# Texas Go Math Grade 6 Lesson 10.3 Answer Key Order of Operations

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## Texas Go Math Grade 6 Lesson 10.3 Answer Key Order of Operations

Reflect

Question 1.
In C, why does it makes sense to write the values as powers? What is the pattern for the number of e-mails in each wave for Amy?
It is easier to write the values as powers to identify the pattern that can be observed in the given situation.
Pattern for the diagram of Amy:
1st wave = 31 = 3
2nd wave = 32 = 9
The pattern is 31 and 32.

Simplify each expression using the order of operations.

Question 2.
(3 – 1)4 + 3 _______________
Evaluate the expression.
= 24 + 3 subtract the numbers inside the parenthesis and evaluate the exponent
= 16 + 3 add the numbers
= 19
The simplified expression is 19.

Question 3.
24 ÷ (3 × 22) _______________
Evaluate the expression.
= 24 ÷ (3 × 4) evaluate the exponent inside the parenthesis and multiply
= 24 ÷ 12 divide the numbers
= 2
The simplified expression is 2.

Simplify each expression using the order of operations.

Question 4.
– 7 × (- 4) ÷ 14 – 22
Evaluate the expression.
= – 7 × (- 4) ÷ 14 – 4 evaluate the exponent
= 28 ÷ 14 – 4 multiply – 7 and – 4 then divide the answer by 14
= 2 – 4 subtract the numbers
= – 2
The simplified expression is – 2.

Question 5.
– 5(- 3 + 1)3 – 3
Evaluate the expression.
= – 5 (- 2)3 – 3 subtract the numbers inside the parenthesis and evaluate the exponent
= – 5(- 8) – 3 multiply – 5 and – 8
= 40 – 3 subtract the numbers
= 37

Question 1.
In a video game, a guppy that escapes a net turns into three goldfish. Each goldfish can turn into two betta fish. Each betta fish can turn into two angelfish. Complete the diagram and write the number of fish at each stage. Write and evaluate an expression for the number of angelfish that can be formed from one guppy.

1 guppy fish
3 goldfish
3 × 2 betta fish
3 × 22 = 12 angel fish

Complete to simplify each expression.

Question 2.
4 + (10 – 7)2 ÷ 3 = 4 + ( ____________ )2 ÷ 3
= 4 + ____________ ÷ 3
= 4 + ____________
= ____________
Evaluate the expression.
= 4 + 32 ÷ 3 subtract the numbers inside the parenthesis and evaluate the exponent
= 4 + 9 ÷ 3 divide 9 by 3
= 4 + 3 add the number
= 7
The simplified expression is 7.

Question 3.
36 ÷ 22 – 4 × 2 = 36 ÷ ____________ – 4 × 2
= ____________ – 4 × 2
= ____________ – 8
= ____________
Evaluate the expression.
= 36 ÷ 4 – 4 × 2 evaluate the exponent
= 9 – 4 × 2 divide 36 by 4 then multiply 4 by 2
= 9 – 8 subtract the numbers
= 1
The simplified expression is 1.

Question 4.
2 + (- 24 ÷ 23) – 9 = – 2 + (- 24 ÷ _________ ) – 9
= 2 + ____________ – 9
=____________ – 9
= ____________
Evaluate the expression
= 2 + (- 24 ÷ 8) – 9 evaluate the exponent and divide the numbers inside the parenthesis
= 2 + (- 3) – 9 subtract the numbers
= – 1 – 9 add the numbers
= – 10
The simplified expression is – 10

Question 5.
– 42 × (- 3 × 2 + 8) = – 42 × (_______ + 8)
= – 42 × _________
= _________ × _________
= _________
Evaluate the expression
= – 42 × (-6 + 8) multiply – 3 by 2 inside the parenthesis and subtract
= – 42 × 2 evaluate the exponent
= 16 × 2 multiply the numbers
= 32
The simplified expression is 32.

Essential Question Check – In

Question 6.
How do you use the order of operations to simplify expressions with exponents?
Order of operations to simplify expressions with exponents starts with simplifying the bracket (if any), solving the numerical value of power first, followed by division, multiplication, addition and then subtraction.

Simplify each expression using the order of operations.

Question 7.
5 × 2 + 32 __________
Solution to this example is given below = 5 × 2 + 32

5 × 2 + 32 = 5 × 2 + 9 Evaluate 32.
= 10 + 9 Multiply.
= 19

Question 8.
15 – 7 × 2 + 23 _____________
Solution to this example is given below
15 – 7 × 2 + 23
15 – 7 × 2 + 23 = 15 – 7 × 2 + 8 Evaluate 2.
= 15 – 14 – 8 Multiply.
= 1 + 8 Subtract.
= 9

Question 9.
(11 – 8)2 – 2 × 6 _____________
Evaluate the expression.
= 32 – 2 × 6 subtract the numbers inside the parenthesis and evaluate the exponent
= 9 – 2 × 6 multiply – 2 by 6
= 9 – 12 subtract the numbers
= – 3
The simplified expression is – 3.

