ACT Math : How to find order of operations

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #1 : How To Find Order Of Operations

5 * (482 – 82) + 100 / (3 + 2)2  = ?

Possible Answers:

21,746

2016

2400

2004

66.7

Correct answer:

2004

Explanation:

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 #2 : How To Find Order Of Operations

Evaluate:

–1 + 2 * –3

Possible Answers:

7

5

–7

3

–3

Correct answer:

–7

Explanation:

First you perform multiplication 2 * –3 = –6

Then you add –1 which gives you -7.

Example Question #3 : How To Find Order Of Operations

Evaluate:

10 – 11 * (–1)2
Possible Answers:

–1

0

21

–21

1

Correct answer:

–1

Explanation:

Evaluate the exponent, then distribute, then add.

Example Question #4 : How To Find Order Of Operations

Evaluate the expression:

(2 + 2)– 1 

Possible Answers:

15

1

16

7

4

Correct answer:

15

Explanation:

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

Example Question #5 : How To Find Order Of Operations

Evaluate:

(–1) + (2)2 * (–3)

Possible Answers:

–9

–13

9

–3

13

Correct answer:

–13

Explanation:

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

Example Question #6 : How To Find Order Of Operations

Solve the following equation:

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

Possible Answers:

1014.5

4500

1500

39

9000

Correct answer:

4500

Explanation:

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

Example Question #7 : How To Find Order Of Operations

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

Explanation:

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:

14

32

10

12

24

Correct answer:

12

Explanation:

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

Example Question #9 : 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:

25

36

86

64

16

Correct answer:

36

Explanation:

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. 

Example Question #10 : How To Find Order Of Operations

The expression \dpi{100} \small a (b+(c+a)) is equivalent to:

Possible Answers:

\dpi{100} \small ab+ac

\dpi{100} \small 2a-ab+ac

\dpi{100} \small a^{2}-ab+ac

\dpi{100} \small a^{2}+ab+ac

\dpi{100} \small 2a+ab+ac

Correct answer:

\dpi{100} \small a^{2}+ab+ac

Explanation:

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

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