ACT Math : Arithmetic
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Example Questions
Example Question #1 : Order Of Operations
5 * (482 – 82) + 100 / (3 + 2)2 = ?
21,746
66.7
2016
2400
2004
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 #2 : Order Of Operations
Evaluate:
–1 + 2 * –3
7
–7
5
–3
3
–7
First you perform multiplication 2 * –3 = –6
Then you add –1 which gives you -7.
Example Question #3 : Order Of Operations
Evaluate:
0
–1
1
21
–21
–1
Evaluate the exponent, then distribute, then add.
Example Question #4 : Order Of Operations
Evaluate the expression:
(2 + 2)2 – 1
4
15
1
16
7
15
First you perform the operation in the parentheses and then you multiply the exponent; after that, subtract one.
Example Question #1 : Arithmetic
Evaluate:
(–1) + (2)2 * (–3)
–9
9
–3
13
–13
–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) * (42 + 2) * (72 + 1) / 2 = ?
39
1014.5
1500
4500
9000
4500
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 #3 : Arithmetic
Solve the following equation:
(4 * 12) / (5 + 6 + 1) + 72 + (2 * 1 + 2)3 = ?
98.6
86
140
90.6
126
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 #3 : Arithmetic
Solve: 4 + 2 * 4 = ?
12
14
10
32
24
12
To solve you must use the order of operations PEMDAS.
Multiplication comes first 4 * 2 = 8. Then add 4 + 8 = 12.
Example Question #4 : Arithmetic
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)?
86
36
64
–25
16
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.
Example Question #2 : How To Find Order Of Operations
The expression 
In order to find the equivalent expression, distribute 
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