## Example Questions

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### Example Question #1 : Arithmetic

(25 * 10)/(5(6 – 4)2) = ?

50

100

200

25

25/2

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?

17z - 17b

21z - 14b

17z - 11b

25z - 17b

17z - 17b

Explanation:

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

### Example Question #1 : Arithmetic

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

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

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

(2L+aL)/2

(La-7K)/-11

(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 #1 : 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

22x – 9y

10x – 5y

30x – 15y

11y – 18x

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 #1 : How To Find Order Of Operations

Evaluate:

(82  + 34/2) ÷ 9 + 1

49/10

33/10

10

81/10

25/10

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 #1 : Arithmetic

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

3548

2288

2452

1652

22032

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 #2 : How To Find Order Of Operations

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

0

-3

1

-1

2

-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 #1 : Order Of Operations

Solve 6-(3+2)-4=

0

1

-2

3

-3

-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 #1 : 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?

4★2

6★3

1★32

3★6

2★4

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 #1 : 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?

–16

4

12

–9

0

–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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