## Envision Math 6th Grade Textbook Answer Key Topic 2.3 Order of Operations

**Order of Operations**

How do you know which operation to perform first?

Evaluate 14 + 8 × 6.

Answer:

**Other Examples**

Evaluate 20 + (30 – 10) ÷ 5.

Using order of operations:

20 + (30 – 10) ÷ 5 ← Compute inside the parentheses first.

20 + 20 ÷ 5 ← Next, divide.

20 + 4 ← Finally, add.

24

Using a scientific calculator:

Press:

Use the order of operations to evaluate.

Evaluate 4^{2} – (4 + 6) ÷ 2.

Using order of operations:

42 – (4 + 6) ÷ 2 ← Compute inside theparentheses first.

42 – 10 ÷ 2 ← Evaluate exponents.

16 – 10 ÷ 2 ← Then divide.

16 – 5 ← Finally, subtract.

11

Using a scientific calculator:

Press:

**Explain It**

Question 1.

To evaluate 3 × (7 + 5), what should you do first and why?

Answer:

First, add 7 + 5 since that operation is inside the parentheses.

Explanation:

Question 2.

In the second example using the scientific calculator, what is the purpose of the key?

Answer:

It is the key that is used to evaluate a base number raised to the power of an exponent.

Explanation:

Mathematicians use a set of rules known as order of operations , the order in which to perform operations in calculations.

1. Compute inside parentheses.

2. Evaluate terms with exponents.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.

Using the correct order of operations, 14 + 8 × 6 = 62.

A scientific calculator uses order of operations.

**Guided Practice**

**Do you know HOW?**

Evaluate each expression.

Question 1.

36 ÷ 6 + 6

Answer:

12

Explanation:

Question 2.

36 ÷ (6 + 6)

Answer:

3

Explanation:

Question 3.

24 ÷ (4 + 8) + 2

Answer:

4

Explanation:

Question 4.

48 ÷ (4 + 8) + 2^{2}

Answer:

8

Explanation:

Question 5.

24 ÷ 4 + 8 + 2

Answer:

16

Explanation:

Question 6.

48 ÷ 4 + 8 + 2^{2}

Answer:

24

Explanation:

**Do you UNDERSTAND?**

Question 7.

Where could you insert parentheses to make this number sentence true? 80 ÷ 8 × 5 + 4= 90

Answer:

See margin.

Explanation:

Question 8.

Donavan entered 12 + 4 × 36 into Lidia’s scientific calculator.The display showed 18. In what order did the calculator complete the operations?

Answer:

See margin.

Explanation:

**Independent Practice**

Evaluate each expression.

Question 9.

3^{3} – 8 × 3

Answer:

3

Explanation:

Question 10.

(5^{2} + 7) ÷ 4

Answer:

8

Explanation:

Question 11.

6 × 4 – 4 + 2

Answer:

8

Explanation:

Question 12.

18 – 3 × 5 + 2

Answer:

5

Explanation:

Question 13.

49 – 4 × (49 ÷ 7)

Answer:

21

Explanation:

Question 14.

(64 ÷ 8) × 3 + 6

Answer:

30

Explanation:

Question 15.

72 ÷ (4 + 4) × 5

Answer:

45

Explanation:

Question 16.

(3 × 3) × (2 × 2) ÷ 36

Answer:

1

Explanation:

Use parentheses to make each number sentence true.

Answer:

See margin.

Explanation:

Question 17.

5 + 4 × 3 × 3 = 41

Answer:

Question 18.

9 × 0 + 4 = 36

Answer:

Question 19.

5^{2} – 6 × 0 = 25

Answer:

Question 20.

8 × 9 – 2 – 3 = 32

Answer:

Question 21 .

5 + 4 × 3 × 3 = 81

Answer:

Question 22.

9 × 0 + 4 = 4

Answer:

Question 23.

5^{2} – 6 × 0 = 0

Answer:

Question 24.

8 × 9 – 2 – 3 = 53

Answer:

Question 25.

1 + 2 × 3 + 4 = 21

Answer:

Question 26.

2^{2} + 4 × 6 = 48

Answer:

Question 27.

5 × 6 × 8 – 7 = 30

Answer:

Question 28.

6^{2} + 7 + 9 × 10 = 133

Answer:

Question 29.

Number Sense Use the symbols +, -, ×, and ÷ to make the number sentence true.

Answer:

Explanation:

Question 30.

Meredith bought 3 T-shirts for $12.00 each. Her grandmother paid for half the total cost. To find how much Meredith paid, evaluate the expression: (3 × 12) ÷ 2.

Answer:

(3 × 12) ÷ 2 = $18. Meredith paid $18.

Explanation:

Question 31.

Luke needs a new fence around his garden, but the gate across the narrow end of the garden will not be replaced. To find how many feet of fencing Luke needs, evaluate the expression: 12 + (2 × 14).

Answer:

40 feet

Explanation:

Question 32.

Writing to Explain If p is greater than zero, tell which of these expressions will result in the higher number: (2 × p) + 5 or 2 × (p + 5). Explain how you know.

Answer:

See margin.

Explanation:

Question 33.

Jaron walked 15 blocks north and then 3 blocks west to school. Marisol walked 3 blocks east and then 15 blocks south to school. Write an expression to show that each traveled the same distance.

Answer:

3 + 15 = 15 + 3

Explanation:

Question 34.

On Saturday, every seat in Mazen Theater was full. The balcony has 10 rows with 22 seats in each. The main floor has 25 rows with 30 seats each. To find the number of people at the theater, evaluate the following expression: (10 × 22) + (25 × 30).

A. 16

B. 87

C. 970

D. 14,100

Answer:

C. 970

Explanation:

Question 35.

On her math test, Bianca scored 5 points on each of 5 questions, 2 points on each of 2 questions, and 3 points on each of 4 questions. To find the number of points she scored, evaluate the expression: 5^{2} + 2^{2} + (3 × 4).

A. 26

B. 40

C. 41

D. 84

Answer:

C. 41

Explanation:

Question 36.

The world’s largest flag measures 505 ft by 225 ft. The flag hangs by a cable through grommets on one of the shorter sides. There is a grommet every 30 in. If there is a grommet at each end, evaluate the expression 1 + (225 × 12) ÷ 30 to find out how many grommets are used to hang the flag.

Answer:

91 grommets

Explanation:

**Going Digital**

Exponents and Order of Operations

Evaluate 5^{6} on a calculator Ono ways.

Evaluate 9^{3} + (27 ÷ 3 + 47) on a calculator two ways

Step 1: Use the calculator’s order of operations.

Step 2: Follow order of operations to verify that the calculator used the correct order of operation.

Practice

Evaluate each expression two ways.

Question 1.

8^{5}

Answer:

32, 768

Explanation:

Question 2.

7^{4}

Answer:

2,401

Explanation:

Question 3.

8 × 19 – 36 + 12^{5}

Answer:

248,948

Explanation:

Question 4.

(72 ÷ 9) + 6 × 3^{5}

Answer:

1,466

Explanation:

Question 5.

3^{7}

Answer:

2,187

Explanation:

Question 6.

1204 ÷ 14 – 2^{5} + 178

Answer:

232

Explanation: