / (3 + 2)^{2 }= ?

**Possible Answers:**

2016

2004

66.7

2400

21,746

**Correct answer:**

2004

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

### Example Question #3 : How To Find Order Of Operations

Evaluate:

–1 + 2 * –3

**Possible Answers:**

–3

–7

5

3

7

**Correct answer:**

–7

First you perform multiplication 2 * –3 = –6

Then you add –1 which gives you -7.

### Example Question #4 : How To Find Order Of Operations

Evaluate:

^{2}

**Possible Answers:**

0

21

–1

–21

1

**Correct answer:**

–1

Evaluate the exponent, then distribute, then add.

### Example Question #2 : How To Find Order Of Operations

Evaluate the expression:

(2 + 2)^{2 }– 1

**Possible Answers:**

16

7

4

1

15

**Correct answer:**

15

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

### Example Question #6 : How To Find Order Of Operations

Evaluate:

(–1) + (2)^{2} * (–3)

**Possible Answers:**

–3

9

13

–9

–13

**Correct answer:**

–13

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

### Example Question #1 : How To Find Order Of Operations

Solve the following equation:

(9 + 1) * (4^{2} + 2) * (7^{2} + 1) / 2 = ?

**Possible Answers:**

1014.5

39

1500

9000

4500

**Correct answer:**

4500

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

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

(9 + 1) * (4^{2} + 2) * (7^{2} + 1) / 2 =

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

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

9000/2 = 4500

### Example Question #4 : Arithmetic

Solve the following equation:

(4 * 12) / (5 + 6 + 1) + 72 + (2 * 1 + 2)^{3} = ?

**Possible Answers:**

140

98.6

86

126

90.6

**Correct answer:**

140

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

### Example Question #8 : How To Find Order Of Operations

Solve: 4 + 2 * 4 = ?

**Possible Answers:**

32

12

10

14

24

**Correct answer:**

12

To solve you must use the order of operations PEMDAS.

Multiplication comes first 4 * 2 = 8. Then add 4 + 8 = 12.

### Example Question #2 : How To Find Order Of Operations

The operation ¤ is defined as “cube the number that is to the right of the ¤ and subtract the result from the number that is to the left of ¤.” What is the value of 100 ¤ (5 ¤ 1)?

**Possible Answers:**

86

36

**–**25

64

16

**Correct answer:**

36

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.

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