ORDER OF OPERATIONS WORKSHEET

Question 1 :

Evaluate :

7(5.8 + 1.2)

Question 2 :

Evaluate :

6(5 - 1.5)

Question 3 :

Evaluate :

(16 + 2)/(11 - 5)

Question 4 :

Evaluate :

3 ⋅ [12 + (9 - 4)]

Question 5 :

Evaluate :

3.75(24 ÷ 6)

Question 6 :

Evaluate :

(56 ÷ 8) + 5 ⋅ (4 + 2) ÷ 10

Question 7 :

Evaluate :

[(44 - 2) ÷ (2² + 3)] ⋅ 3 - 7

Question 8 :

Evaluate the following expression when x = 3 and y = 1.

7(2x + y)

Question 9 :

Evaluate the following expression when x = 7 and y = 5.

3(y - x)²

Question 10 :

Evaluate the following expression when p = -2 and q = 3.

5(p² + q²)

Question 11 :

Evaluate :

2a³ - 8(b² + c) ÷ a + (ab + c)

if a = 4, b = 3 and c = 4.

Question 12 :

In the flag shown below, assume there are about 1500 plants in each of the 50 stars of the flag. And also, assume that there are 64000 plants in each of the 7 short stripes and 105000 plants in each of the 6 long stripes. The blue region contains about 200000.

Use the order of operations to approximate the total number of plants described above.

Question 13 :

A pattern and enough material are bought to make two pillows. The pattern costs $6. Each pillow requires $4.25 worth of fabric and a button that costs $0.80. Find the total cost.

Answers

1. Answer :

= 7(5.8 + 1.2)

Add within parentheses.

= 7(7)

Multiply. 

= 49

2. Answer :

= 6(5 - 1.5)

Subtract within parentheses.

= 6(3.5)

Multiply. 

= 21

3. Answer :

= (16 + 2)/(11 - 5)

Rewrite fraction as division.

= (16 + 2) ÷ (11 - 5)

Evaluate within parentheses.

= 18 ÷ 6

Divide. 

= 3

4. Answer :

= 3 ⋅ [12 + (9 - 4)]

Subtract within parentheses.

= 3 ⋅ [12 + 5]

Add within brackets.

= 3 ⋅ 17

Multiply.  

= 51

5. Answer :

= 3.75(24 ÷ 6)

Divide within parentheses.

= 3.75(4)

Multiply.

= 15

6. Answer :

= (56 ÷ 8) + 5 ⋅ (4 + 2) ÷ 10

Evaluate within parentheses.

= 7 + 5 ⋅ (4 + 2) ÷ 10

= 7 + 5 ⋅ 6 ÷ 10

= 7 + 30 ÷ 10

= 7 + 3

= 10

7. Answer :

= [(44 - 2) ÷ (2² + 3)] ⋅ 3 - 7

Evaluate within parentheses.

= [42 ÷ (2² + 3)] ⋅ 3 - 7

= [42 ÷ (4 + 3)] ⋅ 3 - 7

= [42 ÷ 7] ⋅ 3 - 7

Divide within brackets.

= 6 ⋅ 3 - 7

Multiply.

= 18 - 7

Subtract.

= 11

8. Answer :

= 7(2x + y)

Substitute x = 3 and y = 1.

= 7(2 ⋅ 3 + 1)

Evaluate within parentheses.

= 7(6 + 1)

Add within parentheses.

= 7(7)

Multiply.  

= 49

9. Answer :

= 3(y - x)²

Substitute x = 7 and y = 5.

= 3(5 - 7)²

Subtract within parentheses.

= 3(-2)²

Evaluate power.

= 3(4)

Multiply.  

= 12

10. Answer :

= 5(p² + q²)

Substitute p = -2 and q = 3.

= 5[(-2)² + 3³]

Evaluate powers within brackets.

= 5[4 + 27]

Add within brackets.

= 5 ⋅ 31

Multiply. 

= 155

11. Answer :

2a³ - 8(b² + c) ÷ a + (ab + c)

Substitute a = 4, b = 3 and c = 4.

= 2(4³) - 8(3² + 4) ÷ 4 + (4 ⋅ 3 + 4)

Evaluate within parentheses.

= 2(64) - 8(9 + 4) ÷ 4 + (12 + 4)

= 132 - 8(13) ÷ 4 + 16

Multiply.

= 132 - 104 ÷ 4 + 16

= 132 - 26 + 16

Subtract.

= 106 + 16

Add.

= 122

12. Answer :

Use the order of operations to approximate the total number of plants described above

Write and evaluate the expression.

= 50 ⋅ 1500 + 7 ⋅ 64000 + 6 ⋅ 105000 + 200000

Multiply.

= 75,000 + 448,000 + 630,000 + 200,000

Add.

= 1,353,000

There are approximately 1,353,000 plants in the flag.

13. Answer :

Read and Understand :

One pattern plus fabric and buttons are bought to make pillows. You have to find the total cost.

Make a Plan :

Write a verbal model. 

Solve the Problem :

Write and evaluate the expression.

Substitute values into verbal model.

Total cost :

= 6 + 2(4.25 + 0.80)

= 6 + 2(5.05)

= 6 + 10.10

= 16.10

The total cost is $16.10.

Look Back :

Use estimation to check that the answer is reasonable.  The cost of material for each pillow is about

$4 + $1 = $5

The total cost is about

$6 + 2($5) = $16

The answer is reasonable.

Practice Questions

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