PEMDAS Rules Practice 1 Solutions

Below are the solutions and answers to the problems in PEMDAS Rules Practice 1. Notice that I have color coded the solution to guide you which operation results to which answer. I have also varied the notations like / and ÷ to familiarize you with both of them. In addition, I have also included operations on fractions with expressions in the numerator and the denominator. In a fraction whose numerator and/or denominator contains one or more operations , you have to simplify first both the numerator and the denominator before dividing. The methods in calculating fractions are shown in numbers 7, 9 and 10.

PEMDAS Rules Practice 1 Solutions

1. 2 \times 3 + 4 \times 6

Solution:

Multiply: 2 x 3 + 4 x 6 = 6 + 24

Add: 6 + 24 = 30

Answer: 30

 

2. (-3)(2) + 18 \div 3

Solution:

Multiply: (-3)(2) + 18 \div 3 = -6 + 18 \div 3

Divide: -6 + 18 \div 3 = -6 + 6

Add: -6 + 6 = 0

Answer: 0

 

3. 4 + (6 - 2)^2 + 1

Solution:

Parenthesis: 4 + (6 – 2)2 + 1 = 4 + 42 + 1

Exponent: 4 + 42 + 1 = 4 + 16 + 1

Add: 4 + 16 + 1 = 21

Answer: 21

 

4. 8(6 - 2) \div 2(5 - 3)

Solution:

Parenthesis: 8(6 – 2) ÷ 2(5 – 3) = 8(4) ÷ 2(2)

Multiply:  8(4) ÷ 2(2) = 32 ÷ 2(2)*

Divide: 32 ÷ 2(2)= 16(2)

Multiply: 16(2) = 32

Answer: 32

*This is the case mentioned in the PEMDAS Rules that when multiplication and division are performed consecutively (without any other operations or grouping symbols in between), the perform the operations from the left hand side to the right hand side.

 

5. (-12)(-3) + 8^2

Solution:

Exponent: (-12)(-3) + 82 = 36 + 64

Multiply:  (-12)(-3) + 64= 36 + 64

Add: 36 +64 = 100

Answer: 100

 

6. 4 \div 5 \times 25 + 2

Solution:

Divide: 4/5 x 25 + 2 = 0.8 x 25 + 2*

Multiply: 0.8 x 25 + 2 = 20 + 2

Add: 20 + 2 = 22

Answer: 22

*This is the case mentioned in the PEMDAS Rules that when multiplication and division are performed consecutively (without any other operations or grouping symbols in between), the perform the operations from the left hand side to the right hand side.

 

7. \displaystyle \frac{-9(2 + 1)}{-2(-2-1)}

Solution:

Numerator:

Parenthesis: -9(2 + 1) = -9(3)

Multiply: -9(3) = -27

Denominator:

Parenthesis: -2(-2 – 1) = -2(-3)

Multiply: -2(-3) = 6

Divide the numerator by the denominator: -27/6 = -4.5

Answer: -4.5

 

8. 4( 3 + 1) - 2(5 -2)

Solution:

Parenthesis: 4(3 + 1) – 2(5 -2) = 4(4) – 2(3)

Multiply: 4(4) – 2(3) = 16 – 6

Subtract: 16 – 6 = 10

Answer: 10

 

9. \displaystyle \frac{14}{-3-4}

Solution

Denominator: -3 – 4 = -7

Divide the numerator by the denominator: 14 ÷ -7 = -2

Answer: -2

 

10. \displaystyle \frac{2^2 - 4^2}{-3 - 1}

Numerator: 

Exponent: 2242 = 416

Subtract: 4 – 16 = -12

Denominator: – 3 – 1 = -4

Divide the numerator by the denominator: -12  ÷ -4 = 3

Answer: 3

 

11. -(-3) + 8 \div 4

Solution:

We know that -(-3) = 3, so we only have two operations to perform.

Divide: -(-3) + 8 ÷ 4 = 3 + 2

Add: 3 + 2 = 5

Answer: 5

 

12. 9^2 - 8 - 2^3

Solution:

Exponent: 92 – 8 – 23 = 81 – 8 – 8

Subtract: 81 – 8 – 8= 73 – 8

Subtract: 73 – 8 = 65

Answer: 65

 

13. (-7 - 9) (8 - 4) + 4^3 \div 8

Parenthesis: (-7 – 9) (8 – 4) + 43 ÷ 8 = (-16)(4) + 43 ÷ 8

Exponent: (-16)(4) + 43 ÷ 8 = (-16)(4) + 64 ÷ 8

Multiply: (-16)(4) + 64 ÷ 8  = -64 + 64 ÷ 8

Divide: -64 + 64 ÷ 8  = -64 + 8  

Add: -64 + 8  = 56

Answer: -56

 

14. 6 + 3 \times 2 - 12 \div 4

Multiply: 6 + 3 x 2 – 12/4 = 6 + 6 – 12/4

Divide: 6 + 6 – 12/4  = 6 + 6 – 3

Perform Addition and Subtraction from left to right: 6 + 6 – 3 = 9

Answer: 9

 

15. 7 \times (3 + 2 ) - 5

Parenthesis: 7 x (3 + 2) – 5 = 7 x 5 – 5

Multiply: 7 x 5 – 5  = 35 – 5

Subtract: 35 – 5 = 30

 Answer: 30

In the next post, I discuss on how to calculate expressions with nested parentheses.

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