Question 10.
6 + 3(13 – 2) – 52 _____________
Solution to this example is given below
6 + 3(13 – 2) – 52

6 + 3(13 – 2) – 52 = 6 + 3(13 – 2) – 25 Evaluate 52.
= 6 + 3 × 11 – 25 Perform operations inside parentheses.
= 6 + 33 – 25 Multiply.
= 6 + 8 Subtract.
= 14

Question 11.
12 + $$\frac{9^{2}}{3}$$ _____________
Solution to this example is given below
12 + $$\frac{9^{2}}{3}$$

12 + $$\frac{9^{2}}{3}$$ = 12 + $$\frac{81}{3}$$ Evaluate 92.
= 12 + 27 Divide.
= 39

Question 12.
$$\frac{8+6^{2}}{11}$$ + 7 × 2 _____________
Solution to this example is given below
$$\frac{8+6^{2}}{11}$$ + 7 × 2

$$\frac{8+6^{2}}{11}$$ + 7 × 2 = $$\frac{8+6^{2}}{11}$$ + 7 × 2 Evaluate 62.
= $$\frac{44}{11}$$ + 7 × 2 Add.
= 4 + 7 × 2 Divide.
= 4 + 14 Multiply.

Question 13.
Explain the Error Jay simplified the expression – 3 × (3 + 12 ÷ 3) 4. For his first step, he added 3 + 12 to get 15. What was Jay’s error? Find the correct answer.
Evaluate the expression
= – 3 × (3 + 4) – 4 divide 12 by 3 then add to 3
= – 3 × 7 – 4 multiply – 3 by 7
= – 21 – 4 add the numbers
= – 25
Jay made an error on his first step. In the order of operations, inside a parenthesis, division must be done first than addition, Therefore, the simplified expression is – 25.

Question 14.
Multistep A clothing store has the sign shown in the shop window. Pani sees the sign and wants to buy 3 shirts and 2 pairs of jeans. The S cost of each shirt before the discount is $12, and the cost of each pair of jeans is$19 before the discount.

a. Write and simplify an expression to find the amount Pani pays if a $3 discount is applied to her total. Answer: Evaluate the total cost when only 1$3 off coupon is applied. Therefore, Cost = 3(12) + 2(19) – 3 = $71. b. Pani says she should get a$3 discount on the price of each shirt and a $3 discount on the price of each pair of jeans. Write and simplify an expression to find the amount she would pay if this is true. Answer: Evaluate the total cost when only 1$3 off coupon is applied. on every piece of clothing. Therefore, Cost = 3(12 – 3) + 2(19 – 3) = $59. c. Analyze Relationships Why are the amounts Pani pays in a and b different? Answer: In a, the coupon is applied only once, while in b the coupon is applied for each piece of clothing , so here 5 times. This why the result of b is$12 less than that of a.

d. If you were the shop owner, how would you change the sign? Explain.
It would be better to write that \$3 off the total purchase.

Question 15.
Ellen is playing a video game in which she captures butterflies. There are 3 butterflies on screen, but the number of butterflies doubles every minute. After 4 minutes, she was able to capture 7 of the butterflies.

a. Look for a Pattern Write an expression for the number of butterflies after 4 minutes. Use a power of 2 in your answer.
In the 1st minute there are 3 butterfLies on the screen and they double every minute, so here the repeating number is 2, so the expression for butterflies on the screen after n minutes is given by 3 × 2n.

b. Write an expression for the number of butterflies remaining after Ellen captured the 7 butterflies. Simplify the expression.
Use the expression obtained to soLve for n = 4 and subtract 7 from it, therefore: 3 × 24 – 7 = 41. There were 41 butterflies on the screen after 4 minutes and after Ellen had caught 7.

Question 16.
Show how to write, evaluate and simplify an expression to represent and solve this problem: Jeff and his friend each text four classmates about a concert. Each classmate then texts four students from another school about the concert. If no one receives the message more than once, how many students from the other school receive a text about the concert?
Jeff and his friend, so 2 people are texting 4 people each, so 2 × 4 = 8 people are being notified about the concert. Then each 8 of them texts to 4 more, so the total number of people of the other school to get notified about the concert are 8 × 4 = 32.

H.O.T. Focus on Higher Order Thinking

Question 17.
Geometry The figure shown is a rectangle. The green shape in the figure is a square. The blue and white shapes are rectangles, and the area of the blue rectangle is 24 square inches.

a. Write an expression for the area of the entire figure that includes an exponent. Then find the area.
Area of the blue rectangle is 24 square inches, area of the white rectangle is 2 × 6 = 12 square inches, and area of the square is 62 = 36 square inches. Therefore the total area of the figure is 24 + 12 + 36 = 72 square inches.

b. Find the dimensions of the entire figure.
The side length of the square is 6 inches and then there is an additional 2 units below it so it can be said that the left and right side length of the given figure is 6 + 2 = 8 inches. The area is 72 square inches so this are can be divided by the obtained side length to evaluate the width of the rectangle, therefore: $$\frac{72}{8}$$ = 9 inches. The figure is a rectangle of length of 8 inches and width of 9 inches.

Question 18.
Analyze Relationships Roberto’s teacher writes the following statement on the board: The cube of a number plus one more than the square of the number is equal to the opposite of the number. Show that the number is – 1.
Evaluate the expression.
(- 1)3 + 1 + (- 1)2 = 1 translating the problem
– 1 + 1 + 1 = 1 evaluate the exponents
– 1 + 2 = 1 subtract the numbers
1 = 1
The expression is (- 1)3 + 1 + (- 1)2 = 1.

Question 19.
Persevere in Problem Solving Use parentheses to make this statement true: 8 × 4 – 2 × 3 + 8 ÷ 2 = 25