SAT Math : How to find order of operations

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #1 : Arithmetic

(25 * 10)/(5(6 – 4)2) = ?

Possible Answers:

200

50

25

100

25/2

Correct answer:

25/2

Explanation:

We use the order of operations, PEMDAS to solve this equation.

(25 * 10)/[5(6 – 4)2] =

(25 * 10)/[5(2)2] =

(25 * 10)/[5(4)] =

(25 * 10)/20 =

250/20 = 25/2

Example Question #2 : Arithmetic

 

i) add 3z to -2b

ii) multiply by 7

iii) subtract (4z+3b)

 

 

What is the result of the above steps in order?

 

 

Possible Answers:

21z - 14b

17z - 11b

25z - 17b

17z - 17b

Correct answer:

17z - 17b

Explanation:

7(3z - 2b) - (4z + 3b) = 17z - 17b

 

 

Example Question #1 : Order Of Operations

If L = (9K-11)/(a + 2K), then K =

Possible Answers:

(La-7K)/-11

(2L+aL)/2

(La+11)/(9-2L)

(La+2K)/(2L-9)

Correct answer:

(La+11)/(9-2L)

Explanation:

First multiply both sides by a + 2K to get rid of the denominator. This gives you Step #1: L (a + 2K) = 9K – 11

Step #2: La + 2KL = 9K – 11. Now put all values with K on one side of the equal sign.

Step #3: La + 11 = 9K – 2KL.

Step #4: La + 11 = K (9 – 2L).

Step #5: (La+11)/(9-2L) = K

Example Question #4 : How To Find Order Of Operations

Simplify the result of following the steps below in order.

(1)   Subtract 4x from 2y

(2)   Multiply that value by 5

(3)   Add 2x + y to the product

Possible Answers:

10x – 5y

30x – 15y

11y – 18x

22x – 9y

Correct answer:

11y – 18x

Explanation:

Remember that when it says subtract from, it should look like 2y – 4x. Multiplying this by 5 = 10y – 20x. 10y – 20x + 2x +y = 11y – 18x.

Example Question #2 : Arithmetic

Evaluate:

(82  + 34/2) ÷ 9 + 1

Possible Answers:

81/10

49/10

33/10

25/10

10

Correct answer:

10

Explanation:

Order of operations: PEMDAS

Parenthesis/ exponents: (64 + 17) ÷ 9 + 1

(81) ÷ 9 + 1

Division next, so 81 ÷ 9 = 9

9 + 1 = 10

Example Question #2 : Order Of Operations

(14 / 28) 3  + ( 144 – 12 )*17 + 362 = ?

Possible Answers:

22032

3548

1652

2288

2452

Correct answer:

3548

Explanation:

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

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

(14 / 28) 3  + ( 144 – 12 )*17 + 362 =

(2) 3  + ( 132 )*17 + 362 =

8 + ( 132 )*17 + 1296 =

8 + 2244 + 1296 =

3548

Example Question #5 : Arithmetic

Solve the problem 1+4/(3-1)-6=

 

Possible Answers:

1

0

-1

-3

2

Correct answer:

-3

Explanation:

The order of operations is PEMDAS: Parenthesis, exponents, division and multiplication (performed left to right), addition and subtraction (performed left to right).  “Please Excuse My Dear Aunt Sally” is one way to remember the order. One key is that multiplication and division are equal and addition and subtraction are equal, so they are performed in order from left to right.

 

Step 1. Parenthesis: 1+4/2-6; Step 2. Division 1+2-6; Step 3. Addition/Subtraction: 1+2-6= -3

 

Example Question #3 : Order Of Operations

Solve 6-(3+2)-4=

 

Possible Answers:

-3

1

0

-2

3

Correct answer:

-3

Explanation:

The order of operations is PEMDAS: Parenthesis, exponents, division and multiplication (performed left to right), addition and subtraction (performed left to right).  “Please Excuse My Dear Aunt Sally” is one way to remember the order. One key is that multiplication and division are equal and addition and subtraction are equal, so they are performed in order from left to right. Sowe get 6-5-4=-3

Example Question #9 : How To Find Order Of Operations

For all positive integers, let a b be defined by a b = ab 2. Which of the following is equal to 8★2?

Possible Answers:

6★3

4★2

3★6

1★32

2★4

Correct answer:

2★4

Explanation:

To solve this problem, we first evaluate 8★2 and then see which of the answer choices is equal to the resulting number.  Using the definition of ★, we see that 8★2 = 8(22) = 8(4) = 32. The only answer choice that is equivalent to 32 is 2★4, which evaluates to 2(42) = 32.

(Tip: If we quickly scan the answer choices by squaring the number on the right of the symbol, we immediately see that 3★6 and 1★32 are too big to be 32, even before being multiplied by any of the integers on the left of the symbol.)

Example Question #7 : Arithmetic

Eight more than four is an unknown number less than a quarter of the same unknown number. What is the value of the unknown number? 

Possible Answers:

0

–9

12

4

–16

Correct answer:

–16

Explanation:

Let x be the unknown number.  

4 + 8 = 0.25x – x.

 12 = –0.75x

x = 12/–0.75

x = –16

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